log_heterosked<\/title><script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/require.js\/2.1.10\/require.min.js\"><\/script>\n<style type=\"text\/css\">\n pre { line-height: 125%; }\ntd.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }\nspan.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }\ntd.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }\nspan.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }\n.highlight .hll { background-color: var(--jp-cell-editor-active-background) }\n.highlight { background: var(--jp-cell-editor-background); color: var(--jp-mirror-editor-variable-color) }\n.highlight .c { color: var(--jp-mirror-editor-comment-color); font-style: italic } \/* Comment *\/\n.highlight .err { color: var(--jp-mirror-editor-error-color) } \/* Error *\/\n.highlight .k { color: var(--jp-mirror-editor-keyword-color); font-weight: bold } \/* Keyword *\/\n.highlight .o { color: var(--jp-mirror-editor-operator-color); font-weight: bold } \/* Operator *\/\n.highlight .p { color: var(--jp-mirror-editor-punctuation-color) } \/* Punctuation *\/\n.highlight .ch { color: var(--jp-mirror-editor-comment-color); font-style: italic } \/* Comment.Hashbang *\/\n.highlight .cm { color: var(--jp-mirror-editor-comment-color); font-style: italic } \/* Comment.Multiline *\/\n.highlight .cp { color: var(--jp-mirror-editor-comment-color); font-style: italic } \/* Comment.Preproc *\/\n.highlight .cpf { color: var(--jp-mirror-editor-comment-color); font-style: italic } \/* Comment.PreprocFile *\/\n.highlight .c1 { color: var(--jp-mirror-editor-comment-color); font-style: italic } \/* Comment.Single *\/\n.highlight .cs { color: var(--jp-mirror-editor-comment-color); font-style: italic } \/* Comment.Special *\/\n.highlight .kc { color: var(--jp-mirror-editor-keyword-color); font-weight: bold } \/* Keyword.Constant *\/\n.highlight .kd { color: var(--jp-mirror-editor-keyword-color); font-weight: bold } \/* Keyword.Declaration *\/\n.highlight .kn { color: var(--jp-mirror-editor-keyword-color); font-weight: bold } \/* Keyword.Namespace *\/\n.highlight .kp { color: var(--jp-mirror-editor-keyword-color); font-weight: bold } \/* Keyword.Pseudo *\/\n.highlight .kr { color: var(--jp-mirror-editor-keyword-color); font-weight: bold } \/* Keyword.Reserved *\/\n.highlight .kt { color: var(--jp-mirror-editor-keyword-color); font-weight: bold } \/* Keyword.Type *\/\n.highlight .m { color: var(--jp-mirror-editor-number-color) } \/* Literal.Number *\/\n.highlight .s { color: var(--jp-mirror-editor-string-color) } \/* Literal.String *\/\n.highlight .ow { color: var(--jp-mirror-editor-operator-color); font-weight: bold } \/* Operator.Word *\/\n.highlight .pm { color: var(--jp-mirror-editor-punctuation-color) } \/* Punctuation.Marker *\/\n.highlight .w { color: var(--jp-mirror-editor-variable-color) } \/* Text.Whitespace *\/\n.highlight .mb { color: var(--jp-mirror-editor-number-color) } \/* Literal.Number.Bin *\/\n.highlight .mf { color: var(--jp-mirror-editor-number-color) } \/* Literal.Number.Float *\/\n.highlight .mh { color: var(--jp-mirror-editor-number-color) } \/* Literal.Number.Hex *\/\n.highlight .mi { color: var(--jp-mirror-editor-number-color) } \/* Literal.Number.Integer *\/\n.highlight .mo { color: var(--jp-mirror-editor-number-color) } \/* Literal.Number.Oct *\/\n.highlight .sa { color: var(--jp-mirror-editor-string-color) } \/* Literal.String.Affix *\/\n.highlight .sb { color: var(--jp-mirror-editor-string-color) } \/* Literal.String.Backtick *\/\n.highlight .sc { color: var(--jp-mirror-editor-string-color) } \/* Literal.String.Char *\/\n.highlight .dl { color: var(--jp-mirror-editor-string-color) } \/* Literal.String.Delimiter *\/\n.highlight .sd { color: var(--jp-mirror-editor-string-color) } \/* Literal.String.Doc *\/\n.highlight .s2 { color: var(--jp-mirror-editor-string-color) } \/* Literal.String.Double *\/\n.highlight .se { color: var(--jp-mirror-editor-string-color) } \/* Literal.String.Escape *\/\n.highlight .sh { color: var(--jp-mirror-editor-string-color) } \/* Literal.String.Heredoc *\/\n.highlight .si { color: var(--jp-mirror-editor-string-color) } \/* Literal.String.Interpol *\/\n.highlight .sx { color: var(--jp-mirror-editor-string-color) } \/* Literal.String.Other *\/\n.highlight .sr { color: var(--jp-mirror-editor-string-color) } \/* Literal.String.Regex *\/\n.highlight .s1 { color: var(--jp-mirror-editor-string-color) } \/* Literal.String.Single *\/\n.highlight .ss { color: var(--jp-mirror-editor-string-color) } \/* Literal.String.Symbol *\/\n.highlight .il { color: var(--jp-mirror-editor-number-color) } \/* Literal.Number.Integer.Long *\/\n <\/style>\n<style type=\"text\/css\">\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*\n * Mozilla scrollbar styling\n *\/\n\n\/* use standard opaque scrollbars for most nodes *\/\n[data-jp-theme-scrollbars='true'] {\n scrollbar-color: rgb(var(--jp-scrollbar-thumb-color))\n var(--jp-scrollbar-background-color);\n}\n\n\/* for code nodes, use a transparent style of scrollbar. These selectors\n * will match lower in the tree, and so will override the above *\/\n[data-jp-theme-scrollbars='true'] .CodeMirror-hscrollbar,\n[data-jp-theme-scrollbars='true'] .CodeMirror-vscrollbar {\n scrollbar-color: rgba(var(--jp-scrollbar-thumb-color), 0.5) transparent;\n}\n\n\/* tiny scrollbar *\/\n\n.jp-scrollbar-tiny {\n scrollbar-color: rgba(var(--jp-scrollbar-thumb-color), 0.5) transparent;\n scrollbar-width: thin;\n}\n\n\/* tiny scrollbar *\/\n\n.jp-scrollbar-tiny::-webkit-scrollbar,\n.jp-scrollbar-tiny::-webkit-scrollbar-corner {\n background-color: transparent;\n height: 4px;\n width: 4px;\n}\n\n.jp-scrollbar-tiny::-webkit-scrollbar-thumb {\n background: rgba(var(--jp-scrollbar-thumb-color), 0.5);\n}\n\n.jp-scrollbar-tiny::-webkit-scrollbar-track:horizontal {\n border-left: 0 solid transparent;\n border-right: 0 solid transparent;\n}\n\n.jp-scrollbar-tiny::-webkit-scrollbar-track:vertical {\n border-top: 0 solid transparent;\n border-bottom: 0 solid transparent;\n}\n\n\/*\n * Lumino\n *\/\n\n.lm-ScrollBar[data-orientation='horizontal'] {\n min-height: 16px;\n max-height: 16px;\n min-width: 45px;\n border-top: 1px solid #a0a0a0;\n}\n\n.lm-ScrollBar[data-orientation='vertical'] {\n min-width: 16px;\n max-width: 16px;\n min-height: 45px;\n border-left: 1px solid #a0a0a0;\n}\n\n.lm-ScrollBar-button {\n background-color: #f0f0f0;\n background-position: center center;\n min-height: 15px;\n max-height: 15px;\n min-width: 15px;\n max-width: 15px;\n}\n\n.lm-ScrollBar-button:hover {\n background-color: #dadada;\n}\n\n.lm-ScrollBar-button.lm-mod-active {\n background-color: #cdcdcd;\n}\n\n.lm-ScrollBar-track {\n background: #f0f0f0;\n}\n\n.lm-ScrollBar-thumb {\n background: #cdcdcd;\n}\n\n.lm-ScrollBar-thumb:hover {\n background: #bababa;\n}\n\n.lm-ScrollBar-thumb.lm-mod-active {\n background: #a0a0a0;\n}\n\n.lm-ScrollBar[data-orientation='horizontal'] .lm-ScrollBar-thumb {\n height: 100%;\n min-width: 15px;\n border-left: 1px solid #a0a0a0;\n border-right: 1px solid #a0a0a0;\n}\n\n.lm-ScrollBar[data-orientation='vertical'] .lm-ScrollBar-thumb {\n width: 100%;\n min-height: 15px;\n border-top: 1px solid #a0a0a0;\n border-bottom: 1px solid #a0a0a0;\n}\n\n.lm-ScrollBar[data-orientation='horizontal']\n .lm-ScrollBar-button[data-action='decrement'] {\n background-image: var(--jp-icon-caret-left);\n background-size: 17px;\n}\n\n.lm-ScrollBar[data-orientation='horizontal']\n .lm-ScrollBar-button[data-action='increment'] {\n background-image: var(--jp-icon-caret-right);\n background-size: 17px;\n}\n\n.lm-ScrollBar[data-orientation='vertical']\n .lm-ScrollBar-button[data-action='decrement'] {\n background-image: var(--jp-icon-caret-up);\n background-size: 17px;\n}\n\n.lm-ScrollBar[data-orientation='vertical']\n .lm-ScrollBar-button[data-action='increment'] {\n background-image: var(--jp-icon-caret-down);\n background-size: 17px;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Copyright (c) 2014-2017, PhosphorJS Contributors\n|\n| Distributed under the terms of the BSD 3-Clause License.\n|\n| The full license is in the file LICENSE, distributed with this software.\n|----------------------------------------------------------------------------*\/\n\n.lm-Widget {\n box-sizing: border-box;\n position: relative;\n overflow: hidden;\n}\n\n.lm-Widget.lm-mod-hidden {\n display: none !important;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n.lm-AccordionPanel[data-orientation='horizontal'] > .lm-AccordionPanel-title {\n \/* Title is rotated for horizontal accordion panel using CSS *\/\n display: block;\n transform-origin: top left;\n transform: rotate(-90deg) translate(-100%);\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Copyright (c) 2014-2017, PhosphorJS Contributors\n|\n| Distributed under the terms of the BSD 3-Clause License.\n|\n| The full license is in the file LICENSE, distributed with this software.\n|----------------------------------------------------------------------------*\/\n\n.lm-CommandPalette {\n display: flex;\n flex-direction: column;\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n.lm-CommandPalette-search {\n flex: 0 0 auto;\n}\n\n.lm-CommandPalette-content {\n flex: 1 1 auto;\n margin: 0;\n padding: 0;\n min-height: 0;\n overflow: auto;\n list-style-type: none;\n}\n\n.lm-CommandPalette-header {\n overflow: hidden;\n white-space: nowrap;\n text-overflow: ellipsis;\n}\n\n.lm-CommandPalette-item {\n display: flex;\n flex-direction: row;\n}\n\n.lm-CommandPalette-itemIcon {\n flex: 0 0 auto;\n}\n\n.lm-CommandPalette-itemContent {\n flex: 1 1 auto;\n overflow: hidden;\n}\n\n.lm-CommandPalette-itemShortcut {\n flex: 0 0 auto;\n}\n\n.lm-CommandPalette-itemLabel {\n overflow: hidden;\n white-space: nowrap;\n text-overflow: ellipsis;\n}\n\n.lm-close-icon {\n border: 1px solid transparent;\n background-color: transparent;\n position: absolute;\n z-index: 1;\n right: 3%;\n top: 0;\n bottom: 0;\n margin: auto;\n padding: 7px 0;\n display: none;\n vertical-align: middle;\n outline: 0;\n cursor: pointer;\n}\n.lm-close-icon:after {\n content: 'X';\n display: block;\n width: 15px;\n height: 15px;\n text-align: center;\n color: #000;\n font-weight: normal;\n font-size: 12px;\n cursor: pointer;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Copyright (c) 2014-2017, PhosphorJS Contributors\n|\n| Distributed under the terms of the BSD 3-Clause License.\n|\n| The full license is in the file LICENSE, distributed with this software.\n|----------------------------------------------------------------------------*\/\n\n.lm-DockPanel {\n z-index: 0;\n}\n\n.lm-DockPanel-widget {\n z-index: 0;\n}\n\n.lm-DockPanel-tabBar {\n z-index: 1;\n}\n\n.lm-DockPanel-handle {\n z-index: 2;\n}\n\n.lm-DockPanel-handle.lm-mod-hidden {\n display: none !important;\n}\n\n.lm-DockPanel-handle:after {\n position: absolute;\n top: 0;\n left: 0;\n width: 100%;\n height: 100%;\n content: '';\n}\n\n.lm-DockPanel-handle[data-orientation='horizontal'] {\n cursor: ew-resize;\n}\n\n.lm-DockPanel-handle[data-orientation='vertical'] {\n cursor: ns-resize;\n}\n\n.lm-DockPanel-handle[data-orientation='horizontal']:after {\n left: 50%;\n min-width: 8px;\n transform: translateX(-50%);\n}\n\n.lm-DockPanel-handle[data-orientation='vertical']:after {\n top: 50%;\n min-height: 8px;\n transform: translateY(-50%);\n}\n\n.lm-DockPanel-overlay {\n z-index: 3;\n box-sizing: border-box;\n pointer-events: none;\n}\n\n.lm-DockPanel-overlay.lm-mod-hidden {\n display: none !important;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Copyright (c) 2014-2017, PhosphorJS Contributors\n|\n| Distributed under the terms of the BSD 3-Clause License.\n|\n| The full license is in the file LICENSE, distributed with this software.\n|----------------------------------------------------------------------------*\/\n\n.lm-Menu {\n z-index: 10000;\n position: absolute;\n white-space: nowrap;\n overflow-x: hidden;\n overflow-y: auto;\n outline: none;\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n.lm-Menu-content {\n margin: 0;\n padding: 0;\n display: table;\n list-style-type: none;\n}\n\n.lm-Menu-item {\n display: table-row;\n}\n\n.lm-Menu-item.lm-mod-hidden,\n.lm-Menu-item.lm-mod-collapsed {\n display: none !important;\n}\n\n.lm-Menu-itemIcon,\n.lm-Menu-itemSubmenuIcon {\n display: table-cell;\n text-align: center;\n}\n\n.lm-Menu-itemLabel {\n display: table-cell;\n text-align: left;\n}\n\n.lm-Menu-itemShortcut {\n display: table-cell;\n text-align: right;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Copyright (c) 2014-2017, PhosphorJS Contributors\n|\n| Distributed under the terms of the BSD 3-Clause License.\n|\n| The full license is in the file LICENSE, distributed with this software.\n|----------------------------------------------------------------------------*\/\n\n.lm-MenuBar {\n outline: none;\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n.lm-MenuBar-content {\n margin: 0;\n padding: 0;\n display: flex;\n flex-direction: row;\n list-style-type: none;\n}\n\n.lm-MenuBar-item {\n box-sizing: border-box;\n}\n\n.lm-MenuBar-itemIcon,\n.lm-MenuBar-itemLabel {\n display: inline-block;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Copyright (c) 2014-2017, PhosphorJS Contributors\n|\n| Distributed under the terms of the BSD 3-Clause License.\n|\n| The full license is in the file LICENSE, distributed with this software.\n|----------------------------------------------------------------------------*\/\n\n.lm-ScrollBar {\n display: flex;\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n.lm-ScrollBar[data-orientation='horizontal'] {\n flex-direction: row;\n}\n\n.lm-ScrollBar[data-orientation='vertical'] {\n flex-direction: column;\n}\n\n.lm-ScrollBar-button {\n box-sizing: border-box;\n flex: 0 0 auto;\n}\n\n.lm-ScrollBar-track {\n box-sizing: border-box;\n position: relative;\n overflow: hidden;\n flex: 1 1 auto;\n}\n\n.lm-ScrollBar-thumb {\n box-sizing: border-box;\n position: absolute;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Copyright (c) 2014-2017, PhosphorJS Contributors\n|\n| Distributed under the terms of the BSD 3-Clause License.\n|\n| The full license is in the file LICENSE, distributed with this software.\n|----------------------------------------------------------------------------*\/\n\n.lm-SplitPanel-child {\n z-index: 0;\n}\n\n.lm-SplitPanel-handle {\n z-index: 1;\n}\n\n.lm-SplitPanel-handle.lm-mod-hidden {\n display: none !important;\n}\n\n.lm-SplitPanel-handle:after {\n position: absolute;\n top: 0;\n left: 0;\n width: 100%;\n height: 100%;\n content: '';\n}\n\n.lm-SplitPanel[data-orientation='horizontal'] > .lm-SplitPanel-handle {\n cursor: ew-resize;\n}\n\n.lm-SplitPanel[data-orientation='vertical'] > .lm-SplitPanel-handle {\n cursor: ns-resize;\n}\n\n.lm-SplitPanel[data-orientation='horizontal'] > .lm-SplitPanel-handle:after {\n left: 50%;\n min-width: 8px;\n transform: translateX(-50%);\n}\n\n.lm-SplitPanel[data-orientation='vertical'] > .lm-SplitPanel-handle:after {\n top: 50%;\n min-height: 8px;\n transform: translateY(-50%);\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Copyright (c) 2014-2017, PhosphorJS Contributors\n|\n| Distributed under the terms of the BSD 3-Clause License.\n|\n| The full license is in the file LICENSE, distributed with this software.\n|----------------------------------------------------------------------------*\/\n\n.lm-TabBar {\n display: flex;\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n.lm-TabBar[data-orientation='horizontal'] {\n flex-direction: row;\n align-items: flex-end;\n}\n\n.lm-TabBar[data-orientation='vertical'] {\n flex-direction: column;\n align-items: flex-end;\n}\n\n.lm-TabBar-content {\n margin: 0;\n padding: 0;\n display: flex;\n flex: 1 1 auto;\n list-style-type: none;\n}\n\n.lm-TabBar[data-orientation='horizontal'] > .lm-TabBar-content {\n flex-direction: row;\n}\n\n.lm-TabBar[data-orientation='vertical'] > .lm-TabBar-content {\n flex-direction: column;\n}\n\n.lm-TabBar-tab {\n display: flex;\n flex-direction: row;\n box-sizing: border-box;\n overflow: hidden;\n touch-action: none; \/* Disable native Drag\/Drop *\/\n}\n\n.lm-TabBar-tabIcon,\n.lm-TabBar-tabCloseIcon {\n flex: 0 0 auto;\n}\n\n.lm-TabBar-tabLabel {\n flex: 1 1 auto;\n overflow: hidden;\n white-space: nowrap;\n}\n\n.lm-TabBar-tabInput {\n user-select: all;\n width: 100%;\n box-sizing: border-box;\n}\n\n.lm-TabBar-tab.lm-mod-hidden {\n display: none !important;\n}\n\n.lm-TabBar-addButton.lm-mod-hidden {\n display: none !important;\n}\n\n.lm-TabBar.lm-mod-dragging .lm-TabBar-tab {\n position: relative;\n}\n\n.lm-TabBar.lm-mod-dragging[data-orientation='horizontal'] .lm-TabBar-tab {\n left: 0;\n transition: left 150ms ease;\n}\n\n.lm-TabBar.lm-mod-dragging[data-orientation='vertical'] .lm-TabBar-tab {\n top: 0;\n transition: top 150ms ease;\n}\n\n.lm-TabBar.lm-mod-dragging .lm-TabBar-tab.lm-mod-dragging {\n transition: none;\n}\n\n.lm-TabBar-tabLabel .lm-TabBar-tabInput {\n user-select: all;\n width: 100%;\n box-sizing: border-box;\n background: inherit;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Copyright (c) 2014-2017, PhosphorJS Contributors\n|\n| Distributed under the terms of the BSD 3-Clause License.\n|\n| The full license is in the file LICENSE, distributed with this software.\n|----------------------------------------------------------------------------*\/\n\n.lm-TabPanel-tabBar {\n z-index: 1;\n}\n\n.lm-TabPanel-stackedPanel {\n z-index: 0;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Copyright (c) 2014-2017, PhosphorJS Contributors\n|\n| Distributed under the terms of the BSD 3-Clause License.\n|\n| The full license is in the file LICENSE, distributed with this software.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-Collapse {\n display: flex;\n flex-direction: column;\n align-items: stretch;\n}\n\n.jp-Collapse-header {\n padding: 1px 12px;\n background-color: var(--jp-layout-color1);\n border-bottom: solid var(--jp-border-width) var(--jp-border-color2);\n color: var(--jp-ui-font-color1);\n cursor: pointer;\n display: flex;\n align-items: center;\n font-size: var(--jp-ui-font-size0);\n font-weight: 600;\n text-transform: uppercase;\n user-select: none;\n}\n\n.jp-Collapser-icon {\n height: 16px;\n}\n\n.jp-Collapse-header-collapsed .jp-Collapser-icon {\n transform: rotate(-90deg);\n margin: auto 0;\n}\n\n.jp-Collapser-title {\n line-height: 25px;\n}\n\n.jp-Collapse-contents {\n padding: 0 12px;\n background-color: var(--jp-layout-color1);\n color: var(--jp-ui-font-color1);\n overflow: auto;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/* This file was auto-generated by ensureUiComponents() in @jupyterlab\/buildutils *\/\n\n\/**\n * (DEPRECATED) Support for consuming icons as CSS background images\n *\/\n\n\/* Icons urls *\/\n\n:root {\n --jp-icon-add-above: 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--jp-icon-add-below: 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--jp-icon-add: url(data:image\/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNiIgdmlld0JveD0iMCAwIDI0IDI0Ij4KICA8ZyBjbGFzcz0ianAtaWNvbjMiIGZpbGw9IiM2MTYxNjEiPgogICAgPHBhdGggZD0iTTE5IDEzaC02djZoLTJ2LTZINXYtMmg2VjVoMnY2aDZ2MnoiLz4KICA8L2c+Cjwvc3ZnPgo=);\n --jp-icon-bell: 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--jp-icon-bug: url(data:image\/svg+xml;base64,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);\n --jp-icon-build: 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url(data:image\/svg+xml;base64,PHN2ZyBoZWlnaHQ9IjI0IiB2aWV3Qm94PSIwIDAgMjQgMjQiIHdpZHRoPSIyNCIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj4KICAgIDxnIGNsYXNzPSJqcC1pY29uMyIgZmlsbD0iIzYxNjE2MSI+CiAgICAgICAgPHBhdGggZD0iTTAgMGgyNHYyNEgweiIgZmlsbD0ibm9uZSIvPgogICAgICAgIDxwYXRoIGQ9Ik0yMiAxMVYzaC03djNIOVYzSDJ2OGg3VjhoMnYxMGg0djNoN3YtOGgtN3YzaC0yVjhoMnYzeiIvPgogICAgPC9nPgo8L3N2Zz4K);\n --jp-icon-trusted: url(data:image\/svg+xml;base64,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);\n --jp-icon-undo: url(data:image\/svg+xml;base64,PHN2ZyB2aWV3Qm94PSIwIDAgMjQgMjQiIHdpZHRoPSIxNiIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj4KICA8ZyBjbGFzcz0ianAtaWNvbjMiIGZpbGw9IiM2MTYxNjEiPgogICAgPHBhdGggZD0iTTEyLjUgOGMtMi42NSAwLTUuMDUuOTktNi45IDIuNkwyIDd2OWg5bC0zLjYyLTMuNjJjMS4zOS0xLjE2IDMuMTYtMS44OCA1LjEyLTEuODggMy41NCAwIDYuNTUgMi4zMSA3LjYgNS41bDIuMzctLjc4QzIxLjA4IDExLjAzIDE3LjE1IDggMTIuNSA4eiIvPgogIDwvZz4KPC9zdmc+Cg==);\n --jp-icon-user: url(data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMTYiIHZpZXdCb3g9IjAgMCAyNCAyNCIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj4KICA8ZyBjbGFzcz0ianAtaWNvbjMiIGZpbGw9IiM2MTYxNjEiPgogICAgPHBhdGggZD0iTTE2IDdhNCA0IDAgMTEtOCAwIDQgNCAwIDAxOCAwek0xMiAxNGE3IDcgMCAwMC03IDdoMTRhNyA3IDAgMDAtNy03eiIvPgogIDwvZz4KPC9zdmc+Cg==);\n --jp-icon-users: url(data:image\/svg+xml;base64,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);\n --jp-icon-vega: url(data:image\/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNiIgdmlld0JveD0iMCAwIDIyIDIyIj4KICA8ZyBjbGFzcz0ianAtaWNvbjEganAtaWNvbi1zZWxlY3RhYmxlIiBmaWxsPSIjMjEyMTIxIj4KICAgIDxwYXRoIGQ9Ik0xMC42IDUuNGwyLjItMy4ySDIuMnY3LjNsNC02LjZ6Ii8+CiAgICA8cGF0aCBkPSJNMTUuOCAyLjJsLTQuNCA2LjZMNyA2LjNsLTQuOCA4djUuNWgxNy42VjIuMmgtNHptLTcgMTUuNEg1LjV2LTQuNGgzLjN2NC40em00LjQgMEg5LjhWOS44aDMuNHY3Ljh6bTQuNCAwaC0zLjRWNi41aDMuNHYxMS4xeiIvPgogIDwvZz4KPC9zdmc+Cg==);\n --jp-icon-word: url(data:image\/svg+xml;base64,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);\n --jp-icon-yaml: url(data:image\/svg+xml;base64,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);\n}\n\n\/* Icon CSS class declarations *\/\n\n.jp-AddAboveIcon {\n background-image: var(--jp-icon-add-above);\n}\n\n.jp-AddBelowIcon {\n background-image: var(--jp-icon-add-below);\n}\n\n.jp-AddIcon {\n background-image: var(--jp-icon-add);\n}\n\n.jp-BellIcon {\n background-image: var(--jp-icon-bell);\n}\n\n.jp-BugDotIcon {\n background-image: var(--jp-icon-bug-dot);\n}\n\n.jp-BugIcon {\n background-image: var(--jp-icon-bug);\n}\n\n.jp-BuildIcon {\n background-image: var(--jp-icon-build);\n}\n\n.jp-CaretDownEmptyIcon {\n background-image: var(--jp-icon-caret-down-empty);\n}\n\n.jp-CaretDownEmptyThinIcon {\n background-image: var(--jp-icon-caret-down-empty-thin);\n}\n\n.jp-CaretDownIcon {\n background-image: var(--jp-icon-caret-down);\n}\n\n.jp-CaretLeftIcon {\n background-image: var(--jp-icon-caret-left);\n}\n\n.jp-CaretRightIcon {\n background-image: var(--jp-icon-caret-right);\n}\n\n.jp-CaretUpEmptyThinIcon {\n background-image: var(--jp-icon-caret-up-empty-thin);\n}\n\n.jp-CaretUpIcon {\n background-image: var(--jp-icon-caret-up);\n}\n\n.jp-CaseSensitiveIcon {\n background-image: var(--jp-icon-case-sensitive);\n}\n\n.jp-CheckIcon {\n background-image: var(--jp-icon-check);\n}\n\n.jp-CircleEmptyIcon {\n background-image: var(--jp-icon-circle-empty);\n}\n\n.jp-CircleIcon {\n background-image: var(--jp-icon-circle);\n}\n\n.jp-ClearIcon {\n background-image: var(--jp-icon-clear);\n}\n\n.jp-CloseIcon {\n background-image: var(--jp-icon-close);\n}\n\n.jp-CodeCheckIcon {\n background-image: var(--jp-icon-code-check);\n}\n\n.jp-CodeIcon {\n background-image: var(--jp-icon-code);\n}\n\n.jp-CollapseAllIcon {\n background-image: var(--jp-icon-collapse-all);\n}\n\n.jp-ConsoleIcon {\n background-image: var(--jp-icon-console);\n}\n\n.jp-CopyIcon {\n background-image: var(--jp-icon-copy);\n}\n\n.jp-CopyrightIcon {\n background-image: var(--jp-icon-copyright);\n}\n\n.jp-CutIcon {\n background-image: var(--jp-icon-cut);\n}\n\n.jp-DeleteIcon {\n background-image: var(--jp-icon-delete);\n}\n\n.jp-DownloadIcon {\n background-image: var(--jp-icon-download);\n}\n\n.jp-DuplicateIcon {\n background-image: var(--jp-icon-duplicate);\n}\n\n.jp-EditIcon {\n background-image: var(--jp-icon-edit);\n}\n\n.jp-EllipsesIcon {\n background-image: var(--jp-icon-ellipses);\n}\n\n.jp-ErrorIcon {\n background-image: var(--jp-icon-error);\n}\n\n.jp-ExpandAllIcon {\n background-image: var(--jp-icon-expand-all);\n}\n\n.jp-ExtensionIcon {\n background-image: var(--jp-icon-extension);\n}\n\n.jp-FastForwardIcon {\n background-image: var(--jp-icon-fast-forward);\n}\n\n.jp-FileIcon {\n background-image: var(--jp-icon-file);\n}\n\n.jp-FileUploadIcon {\n background-image: var(--jp-icon-file-upload);\n}\n\n.jp-FilterDotIcon {\n background-image: var(--jp-icon-filter-dot);\n}\n\n.jp-FilterIcon {\n background-image: var(--jp-icon-filter);\n}\n\n.jp-FilterListIcon {\n background-image: var(--jp-icon-filter-list);\n}\n\n.jp-FolderFavoriteIcon {\n background-image: var(--jp-icon-folder-favorite);\n}\n\n.jp-FolderIcon {\n background-image: var(--jp-icon-folder);\n}\n\n.jp-HomeIcon {\n background-image: var(--jp-icon-home);\n}\n\n.jp-Html5Icon {\n background-image: var(--jp-icon-html5);\n}\n\n.jp-ImageIcon {\n background-image: var(--jp-icon-image);\n}\n\n.jp-InfoIcon {\n background-image: var(--jp-icon-info);\n}\n\n.jp-InspectorIcon {\n background-image: var(--jp-icon-inspector);\n}\n\n.jp-JsonIcon {\n background-image: var(--jp-icon-json);\n}\n\n.jp-JuliaIcon {\n background-image: var(--jp-icon-julia);\n}\n\n.jp-JupyterFaviconIcon {\n background-image: var(--jp-icon-jupyter-favicon);\n}\n\n.jp-JupyterIcon {\n background-image: var(--jp-icon-jupyter);\n}\n\n.jp-JupyterlabWordmarkIcon {\n background-image: var(--jp-icon-jupyterlab-wordmark);\n}\n\n.jp-KernelIcon {\n background-image: var(--jp-icon-kernel);\n}\n\n.jp-KeyboardIcon {\n background-image: var(--jp-icon-keyboard);\n}\n\n.jp-LaunchIcon {\n background-image: var(--jp-icon-launch);\n}\n\n.jp-LauncherIcon {\n background-image: var(--jp-icon-launcher);\n}\n\n.jp-LineFormIcon {\n background-image: var(--jp-icon-line-form);\n}\n\n.jp-LinkIcon {\n background-image: var(--jp-icon-link);\n}\n\n.jp-ListIcon {\n background-image: var(--jp-icon-list);\n}\n\n.jp-MarkdownIcon {\n background-image: var(--jp-icon-markdown);\n}\n\n.jp-MoveDownIcon {\n background-image: var(--jp-icon-move-down);\n}\n\n.jp-MoveUpIcon {\n background-image: var(--jp-icon-move-up);\n}\n\n.jp-NewFolderIcon {\n background-image: var(--jp-icon-new-folder);\n}\n\n.jp-NotTrustedIcon {\n background-image: var(--jp-icon-not-trusted);\n}\n\n.jp-NotebookIcon {\n background-image: var(--jp-icon-notebook);\n}\n\n.jp-NumberingIcon {\n background-image: var(--jp-icon-numbering);\n}\n\n.jp-OfflineBoltIcon {\n background-image: var(--jp-icon-offline-bolt);\n}\n\n.jp-PaletteIcon {\n background-image: var(--jp-icon-palette);\n}\n\n.jp-PasteIcon {\n background-image: var(--jp-icon-paste);\n}\n\n.jp-PdfIcon {\n background-image: var(--jp-icon-pdf);\n}\n\n.jp-PythonIcon {\n background-image: var(--jp-icon-python);\n}\n\n.jp-RKernelIcon {\n background-image: var(--jp-icon-r-kernel);\n}\n\n.jp-ReactIcon {\n background-image: var(--jp-icon-react);\n}\n\n.jp-RedoIcon {\n background-image: var(--jp-icon-redo);\n}\n\n.jp-RefreshIcon {\n background-image: var(--jp-icon-refresh);\n}\n\n.jp-RegexIcon {\n background-image: var(--jp-icon-regex);\n}\n\n.jp-RunIcon {\n background-image: var(--jp-icon-run);\n}\n\n.jp-RunningIcon {\n background-image: var(--jp-icon-running);\n}\n\n.jp-SaveIcon {\n background-image: var(--jp-icon-save);\n}\n\n.jp-SearchIcon {\n background-image: var(--jp-icon-search);\n}\n\n.jp-SettingsIcon {\n background-image: var(--jp-icon-settings);\n}\n\n.jp-ShareIcon {\n background-image: var(--jp-icon-share);\n}\n\n.jp-SpreadsheetIcon {\n background-image: var(--jp-icon-spreadsheet);\n}\n\n.jp-StopIcon {\n background-image: var(--jp-icon-stop);\n}\n\n.jp-TabIcon {\n background-image: var(--jp-icon-tab);\n}\n\n.jp-TableRowsIcon {\n background-image: var(--jp-icon-table-rows);\n}\n\n.jp-TagIcon {\n background-image: var(--jp-icon-tag);\n}\n\n.jp-TerminalIcon {\n background-image: var(--jp-icon-terminal);\n}\n\n.jp-TextEditorIcon {\n background-image: var(--jp-icon-text-editor);\n}\n\n.jp-TocIcon {\n background-image: var(--jp-icon-toc);\n}\n\n.jp-TreeViewIcon {\n background-image: var(--jp-icon-tree-view);\n}\n\n.jp-TrustedIcon {\n background-image: var(--jp-icon-trusted);\n}\n\n.jp-UndoIcon {\n background-image: var(--jp-icon-undo);\n}\n\n.jp-UserIcon {\n background-image: var(--jp-icon-user);\n}\n\n.jp-UsersIcon {\n background-image: var(--jp-icon-users);\n}\n\n.jp-VegaIcon {\n background-image: var(--jp-icon-vega);\n}\n\n.jp-WordIcon {\n background-image: var(--jp-icon-word);\n}\n\n.jp-YamlIcon {\n background-image: var(--jp-icon-yaml);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/**\n * (DEPRECATED) Support for consuming icons as CSS background images\n *\/\n\n.jp-Icon,\n.jp-MaterialIcon {\n background-position: center;\n background-repeat: no-repeat;\n background-size: 16px;\n min-width: 16px;\n min-height: 16px;\n}\n\n.jp-Icon-cover {\n background-position: center;\n background-repeat: no-repeat;\n background-size: cover;\n}\n\n\/**\n * (DEPRECATED) Support for specific CSS icon sizes\n *\/\n\n.jp-Icon-16 {\n background-size: 16px;\n min-width: 16px;\n min-height: 16px;\n}\n\n.jp-Icon-18 {\n background-size: 18px;\n min-width: 18px;\n min-height: 18px;\n}\n\n.jp-Icon-20 {\n background-size: 20px;\n min-width: 20px;\n min-height: 20px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.lm-TabBar .lm-TabBar-addButton {\n align-items: center;\n display: flex;\n padding: 4px;\n padding-bottom: 5px;\n margin-right: 1px;\n background-color: var(--jp-layout-color2);\n}\n\n.lm-TabBar .lm-TabBar-addButton:hover {\n background-color: var(--jp-layout-color1);\n}\n\n.lm-DockPanel-tabBar .lm-TabBar-tab {\n width: var(--jp-private-horizontal-tab-width);\n}\n\n.lm-DockPanel-tabBar .lm-TabBar-content {\n flex: unset;\n}\n\n.lm-DockPanel-tabBar[data-orientation='horizontal'] {\n flex: 1 1 auto;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/**\n * Support for icons as inline SVG HTMLElements\n *\/\n\n\/* recolor the primary elements of an icon *\/\n.jp-icon0[fill] {\n fill: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon1[fill] {\n fill: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon2[fill] {\n fill: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon3[fill] {\n fill: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon4[fill] {\n fill: var(--jp-inverse-layout-color4);\n}\n\n.jp-icon0[stroke] {\n stroke: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon1[stroke] {\n stroke: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon2[stroke] {\n stroke: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon3[stroke] {\n stroke: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon4[stroke] {\n stroke: var(--jp-inverse-layout-color4);\n}\n\n\/* recolor the accent elements of an icon *\/\n.jp-icon-accent0[fill] {\n fill: var(--jp-layout-color0);\n}\n\n.jp-icon-accent1[fill] {\n fill: var(--jp-layout-color1);\n}\n\n.jp-icon-accent2[fill] {\n fill: var(--jp-layout-color2);\n}\n\n.jp-icon-accent3[fill] {\n fill: var(--jp-layout-color3);\n}\n\n.jp-icon-accent4[fill] {\n fill: var(--jp-layout-color4);\n}\n\n.jp-icon-accent0[stroke] {\n stroke: var(--jp-layout-color0);\n}\n\n.jp-icon-accent1[stroke] {\n stroke: var(--jp-layout-color1);\n}\n\n.jp-icon-accent2[stroke] {\n stroke: var(--jp-layout-color2);\n}\n\n.jp-icon-accent3[stroke] {\n stroke: var(--jp-layout-color3);\n}\n\n.jp-icon-accent4[stroke] {\n stroke: var(--jp-layout-color4);\n}\n\n\/* set the color of an icon to transparent *\/\n.jp-icon-none[fill] {\n fill: none;\n}\n\n.jp-icon-none[stroke] {\n stroke: none;\n}\n\n\/* brand icon colors. Same for light and dark *\/\n.jp-icon-brand0[fill] {\n fill: var(--jp-brand-color0);\n}\n\n.jp-icon-brand1[fill] {\n fill: var(--jp-brand-color1);\n}\n\n.jp-icon-brand2[fill] {\n fill: var(--jp-brand-color2);\n}\n\n.jp-icon-brand3[fill] {\n fill: var(--jp-brand-color3);\n}\n\n.jp-icon-brand4[fill] {\n fill: var(--jp-brand-color4);\n}\n\n.jp-icon-brand0[stroke] {\n stroke: var(--jp-brand-color0);\n}\n\n.jp-icon-brand1[stroke] {\n stroke: var(--jp-brand-color1);\n}\n\n.jp-icon-brand2[stroke] {\n stroke: var(--jp-brand-color2);\n}\n\n.jp-icon-brand3[stroke] {\n stroke: var(--jp-brand-color3);\n}\n\n.jp-icon-brand4[stroke] {\n stroke: var(--jp-brand-color4);\n}\n\n\/* warn icon colors. Same for light and dark *\/\n.jp-icon-warn0[fill] {\n fill: var(--jp-warn-color0);\n}\n\n.jp-icon-warn1[fill] {\n fill: var(--jp-warn-color1);\n}\n\n.jp-icon-warn2[fill] {\n fill: var(--jp-warn-color2);\n}\n\n.jp-icon-warn3[fill] {\n fill: var(--jp-warn-color3);\n}\n\n.jp-icon-warn0[stroke] {\n stroke: var(--jp-warn-color0);\n}\n\n.jp-icon-warn1[stroke] {\n stroke: var(--jp-warn-color1);\n}\n\n.jp-icon-warn2[stroke] {\n stroke: var(--jp-warn-color2);\n}\n\n.jp-icon-warn3[stroke] {\n stroke: var(--jp-warn-color3);\n}\n\n\/* icon colors that contrast well with each other and most backgrounds *\/\n.jp-icon-contrast0[fill] {\n fill: var(--jp-icon-contrast-color0);\n}\n\n.jp-icon-contrast1[fill] {\n fill: var(--jp-icon-contrast-color1);\n}\n\n.jp-icon-contrast2[fill] {\n fill: var(--jp-icon-contrast-color2);\n}\n\n.jp-icon-contrast3[fill] {\n fill: var(--jp-icon-contrast-color3);\n}\n\n.jp-icon-contrast0[stroke] {\n stroke: var(--jp-icon-contrast-color0);\n}\n\n.jp-icon-contrast1[stroke] {\n stroke: var(--jp-icon-contrast-color1);\n}\n\n.jp-icon-contrast2[stroke] {\n stroke: var(--jp-icon-contrast-color2);\n}\n\n.jp-icon-contrast3[stroke] {\n stroke: var(--jp-icon-contrast-color3);\n}\n\n.jp-icon-dot[fill] {\n fill: var(--jp-warn-color0);\n}\n\n.jp-jupyter-icon-color[fill] {\n fill: var(--jp-jupyter-icon-color, var(--jp-warn-color0));\n}\n\n.jp-notebook-icon-color[fill] {\n fill: var(--jp-notebook-icon-color, var(--jp-warn-color0));\n}\n\n.jp-json-icon-color[fill] {\n fill: var(--jp-json-icon-color, var(--jp-warn-color1));\n}\n\n.jp-console-icon-color[fill] {\n fill: var(--jp-console-icon-color, white);\n}\n\n.jp-console-icon-background-color[fill] {\n fill: var(--jp-console-icon-background-color, var(--jp-brand-color1));\n}\n\n.jp-terminal-icon-color[fill] {\n fill: var(--jp-terminal-icon-color, var(--jp-layout-color2));\n}\n\n.jp-terminal-icon-background-color[fill] {\n fill: var(\n --jp-terminal-icon-background-color,\n var(--jp-inverse-layout-color2)\n );\n}\n\n.jp-text-editor-icon-color[fill] {\n fill: var(--jp-text-editor-icon-color, var(--jp-inverse-layout-color3));\n}\n\n.jp-inspector-icon-color[fill] {\n fill: var(--jp-inspector-icon-color, var(--jp-inverse-layout-color3));\n}\n\n\/* CSS for icons in selected filebrowser listing items *\/\n.jp-DirListing-item.jp-mod-selected .jp-icon-selectable[fill] {\n fill: #fff;\n}\n\n.jp-DirListing-item.jp-mod-selected .jp-icon-selectable-inverse[fill] {\n fill: var(--jp-brand-color1);\n}\n\n\/* stylelint-disable selector-max-class, selector-max-compound-selectors *\/\n\n\/**\n* TODO: come up with non css-hack solution for showing the busy icon on top\n* of the close icon\n* CSS for complex behavior of close icon of tabs in the main area tabbar\n*\/\n.lm-DockPanel-tabBar\n .lm-TabBar-tab.lm-mod-closable.jp-mod-dirty\n > .lm-TabBar-tabCloseIcon\n > :not(:hover)\n > .jp-icon3[fill] {\n fill: none;\n}\n\n.lm-DockPanel-tabBar\n .lm-TabBar-tab.lm-mod-closable.jp-mod-dirty\n > .lm-TabBar-tabCloseIcon\n > :not(:hover)\n > .jp-icon-busy[fill] {\n fill: var(--jp-inverse-layout-color3);\n}\n\n\/* stylelint-enable selector-max-class, selector-max-compound-selectors *\/\n\n\/* CSS for icons in status bar *\/\n#jp-main-statusbar .jp-mod-selected .jp-icon-selectable[fill] {\n fill: #fff;\n}\n\n#jp-main-statusbar .jp-mod-selected .jp-icon-selectable-inverse[fill] {\n fill: var(--jp-brand-color1);\n}\n\n\/* special handling for splash icon CSS. While the theme CSS reloads during\n splash, the splash icon can loose theming. To prevent that, we set a\n default for its color variable *\/\n:root {\n --jp-warn-color0: var(--md-orange-700);\n}\n\n\/* not sure what to do with this one, used in filebrowser listing *\/\n.jp-DragIcon {\n margin-right: 4px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/**\n * Support for alt colors for icons as inline SVG HTMLElements\n *\/\n\n\/* alt recolor the primary elements of an icon *\/\n.jp-icon-alt .jp-icon0[fill] {\n fill: var(--jp-layout-color0);\n}\n\n.jp-icon-alt .jp-icon1[fill] {\n fill: var(--jp-layout-color1);\n}\n\n.jp-icon-alt .jp-icon2[fill] {\n fill: var(--jp-layout-color2);\n}\n\n.jp-icon-alt .jp-icon3[fill] {\n fill: var(--jp-layout-color3);\n}\n\n.jp-icon-alt .jp-icon4[fill] {\n fill: var(--jp-layout-color4);\n}\n\n.jp-icon-alt .jp-icon0[stroke] {\n stroke: var(--jp-layout-color0);\n}\n\n.jp-icon-alt .jp-icon1[stroke] {\n stroke: var(--jp-layout-color1);\n}\n\n.jp-icon-alt .jp-icon2[stroke] {\n stroke: var(--jp-layout-color2);\n}\n\n.jp-icon-alt .jp-icon3[stroke] {\n stroke: var(--jp-layout-color3);\n}\n\n.jp-icon-alt .jp-icon4[stroke] {\n stroke: var(--jp-layout-color4);\n}\n\n\/* alt recolor the accent elements of an icon *\/\n.jp-icon-alt .jp-icon-accent0[fill] {\n fill: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon-alt .jp-icon-accent1[fill] {\n fill: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon-alt .jp-icon-accent2[fill] {\n fill: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon-alt .jp-icon-accent3[fill] {\n fill: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon-alt .jp-icon-accent4[fill] {\n fill: var(--jp-inverse-layout-color4);\n}\n\n.jp-icon-alt .jp-icon-accent0[stroke] {\n stroke: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon-alt .jp-icon-accent1[stroke] {\n stroke: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon-alt .jp-icon-accent2[stroke] {\n stroke: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon-alt .jp-icon-accent3[stroke] {\n stroke: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon-alt .jp-icon-accent4[stroke] {\n stroke: var(--jp-inverse-layout-color4);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-icon-hoverShow:not(:hover) .jp-icon-hoverShow-content {\n display: none !important;\n}\n\n\/**\n * Support for hover colors for icons as inline SVG HTMLElements\n *\/\n\n\/**\n * regular colors\n *\/\n\n\/* recolor the primary elements of an icon *\/\n.jp-icon-hover :hover .jp-icon0-hover[fill] {\n fill: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon-hover :hover .jp-icon1-hover[fill] {\n fill: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon-hover :hover .jp-icon2-hover[fill] {\n fill: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon-hover :hover .jp-icon3-hover[fill] {\n fill: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon-hover :hover .jp-icon4-hover[fill] {\n fill: var(--jp-inverse-layout-color4);\n}\n\n.jp-icon-hover :hover .jp-icon0-hover[stroke] {\n stroke: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon-hover :hover .jp-icon1-hover[stroke] {\n stroke: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon-hover :hover .jp-icon2-hover[stroke] {\n stroke: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon-hover :hover .jp-icon3-hover[stroke] {\n stroke: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon-hover :hover .jp-icon4-hover[stroke] {\n stroke: var(--jp-inverse-layout-color4);\n}\n\n\/* recolor the accent elements of an icon *\/\n.jp-icon-hover :hover .jp-icon-accent0-hover[fill] {\n fill: var(--jp-layout-color0);\n}\n\n.jp-icon-hover :hover .jp-icon-accent1-hover[fill] {\n fill: var(--jp-layout-color1);\n}\n\n.jp-icon-hover :hover .jp-icon-accent2-hover[fill] {\n fill: var(--jp-layout-color2);\n}\n\n.jp-icon-hover :hover .jp-icon-accent3-hover[fill] {\n fill: var(--jp-layout-color3);\n}\n\n.jp-icon-hover :hover .jp-icon-accent4-hover[fill] {\n fill: var(--jp-layout-color4);\n}\n\n.jp-icon-hover :hover .jp-icon-accent0-hover[stroke] {\n stroke: var(--jp-layout-color0);\n}\n\n.jp-icon-hover :hover .jp-icon-accent1-hover[stroke] {\n stroke: var(--jp-layout-color1);\n}\n\n.jp-icon-hover :hover .jp-icon-accent2-hover[stroke] {\n stroke: var(--jp-layout-color2);\n}\n\n.jp-icon-hover :hover .jp-icon-accent3-hover[stroke] {\n stroke: var(--jp-layout-color3);\n}\n\n.jp-icon-hover :hover .jp-icon-accent4-hover[stroke] {\n stroke: var(--jp-layout-color4);\n}\n\n\/* set the color of an icon to transparent *\/\n.jp-icon-hover :hover .jp-icon-none-hover[fill] {\n fill: none;\n}\n\n.jp-icon-hover :hover .jp-icon-none-hover[stroke] {\n stroke: none;\n}\n\n\/**\n * inverse colors\n *\/\n\n\/* inverse recolor the primary elements of an icon *\/\n.jp-icon-hover.jp-icon-alt :hover .jp-icon0-hover[fill] {\n fill: var(--jp-layout-color0);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon1-hover[fill] {\n fill: var(--jp-layout-color1);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon2-hover[fill] {\n fill: var(--jp-layout-color2);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon3-hover[fill] {\n fill: var(--jp-layout-color3);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon4-hover[fill] {\n fill: var(--jp-layout-color4);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon0-hover[stroke] {\n stroke: var(--jp-layout-color0);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon1-hover[stroke] {\n stroke: var(--jp-layout-color1);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon2-hover[stroke] {\n stroke: var(--jp-layout-color2);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon3-hover[stroke] {\n stroke: var(--jp-layout-color3);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon4-hover[stroke] {\n stroke: var(--jp-layout-color4);\n}\n\n\/* inverse recolor the accent elements of an icon *\/\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent0-hover[fill] {\n fill: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent1-hover[fill] {\n fill: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent2-hover[fill] {\n fill: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent3-hover[fill] {\n fill: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent4-hover[fill] {\n fill: var(--jp-inverse-layout-color4);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent0-hover[stroke] {\n stroke: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent1-hover[stroke] {\n stroke: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent2-hover[stroke] {\n stroke: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent3-hover[stroke] {\n stroke: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent4-hover[stroke] {\n stroke: var(--jp-inverse-layout-color4);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-IFrame {\n width: 100%;\n height: 100%;\n}\n\n.jp-IFrame > iframe {\n border: none;\n}\n\n\/*\nWhen drag events occur, `lm-mod-override-cursor` is added to the body.\nBecause iframes steal all cursor events, the following two rules are necessary\nto suppress pointer events while resize drags are occurring. There may be a\nbetter solution to this problem.\n*\/\nbody.lm-mod-override-cursor .jp-IFrame {\n position: relative;\n}\n\nbody.lm-mod-override-cursor .jp-IFrame::before {\n content: '';\n position: absolute;\n top: 0;\n left: 0;\n right: 0;\n bottom: 0;\n background: transparent;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2016, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-HoverBox {\n position: fixed;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-FormGroup-content fieldset {\n border: none;\n padding: 0;\n min-width: 0;\n width: 100%;\n}\n\n\/* stylelint-disable selector-max-type *\/\n\n.jp-FormGroup-content fieldset .jp-inputFieldWrapper input,\n.jp-FormGroup-content fieldset .jp-inputFieldWrapper select,\n.jp-FormGroup-content fieldset .jp-inputFieldWrapper textarea {\n font-size: var(--jp-content-font-size2);\n border-color: var(--jp-input-border-color);\n border-style: solid;\n border-radius: var(--jp-border-radius);\n border-width: 1px;\n padding: 6px 8px;\n background: none;\n color: var(--jp-ui-font-color0);\n height: inherit;\n}\n\n.jp-FormGroup-content fieldset input[type='checkbox'] {\n position: relative;\n top: 2px;\n margin-left: 0;\n}\n\n.jp-FormGroup-content button.jp-mod-styled {\n cursor: pointer;\n}\n\n.jp-FormGroup-content .checkbox label {\n cursor: pointer;\n font-size: var(--jp-content-font-size1);\n}\n\n.jp-FormGroup-content .jp-root > fieldset > legend {\n display: none;\n}\n\n.jp-FormGroup-content .jp-root > fieldset > p {\n display: none;\n}\n\n\/** copy of `input.jp-mod-styled:focus` style *\/\n.jp-FormGroup-content fieldset input:focus,\n.jp-FormGroup-content fieldset select:focus {\n -moz-outline-radius: unset;\n outline: var(--jp-border-width) solid var(--md-blue-500);\n outline-offset: -1px;\n box-shadow: inset 0 0 4px var(--md-blue-300);\n}\n\n.jp-FormGroup-content fieldset input:hover:not(:focus),\n.jp-FormGroup-content fieldset select:hover:not(:focus) {\n background-color: var(--jp-border-color2);\n}\n\n\/* stylelint-enable selector-max-type *\/\n\n.jp-FormGroup-content .checkbox .field-description {\n \/* Disable default description field for checkbox:\n because other widgets do not have description fields,\n we add descriptions to each widget on the field level.\n *\/\n display: none;\n}\n\n.jp-FormGroup-content #root__description {\n display: none;\n}\n\n.jp-FormGroup-content .jp-modifiedIndicator {\n width: 5px;\n background-color: var(--jp-brand-color2);\n margin-top: 0;\n margin-left: calc(var(--jp-private-settingeditor-modifier-indent) * -1);\n flex-shrink: 0;\n}\n\n.jp-FormGroup-content .jp-modifiedIndicator.jp-errorIndicator {\n background-color: var(--jp-error-color0);\n margin-right: 0.5em;\n}\n\n\/* RJSF ARRAY style *\/\n\n.jp-arrayFieldWrapper legend {\n font-size: var(--jp-content-font-size2);\n color: var(--jp-ui-font-color0);\n flex-basis: 100%;\n padding: 4px 0;\n font-weight: var(--jp-content-heading-font-weight);\n border-bottom: 1px solid var(--jp-border-color2);\n}\n\n.jp-arrayFieldWrapper .field-description {\n padding: 4px 0;\n white-space: pre-wrap;\n}\n\n.jp-arrayFieldWrapper .array-item {\n width: 100%;\n border: 1px solid var(--jp-border-color2);\n border-radius: 4px;\n margin: 4px;\n}\n\n.jp-ArrayOperations {\n display: flex;\n margin-left: 8px;\n}\n\n.jp-ArrayOperationsButton {\n margin: 2px;\n}\n\n.jp-ArrayOperationsButton .jp-icon3[fill] {\n fill: var(--jp-ui-font-color0);\n}\n\nbutton.jp-ArrayOperationsButton.jp-mod-styled:disabled {\n cursor: not-allowed;\n opacity: 0.5;\n}\n\n\/* RJSF form validation error *\/\n\n.jp-FormGroup-content .validationErrors {\n color: var(--jp-error-color0);\n}\n\n\/* Hide panel level error as duplicated the field level error *\/\n.jp-FormGroup-content .panel.errors {\n display: none;\n}\n\n\/* RJSF normal content (settings-editor) *\/\n\n.jp-FormGroup-contentNormal {\n display: flex;\n align-items: center;\n flex-wrap: wrap;\n}\n\n.jp-FormGroup-contentNormal .jp-FormGroup-contentItem {\n margin-left: 7px;\n color: var(--jp-ui-font-color0);\n}\n\n.jp-FormGroup-contentNormal .jp-FormGroup-description {\n flex-basis: 100%;\n padding: 4px 7px;\n}\n\n.jp-FormGroup-contentNormal .jp-FormGroup-default {\n flex-basis: 100%;\n padding: 4px 7px;\n}\n\n.jp-FormGroup-contentNormal .jp-FormGroup-fieldLabel {\n font-size: var(--jp-content-font-size1);\n font-weight: normal;\n min-width: 120px;\n}\n\n.jp-FormGroup-contentNormal fieldset:not(:first-child) {\n margin-left: 7px;\n}\n\n.jp-FormGroup-contentNormal .field-array-of-string .array-item {\n \/* Display `jp-ArrayOperations` buttons side-by-side with content except\n for small screens where flex-wrap will place them one below the other.\n *\/\n display: flex;\n align-items: center;\n flex-wrap: wrap;\n}\n\n.jp-FormGroup-contentNormal .jp-objectFieldWrapper .form-group {\n padding: 2px 8px 2px var(--jp-private-settingeditor-modifier-indent);\n margin-top: 2px;\n}\n\n\/* RJSF compact content (metadata-form) *\/\n\n.jp-FormGroup-content.jp-FormGroup-contentCompact {\n width: 100%;\n}\n\n.jp-FormGroup-contentCompact .form-group {\n display: flex;\n padding: 0.5em 0.2em 0.5em 0;\n}\n\n.jp-FormGroup-contentCompact\n .jp-FormGroup-compactTitle\n .jp-FormGroup-description {\n font-size: var(--jp-ui-font-size1);\n color: var(--jp-ui-font-color2);\n}\n\n.jp-FormGroup-contentCompact .jp-FormGroup-fieldLabel {\n padding-bottom: 0.3em;\n}\n\n.jp-FormGroup-contentCompact .jp-inputFieldWrapper .form-control {\n width: 100%;\n box-sizing: border-box;\n}\n\n.jp-FormGroup-contentCompact .jp-arrayFieldWrapper .jp-FormGroup-compactTitle {\n padding-bottom: 7px;\n}\n\n.jp-FormGroup-contentCompact\n .jp-objectFieldWrapper\n .jp-objectFieldWrapper\n .form-group {\n padding: 2px 8px 2px var(--jp-private-settingeditor-modifier-indent);\n margin-top: 2px;\n}\n\n.jp-FormGroup-contentCompact ul.error-detail {\n margin-block-start: 0.5em;\n margin-block-end: 0.5em;\n padding-inline-start: 1em;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n.jp-SidePanel {\n display: flex;\n flex-direction: column;\n min-width: var(--jp-sidebar-min-width);\n overflow-y: auto;\n color: var(--jp-ui-font-color1);\n background: var(--jp-layout-color1);\n font-size: var(--jp-ui-font-size1);\n}\n\n.jp-SidePanel-header {\n flex: 0 0 auto;\n display: flex;\n border-bottom: var(--jp-border-width) solid var(--jp-border-color2);\n font-size: var(--jp-ui-font-size0);\n font-weight: 600;\n letter-spacing: 1px;\n margin: 0;\n padding: 2px;\n text-transform: uppercase;\n}\n\n.jp-SidePanel-toolbar {\n flex: 0 0 auto;\n}\n\n.jp-SidePanel-content {\n flex: 1 1 auto;\n}\n\n.jp-SidePanel-toolbar,\n.jp-AccordionPanel-toolbar {\n height: var(--jp-private-toolbar-height);\n}\n\n.jp-SidePanel-toolbar.jp-Toolbar-micro {\n display: none;\n}\n\n.lm-AccordionPanel .jp-AccordionPanel-title {\n box-sizing: border-box;\n line-height: 25px;\n margin: 0;\n display: flex;\n align-items: center;\n background: var(--jp-layout-color1);\n color: var(--jp-ui-font-color1);\n border-bottom: var(--jp-border-width) solid var(--jp-toolbar-border-color);\n box-shadow: var(--jp-toolbar-box-shadow);\n font-size: var(--jp-ui-font-size0);\n}\n\n.jp-AccordionPanel-title {\n cursor: pointer;\n user-select: none;\n -moz-user-select: none;\n -webkit-user-select: none;\n text-transform: uppercase;\n}\n\n.lm-AccordionPanel[data-orientation='horizontal'] > .jp-AccordionPanel-title {\n \/* Title is rotated for horizontal accordion panel using CSS *\/\n display: block;\n transform-origin: top left;\n transform: rotate(-90deg) translate(-100%);\n}\n\n.jp-AccordionPanel-title .lm-AccordionPanel-titleLabel {\n user-select: none;\n text-overflow: ellipsis;\n white-space: nowrap;\n overflow: hidden;\n}\n\n.jp-AccordionPanel-title .lm-AccordionPanel-titleCollapser {\n transform: rotate(-90deg);\n margin: auto 0;\n height: 16px;\n}\n\n.jp-AccordionPanel-title.lm-mod-expanded .lm-AccordionPanel-titleCollapser {\n transform: rotate(0deg);\n}\n\n.lm-AccordionPanel .jp-AccordionPanel-toolbar {\n background: none;\n box-shadow: none;\n border: none;\n margin-left: auto;\n}\n\n.lm-AccordionPanel .lm-SplitPanel-handle:hover {\n background: var(--jp-layout-color3);\n}\n\n.jp-text-truncated {\n overflow: hidden;\n text-overflow: ellipsis;\n white-space: nowrap;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2017, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-Spinner {\n position: absolute;\n display: flex;\n justify-content: center;\n align-items: center;\n z-index: 10;\n left: 0;\n top: 0;\n width: 100%;\n height: 100%;\n background: var(--jp-layout-color0);\n outline: none;\n}\n\n.jp-SpinnerContent {\n font-size: 10px;\n margin: 50px auto;\n text-indent: -9999em;\n width: 3em;\n height: 3em;\n border-radius: 50%;\n background: var(--jp-brand-color3);\n background: linear-gradient(\n to right,\n #f37626 10%,\n rgba(255, 255, 255, 0) 42%\n );\n position: relative;\n animation: load3 1s infinite linear, fadeIn 1s;\n}\n\n.jp-SpinnerContent::before {\n width: 50%;\n height: 50%;\n background: #f37626;\n border-radius: 100% 0 0;\n position: absolute;\n top: 0;\n left: 0;\n content: '';\n}\n\n.jp-SpinnerContent::after {\n background: var(--jp-layout-color0);\n width: 75%;\n height: 75%;\n border-radius: 50%;\n content: '';\n margin: auto;\n position: absolute;\n top: 0;\n left: 0;\n bottom: 0;\n right: 0;\n}\n\n@keyframes fadeIn {\n 0% {\n opacity: 0;\n }\n\n 100% {\n opacity: 1;\n }\n}\n\n@keyframes load3 {\n 0% {\n transform: rotate(0deg);\n }\n\n 100% {\n transform: rotate(360deg);\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2017, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\nbutton.jp-mod-styled {\n font-size: var(--jp-ui-font-size1);\n color: var(--jp-ui-font-color0);\n border: none;\n box-sizing: border-box;\n text-align: center;\n line-height: 32px;\n height: 32px;\n padding: 0 12px;\n letter-spacing: 0.8px;\n outline: none;\n appearance: none;\n -webkit-appearance: none;\n -moz-appearance: none;\n}\n\ninput.jp-mod-styled {\n background: var(--jp-input-background);\n height: 28px;\n box-sizing: border-box;\n border: var(--jp-border-width) solid var(--jp-border-color1);\n padding-left: 7px;\n padding-right: 7px;\n font-size: var(--jp-ui-font-size2);\n color: var(--jp-ui-font-color0);\n outline: none;\n appearance: none;\n -webkit-appearance: none;\n -moz-appearance: none;\n}\n\ninput[type='checkbox'].jp-mod-styled {\n appearance: checkbox;\n -webkit-appearance: checkbox;\n -moz-appearance: checkbox;\n height: auto;\n}\n\ninput.jp-mod-styled:focus {\n border: var(--jp-border-width) solid var(--md-blue-500);\n box-shadow: inset 0 0 4px var(--md-blue-300);\n}\n\n.jp-select-wrapper {\n display: flex;\n position: relative;\n flex-direction: column;\n padding: 1px;\n background-color: var(--jp-layout-color1);\n box-sizing: border-box;\n margin-bottom: 12px;\n}\n\n.jp-select-wrapper:not(.multiple) {\n height: 28px;\n}\n\n.jp-select-wrapper.jp-mod-focused select.jp-mod-styled {\n border: var(--jp-border-width) solid var(--jp-input-active-border-color);\n box-shadow: var(--jp-input-box-shadow);\n background-color: var(--jp-input-active-background);\n}\n\nselect.jp-mod-styled:hover {\n cursor: pointer;\n color: var(--jp-ui-font-color0);\n background-color: var(--jp-input-hover-background);\n box-shadow: inset 0 0 1px rgba(0, 0, 0, 0.5);\n}\n\nselect.jp-mod-styled {\n flex: 1 1 auto;\n width: 100%;\n font-size: var(--jp-ui-font-size2);\n background: var(--jp-input-background);\n color: var(--jp-ui-font-color0);\n padding: 0 25px 0 8px;\n border: var(--jp-border-width) solid var(--jp-input-border-color);\n border-radius: 0;\n outline: none;\n appearance: none;\n -webkit-appearance: none;\n -moz-appearance: none;\n}\n\nselect.jp-mod-styled:not([multiple]) {\n height: 32px;\n}\n\nselect.jp-mod-styled[multiple] {\n max-height: 200px;\n overflow-y: auto;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-switch {\n display: flex;\n align-items: center;\n padding-left: 4px;\n padding-right: 4px;\n font-size: var(--jp-ui-font-size1);\n background-color: transparent;\n color: var(--jp-ui-font-color1);\n border: none;\n height: 20px;\n}\n\n.jp-switch:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-switch-label {\n margin-right: 5px;\n font-family: var(--jp-ui-font-family);\n}\n\n.jp-switch-track {\n cursor: pointer;\n background-color: var(--jp-switch-color, var(--jp-border-color1));\n -webkit-transition: 0.4s;\n transition: 0.4s;\n border-radius: 34px;\n height: 16px;\n width: 35px;\n position: relative;\n}\n\n.jp-switch-track::before {\n content: '';\n position: absolute;\n height: 10px;\n width: 10px;\n margin: 3px;\n left: 0;\n background-color: var(--jp-ui-inverse-font-color1);\n -webkit-transition: 0.4s;\n transition: 0.4s;\n border-radius: 50%;\n}\n\n.jp-switch[aria-checked='true'] .jp-switch-track {\n background-color: var(--jp-switch-true-position-color, var(--jp-warn-color0));\n}\n\n.jp-switch[aria-checked='true'] .jp-switch-track::before {\n \/* track width (35) - margins (3 + 3) - thumb width (10) *\/\n left: 19px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2016, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-private-toolbar-height: calc(\n 28px + var(--jp-border-width)\n ); \/* leave 28px for content *\/\n}\n\n.jp-Toolbar {\n color: var(--jp-ui-font-color1);\n flex: 0 0 auto;\n display: flex;\n flex-direction: row;\n border-bottom: var(--jp-border-width) solid var(--jp-toolbar-border-color);\n box-shadow: var(--jp-toolbar-box-shadow);\n background: var(--jp-toolbar-background);\n min-height: var(--jp-toolbar-micro-height);\n padding: 2px;\n z-index: 8;\n overflow-x: hidden;\n}\n\n\/* Toolbar items *\/\n\n.jp-Toolbar > .jp-Toolbar-item.jp-Toolbar-spacer {\n flex-grow: 1;\n flex-shrink: 1;\n}\n\n.jp-Toolbar-item.jp-Toolbar-kernelStatus {\n display: inline-block;\n width: 32px;\n background-repeat: no-repeat;\n background-position: center;\n background-size: 16px;\n}\n\n.jp-Toolbar > .jp-Toolbar-item {\n flex: 0 0 auto;\n display: flex;\n padding-left: 1px;\n padding-right: 1px;\n font-size: var(--jp-ui-font-size1);\n line-height: var(--jp-private-toolbar-height);\n height: 100%;\n}\n\n\/* Toolbar buttons *\/\n\n\/* This is the div we use to wrap the react component into a Widget *\/\ndiv.jp-ToolbarButton {\n color: transparent;\n border: none;\n box-sizing: border-box;\n outline: none;\n appearance: none;\n -webkit-appearance: none;\n -moz-appearance: none;\n padding: 0;\n margin: 0;\n}\n\nbutton.jp-ToolbarButtonComponent {\n background: var(--jp-layout-color1);\n border: none;\n box-sizing: border-box;\n outline: none;\n appearance: none;\n -webkit-appearance: none;\n -moz-appearance: none;\n padding: 0 6px;\n margin: 0;\n height: 24px;\n border-radius: var(--jp-border-radius);\n display: flex;\n align-items: center;\n text-align: center;\n font-size: 14px;\n min-width: unset;\n min-height: unset;\n}\n\nbutton.jp-ToolbarButtonComponent:disabled {\n opacity: 0.4;\n}\n\nbutton.jp-ToolbarButtonComponent > span {\n padding: 0;\n flex: 0 0 auto;\n}\n\nbutton.jp-ToolbarButtonComponent .jp-ToolbarButtonComponent-label {\n font-size: var(--jp-ui-font-size1);\n line-height: 100%;\n padding-left: 2px;\n color: var(--jp-ui-font-color1);\n font-family: var(--jp-ui-font-family);\n}\n\n#jp-main-dock-panel[data-mode='single-document']\n .jp-MainAreaWidget\n > .jp-Toolbar.jp-Toolbar-micro {\n padding: 0;\n min-height: 0;\n}\n\n#jp-main-dock-panel[data-mode='single-document']\n .jp-MainAreaWidget\n > .jp-Toolbar {\n border: none;\n box-shadow: none;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n.jp-WindowedPanel-outer {\n position: relative;\n overflow-y: auto;\n}\n\n.jp-WindowedPanel-inner {\n position: relative;\n}\n\n.jp-WindowedPanel-window {\n position: absolute;\n left: 0;\n right: 0;\n overflow: visible;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/* Sibling imports *\/\n\nbody {\n color: var(--jp-ui-font-color1);\n font-size: var(--jp-ui-font-size1);\n}\n\n\/* Disable native link decoration styles everywhere outside of dialog boxes *\/\na {\n text-decoration: unset;\n color: unset;\n}\n\na:hover {\n text-decoration: unset;\n color: unset;\n}\n\n\/* Accessibility for links inside dialog box text *\/\n.jp-Dialog-content a {\n text-decoration: revert;\n color: var(--jp-content-link-color);\n}\n\n.jp-Dialog-content a:hover {\n text-decoration: revert;\n}\n\n\/* Styles for ui-components *\/\n.jp-Button {\n color: var(--jp-ui-font-color2);\n border-radius: var(--jp-border-radius);\n padding: 0 12px;\n font-size: var(--jp-ui-font-size1);\n\n \/* Copy from blueprint 3 *\/\n display: inline-flex;\n flex-direction: row;\n border: none;\n cursor: pointer;\n align-items: center;\n justify-content: center;\n text-align: left;\n vertical-align: middle;\n min-height: 30px;\n min-width: 30px;\n}\n\n.jp-Button:disabled {\n cursor: not-allowed;\n}\n\n.jp-Button:empty {\n padding: 0 !important;\n}\n\n.jp-Button.jp-mod-small {\n min-height: 24px;\n min-width: 24px;\n font-size: 12px;\n padding: 0 7px;\n}\n\n\/* Use our own theme for hover styles *\/\n.jp-Button.jp-mod-minimal:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-Button.jp-mod-minimal {\n background: none;\n}\n\n.jp-InputGroup {\n display: block;\n position: relative;\n}\n\n.jp-InputGroup input {\n box-sizing: border-box;\n border: none;\n border-radius: 0;\n background-color: transparent;\n color: var(--jp-ui-font-color0);\n box-shadow: inset 0 0 0 var(--jp-border-width) var(--jp-input-border-color);\n padding-bottom: 0;\n padding-top: 0;\n padding-left: 10px;\n padding-right: 28px;\n position: relative;\n width: 100%;\n -webkit-appearance: none;\n -moz-appearance: none;\n appearance: none;\n font-size: 14px;\n font-weight: 400;\n height: 30px;\n line-height: 30px;\n outline: none;\n vertical-align: middle;\n}\n\n.jp-InputGroup input:focus {\n box-shadow: inset 0 0 0 var(--jp-border-width)\n var(--jp-input-active-box-shadow-color),\n inset 0 0 0 3px var(--jp-input-active-box-shadow-color);\n}\n\n.jp-InputGroup input:disabled {\n cursor: not-allowed;\n resize: block;\n background-color: var(--jp-layout-color2);\n color: var(--jp-ui-font-color2);\n}\n\n.jp-InputGroup input:disabled ~ span {\n cursor: not-allowed;\n color: var(--jp-ui-font-color2);\n}\n\n.jp-InputGroup input::placeholder,\ninput::placeholder {\n color: var(--jp-ui-font-color2);\n}\n\n.jp-InputGroupAction {\n position: absolute;\n bottom: 1px;\n right: 0;\n padding: 6px;\n}\n\n.jp-HTMLSelect.jp-DefaultStyle select {\n background-color: initial;\n border: none;\n border-radius: 0;\n box-shadow: none;\n color: var(--jp-ui-font-color0);\n display: block;\n font-size: var(--jp-ui-font-size1);\n font-family: var(--jp-ui-font-family);\n height: 24px;\n line-height: 14px;\n padding: 0 25px 0 10px;\n text-align: left;\n -moz-appearance: none;\n -webkit-appearance: none;\n}\n\n.jp-HTMLSelect.jp-DefaultStyle select:disabled {\n background-color: var(--jp-layout-color2);\n color: var(--jp-ui-font-color2);\n cursor: not-allowed;\n resize: block;\n}\n\n.jp-HTMLSelect.jp-DefaultStyle select:disabled ~ span {\n cursor: not-allowed;\n}\n\n\/* Use our own theme for hover and option styles *\/\n\/* stylelint-disable-next-line selector-max-type *\/\n.jp-HTMLSelect.jp-DefaultStyle select:hover,\n.jp-HTMLSelect.jp-DefaultStyle select > option {\n background-color: var(--jp-layout-color2);\n color: var(--jp-ui-font-color0);\n}\n\nselect {\n box-sizing: border-box;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Styles\n|----------------------------------------------------------------------------*\/\n\n.jp-StatusBar-Widget {\n display: flex;\n align-items: center;\n background: var(--jp-layout-color2);\n min-height: var(--jp-statusbar-height);\n justify-content: space-between;\n padding: 0 10px;\n}\n\n.jp-StatusBar-Left {\n display: flex;\n align-items: center;\n flex-direction: row;\n}\n\n.jp-StatusBar-Middle {\n display: flex;\n align-items: center;\n}\n\n.jp-StatusBar-Right {\n display: flex;\n align-items: center;\n flex-direction: row-reverse;\n}\n\n.jp-StatusBar-Item {\n max-height: var(--jp-statusbar-height);\n margin: 0 2px;\n height: var(--jp-statusbar-height);\n white-space: nowrap;\n text-overflow: ellipsis;\n color: var(--jp-ui-font-color1);\n padding: 0 6px;\n}\n\n.jp-mod-highlighted:hover {\n background-color: var(--jp-layout-color3);\n}\n\n.jp-mod-clicked {\n background-color: var(--jp-brand-color1);\n}\n\n.jp-mod-clicked:hover {\n background-color: var(--jp-brand-color0);\n}\n\n.jp-mod-clicked .jp-StatusBar-TextItem {\n color: var(--jp-ui-inverse-font-color1);\n}\n\n.jp-StatusBar-HoverItem {\n box-shadow: '0px 4px 4px rgba(0, 0, 0, 0.25)';\n}\n\n.jp-StatusBar-TextItem {\n font-size: var(--jp-ui-font-size1);\n font-family: var(--jp-ui-font-family);\n line-height: 24px;\n color: var(--jp-ui-font-color1);\n}\n\n.jp-StatusBar-GroupItem {\n display: flex;\n align-items: center;\n flex-direction: row;\n}\n\n.jp-Statusbar-ProgressCircle svg {\n display: block;\n margin: 0 auto;\n width: 16px;\n height: 24px;\n align-self: normal;\n}\n\n.jp-Statusbar-ProgressCircle path {\n fill: var(--jp-inverse-layout-color3);\n}\n\n.jp-Statusbar-ProgressBar-progress-bar {\n height: 10px;\n width: 100px;\n border: solid 0.25px var(--jp-brand-color2);\n border-radius: 3px;\n overflow: hidden;\n align-self: center;\n}\n\n.jp-Statusbar-ProgressBar-progress-bar > div {\n background-color: var(--jp-brand-color2);\n background-image: linear-gradient(\n -45deg,\n rgba(255, 255, 255, 0.2) 25%,\n transparent 25%,\n transparent 50%,\n rgba(255, 255, 255, 0.2) 50%,\n rgba(255, 255, 255, 0.2) 75%,\n transparent 75%,\n transparent\n );\n background-size: 40px 40px;\n float: left;\n width: 0%;\n height: 100%;\n font-size: 12px;\n line-height: 14px;\n color: #fff;\n text-align: center;\n animation: jp-Statusbar-ExecutionTime-progress-bar 2s linear infinite;\n}\n\n.jp-Statusbar-ProgressBar-progress-bar p {\n color: var(--jp-ui-font-color1);\n font-family: var(--jp-ui-font-family);\n font-size: var(--jp-ui-font-size1);\n line-height: 10px;\n width: 100px;\n}\n\n@keyframes jp-Statusbar-ExecutionTime-progress-bar {\n 0% {\n background-position: 0 0;\n }\n\n 100% {\n background-position: 40px 40px;\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Variables\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-private-commandpalette-search-height: 28px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Overall styles\n|----------------------------------------------------------------------------*\/\n\n.lm-CommandPalette {\n padding-bottom: 0;\n color: var(--jp-ui-font-color1);\n background: var(--jp-layout-color1);\n\n \/* This is needed so that all font sizing of children done in ems is\n * relative to this base size *\/\n font-size: var(--jp-ui-font-size1);\n}\n\n\/*-----------------------------------------------------------------------------\n| Modal variant\n|----------------------------------------------------------------------------*\/\n\n.jp-ModalCommandPalette {\n position: absolute;\n z-index: 10000;\n top: 38px;\n left: 30%;\n margin: 0;\n padding: 4px;\n width: 40%;\n box-shadow: var(--jp-elevation-z4);\n border-radius: 4px;\n background: var(--jp-layout-color0);\n}\n\n.jp-ModalCommandPalette .lm-CommandPalette {\n max-height: 40vh;\n}\n\n.jp-ModalCommandPalette .lm-CommandPalette .lm-close-icon::after {\n display: none;\n}\n\n.jp-ModalCommandPalette .lm-CommandPalette .lm-CommandPalette-header {\n display: none;\n}\n\n.jp-ModalCommandPalette .lm-CommandPalette .lm-CommandPalette-item {\n margin-left: 4px;\n margin-right: 4px;\n}\n\n.jp-ModalCommandPalette\n .lm-CommandPalette\n .lm-CommandPalette-item.lm-mod-disabled {\n display: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Search\n|----------------------------------------------------------------------------*\/\n\n.lm-CommandPalette-search {\n padding: 4px;\n background-color: var(--jp-layout-color1);\n z-index: 2;\n}\n\n.lm-CommandPalette-wrapper {\n overflow: overlay;\n padding: 0 9px;\n background-color: var(--jp-input-active-background);\n height: 30px;\n box-shadow: inset 0 0 0 var(--jp-border-width) var(--jp-input-border-color);\n}\n\n.lm-CommandPalette.lm-mod-focused .lm-CommandPalette-wrapper {\n box-shadow: inset 0 0 0 1px var(--jp-input-active-box-shadow-color),\n inset 0 0 0 3px var(--jp-input-active-box-shadow-color);\n}\n\n.jp-SearchIconGroup {\n color: white;\n background-color: var(--jp-brand-color1);\n position: absolute;\n top: 4px;\n right: 4px;\n padding: 5px 5px 1px;\n}\n\n.jp-SearchIconGroup svg {\n height: 20px;\n width: 20px;\n}\n\n.jp-SearchIconGroup .jp-icon3[fill] {\n fill: var(--jp-layout-color0);\n}\n\n.lm-CommandPalette-input {\n background: transparent;\n width: calc(100% - 18px);\n float: left;\n border: none;\n outline: none;\n font-size: var(--jp-ui-font-size1);\n color: var(--jp-ui-font-color0);\n line-height: var(--jp-private-commandpalette-search-height);\n}\n\n.lm-CommandPalette-input::-webkit-input-placeholder,\n.lm-CommandPalette-input::-moz-placeholder,\n.lm-CommandPalette-input:-ms-input-placeholder {\n color: var(--jp-ui-font-color2);\n font-size: var(--jp-ui-font-size1);\n}\n\n\/*-----------------------------------------------------------------------------\n| Results\n|----------------------------------------------------------------------------*\/\n\n.lm-CommandPalette-header:first-child {\n margin-top: 0;\n}\n\n.lm-CommandPalette-header {\n border-bottom: solid var(--jp-border-width) var(--jp-border-color2);\n color: var(--jp-ui-font-color1);\n cursor: pointer;\n display: flex;\n font-size: var(--jp-ui-font-size0);\n font-weight: 600;\n letter-spacing: 1px;\n margin-top: 8px;\n padding: 8px 0 8px 12px;\n text-transform: uppercase;\n}\n\n.lm-CommandPalette-header.lm-mod-active {\n background: var(--jp-layout-color2);\n}\n\n.lm-CommandPalette-header > mark {\n background-color: transparent;\n font-weight: bold;\n color: var(--jp-ui-font-color1);\n}\n\n.lm-CommandPalette-item {\n padding: 4px 12px 4px 4px;\n color: var(--jp-ui-font-color1);\n font-size: var(--jp-ui-font-size1);\n font-weight: 400;\n display: flex;\n}\n\n.lm-CommandPalette-item.lm-mod-disabled {\n color: var(--jp-ui-font-color2);\n}\n\n.lm-CommandPalette-item.lm-mod-active {\n color: var(--jp-ui-inverse-font-color1);\n background: var(--jp-brand-color1);\n}\n\n.lm-CommandPalette-item.lm-mod-active .lm-CommandPalette-itemLabel > mark {\n color: var(--jp-ui-inverse-font-color0);\n}\n\n.lm-CommandPalette-item.lm-mod-active .jp-icon-selectable[fill] {\n fill: var(--jp-layout-color0);\n}\n\n.lm-CommandPalette-item.lm-mod-active:hover:not(.lm-mod-disabled) {\n color: var(--jp-ui-inverse-font-color1);\n background: var(--jp-brand-color1);\n}\n\n.lm-CommandPalette-item:hover:not(.lm-mod-active):not(.lm-mod-disabled) {\n background: var(--jp-layout-color2);\n}\n\n.lm-CommandPalette-itemContent {\n overflow: hidden;\n}\n\n.lm-CommandPalette-itemLabel > mark {\n color: var(--jp-ui-font-color0);\n background-color: transparent;\n font-weight: bold;\n}\n\n.lm-CommandPalette-item.lm-mod-disabled mark {\n color: var(--jp-ui-font-color2);\n}\n\n.lm-CommandPalette-item .lm-CommandPalette-itemIcon {\n margin: 0 4px 0 0;\n position: relative;\n width: 16px;\n top: 2px;\n flex: 0 0 auto;\n}\n\n.lm-CommandPalette-item.lm-mod-disabled .lm-CommandPalette-itemIcon {\n opacity: 0.6;\n}\n\n.lm-CommandPalette-item .lm-CommandPalette-itemShortcut {\n flex: 0 0 auto;\n}\n\n.lm-CommandPalette-itemCaption {\n display: none;\n}\n\n.lm-CommandPalette-content {\n background-color: var(--jp-layout-color1);\n}\n\n.lm-CommandPalette-content:empty::after {\n content: 'No results';\n margin: auto;\n margin-top: 20px;\n width: 100px;\n display: block;\n font-size: var(--jp-ui-font-size2);\n font-family: var(--jp-ui-font-family);\n font-weight: lighter;\n}\n\n.lm-CommandPalette-emptyMessage {\n text-align: center;\n margin-top: 24px;\n line-height: 1.32;\n padding: 0 8px;\n color: var(--jp-content-font-color3);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2017, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-Dialog {\n position: absolute;\n z-index: 10000;\n display: flex;\n flex-direction: column;\n align-items: center;\n justify-content: center;\n top: 0;\n left: 0;\n margin: 0;\n padding: 0;\n width: 100%;\n height: 100%;\n background: var(--jp-dialog-background);\n}\n\n.jp-Dialog-content {\n display: flex;\n flex-direction: column;\n margin-left: auto;\n margin-right: auto;\n background: var(--jp-layout-color1);\n padding: 24px 24px 12px;\n min-width: 300px;\n min-height: 150px;\n max-width: 1000px;\n max-height: 500px;\n box-sizing: border-box;\n box-shadow: var(--jp-elevation-z20);\n word-wrap: break-word;\n border-radius: var(--jp-border-radius);\n\n \/* This is needed so that all font sizing of children done in ems is\n * relative to this base size *\/\n font-size: var(--jp-ui-font-size1);\n color: var(--jp-ui-font-color1);\n resize: both;\n}\n\n.jp-Dialog-content.jp-Dialog-content-small {\n max-width: 500px;\n}\n\n.jp-Dialog-button {\n overflow: visible;\n}\n\nbutton.jp-Dialog-button:focus {\n outline: 1px solid var(--jp-brand-color1);\n outline-offset: 4px;\n -moz-outline-radius: 0;\n}\n\nbutton.jp-Dialog-button:focus::-moz-focus-inner {\n border: 0;\n}\n\nbutton.jp-Dialog-button.jp-mod-styled.jp-mod-accept:focus,\nbutton.jp-Dialog-button.jp-mod-styled.jp-mod-warn:focus,\nbutton.jp-Dialog-button.jp-mod-styled.jp-mod-reject:focus {\n outline-offset: 4px;\n -moz-outline-radius: 0;\n}\n\nbutton.jp-Dialog-button.jp-mod-styled.jp-mod-accept:focus {\n outline: 1px solid var(--jp-accept-color-normal, var(--jp-brand-color1));\n}\n\nbutton.jp-Dialog-button.jp-mod-styled.jp-mod-warn:focus {\n outline: 1px solid var(--jp-warn-color-normal, var(--jp-error-color1));\n}\n\nbutton.jp-Dialog-button.jp-mod-styled.jp-mod-reject:focus {\n outline: 1px solid var(--jp-reject-color-normal, var(--md-grey-600));\n}\n\nbutton.jp-Dialog-close-button {\n padding: 0;\n height: 100%;\n min-width: unset;\n min-height: unset;\n}\n\n.jp-Dialog-header {\n display: flex;\n justify-content: space-between;\n flex: 0 0 auto;\n padding-bottom: 12px;\n font-size: var(--jp-ui-font-size3);\n font-weight: 400;\n color: var(--jp-ui-font-color1);\n}\n\n.jp-Dialog-body {\n display: flex;\n flex-direction: column;\n flex: 1 1 auto;\n font-size: var(--jp-ui-font-size1);\n background: var(--jp-layout-color1);\n color: var(--jp-ui-font-color1);\n overflow: auto;\n}\n\n.jp-Dialog-footer {\n display: flex;\n flex-direction: row;\n justify-content: flex-end;\n align-items: center;\n flex: 0 0 auto;\n margin-left: -12px;\n margin-right: -12px;\n padding: 12px;\n}\n\n.jp-Dialog-checkbox {\n padding-right: 5px;\n}\n\n.jp-Dialog-checkbox > input:focus-visible {\n outline: 1px solid var(--jp-input-active-border-color);\n outline-offset: 1px;\n}\n\n.jp-Dialog-spacer {\n flex: 1 1 auto;\n}\n\n.jp-Dialog-title {\n overflow: hidden;\n white-space: nowrap;\n text-overflow: ellipsis;\n}\n\n.jp-Dialog-body > .jp-select-wrapper {\n width: 100%;\n}\n\n.jp-Dialog-body > button {\n padding: 0 16px;\n}\n\n.jp-Dialog-body > label {\n line-height: 1.4;\n color: var(--jp-ui-font-color0);\n}\n\n.jp-Dialog-button.jp-mod-styled:not(:last-child) {\n margin-right: 12px;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n.jp-Input-Boolean-Dialog {\n flex-direction: row-reverse;\n align-items: end;\n width: 100%;\n}\n\n.jp-Input-Boolean-Dialog > label {\n flex: 1 1 auto;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2016, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-MainAreaWidget > :focus {\n outline: none;\n}\n\n.jp-MainAreaWidget .jp-MainAreaWidget-error {\n padding: 6px;\n}\n\n.jp-MainAreaWidget .jp-MainAreaWidget-error > pre {\n width: auto;\n padding: 10px;\n background: var(--jp-error-color3);\n border: var(--jp-border-width) solid var(--jp-error-color1);\n border-radius: var(--jp-border-radius);\n color: var(--jp-ui-font-color1);\n font-size: var(--jp-ui-font-size1);\n white-space: pre-wrap;\n word-wrap: break-word;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/**\n * google-material-color v1.2.6\n * https:\/\/github.com\/danlevan\/google-material-color\n *\/\n:root {\n --md-red-50: #ffebee;\n --md-red-100: #ffcdd2;\n --md-red-200: #ef9a9a;\n --md-red-300: #e57373;\n --md-red-400: #ef5350;\n --md-red-500: #f44336;\n --md-red-600: #e53935;\n --md-red-700: #d32f2f;\n --md-red-800: #c62828;\n --md-red-900: #b71c1c;\n --md-red-A100: #ff8a80;\n --md-red-A200: #ff5252;\n --md-red-A400: #ff1744;\n --md-red-A700: #d50000;\n --md-pink-50: #fce4ec;\n --md-pink-100: #f8bbd0;\n --md-pink-200: #f48fb1;\n --md-pink-300: #f06292;\n --md-pink-400: #ec407a;\n --md-pink-500: #e91e63;\n --md-pink-600: #d81b60;\n --md-pink-700: #c2185b;\n --md-pink-800: #ad1457;\n --md-pink-900: #880e4f;\n --md-pink-A100: #ff80ab;\n --md-pink-A200: #ff4081;\n --md-pink-A400: #f50057;\n --md-pink-A700: #c51162;\n --md-purple-50: #f3e5f5;\n --md-purple-100: #e1bee7;\n --md-purple-200: #ce93d8;\n --md-purple-300: #ba68c8;\n --md-purple-400: #ab47bc;\n --md-purple-500: #9c27b0;\n --md-purple-600: #8e24aa;\n --md-purple-700: #7b1fa2;\n --md-purple-800: #6a1b9a;\n --md-purple-900: #4a148c;\n --md-purple-A100: #ea80fc;\n --md-purple-A200: #e040fb;\n --md-purple-A400: #d500f9;\n --md-purple-A700: #a0f;\n --md-deep-purple-50: #ede7f6;\n --md-deep-purple-100: #d1c4e9;\n --md-deep-purple-200: #b39ddb;\n --md-deep-purple-300: #9575cd;\n --md-deep-purple-400: #7e57c2;\n --md-deep-purple-500: #673ab7;\n --md-deep-purple-600: #5e35b1;\n --md-deep-purple-700: #512da8;\n --md-deep-purple-800: #4527a0;\n --md-deep-purple-900: #311b92;\n --md-deep-purple-A100: #b388ff;\n --md-deep-purple-A200: #7c4dff;\n --md-deep-purple-A400: #651fff;\n --md-deep-purple-A700: #6200ea;\n --md-indigo-50: #e8eaf6;\n --md-indigo-100: #c5cae9;\n --md-indigo-200: #9fa8da;\n --md-indigo-300: #7986cb;\n --md-indigo-400: #5c6bc0;\n --md-indigo-500: #3f51b5;\n --md-indigo-600: #3949ab;\n --md-indigo-700: #303f9f;\n --md-indigo-800: #283593;\n --md-indigo-900: #1a237e;\n --md-indigo-A100: #8c9eff;\n --md-indigo-A200: #536dfe;\n --md-indigo-A400: #3d5afe;\n --md-indigo-A700: #304ffe;\n --md-blue-50: #e3f2fd;\n --md-blue-100: #bbdefb;\n --md-blue-200: #90caf9;\n --md-blue-300: #64b5f6;\n --md-blue-400: #42a5f5;\n --md-blue-500: #2196f3;\n --md-blue-600: #1e88e5;\n --md-blue-700: #1976d2;\n --md-blue-800: #1565c0;\n --md-blue-900: #0d47a1;\n --md-blue-A100: #82b1ff;\n --md-blue-A200: #448aff;\n --md-blue-A400: #2979ff;\n --md-blue-A700: #2962ff;\n --md-light-blue-50: #e1f5fe;\n --md-light-blue-100: #b3e5fc;\n --md-light-blue-200: #81d4fa;\n --md-light-blue-300: #4fc3f7;\n --md-light-blue-400: #29b6f6;\n --md-light-blue-500: #03a9f4;\n --md-light-blue-600: #039be5;\n --md-light-blue-700: #0288d1;\n --md-light-blue-800: #0277bd;\n --md-light-blue-900: #01579b;\n --md-light-blue-A100: #80d8ff;\n --md-light-blue-A200: #40c4ff;\n --md-light-blue-A400: #00b0ff;\n --md-light-blue-A700: #0091ea;\n --md-cyan-50: #e0f7fa;\n --md-cyan-100: #b2ebf2;\n --md-cyan-200: #80deea;\n --md-cyan-300: #4dd0e1;\n --md-cyan-400: #26c6da;\n --md-cyan-500: #00bcd4;\n --md-cyan-600: #00acc1;\n --md-cyan-700: #0097a7;\n --md-cyan-800: #00838f;\n --md-cyan-900: #006064;\n --md-cyan-A100: #84ffff;\n --md-cyan-A200: #18ffff;\n --md-cyan-A400: #00e5ff;\n --md-cyan-A700: #00b8d4;\n --md-teal-50: #e0f2f1;\n --md-teal-100: #b2dfdb;\n --md-teal-200: #80cbc4;\n --md-teal-300: #4db6ac;\n --md-teal-400: #26a69a;\n --md-teal-500: #009688;\n --md-teal-600: #00897b;\n --md-teal-700: #00796b;\n --md-teal-800: #00695c;\n --md-teal-900: #004d40;\n --md-teal-A100: #a7ffeb;\n --md-teal-A200: #64ffda;\n --md-teal-A400: #1de9b6;\n --md-teal-A700: #00bfa5;\n --md-green-50: #e8f5e9;\n --md-green-100: #c8e6c9;\n --md-green-200: #a5d6a7;\n --md-green-300: #81c784;\n --md-green-400: #66bb6a;\n --md-green-500: #4caf50;\n --md-green-600: #43a047;\n --md-green-700: #388e3c;\n --md-green-800: #2e7d32;\n --md-green-900: #1b5e20;\n --md-green-A100: #b9f6ca;\n --md-green-A200: #69f0ae;\n --md-green-A400: #00e676;\n --md-green-A700: #00c853;\n --md-light-green-50: #f1f8e9;\n --md-light-green-100: #dcedc8;\n --md-light-green-200: #c5e1a5;\n --md-light-green-300: #aed581;\n --md-light-green-400: #9ccc65;\n --md-light-green-500: #8bc34a;\n --md-light-green-600: #7cb342;\n --md-light-green-700: #689f38;\n --md-light-green-800: #558b2f;\n --md-light-green-900: #33691e;\n --md-light-green-A100: #ccff90;\n --md-light-green-A200: #b2ff59;\n --md-light-green-A400: #76ff03;\n --md-light-green-A700: #64dd17;\n --md-lime-50: #f9fbe7;\n --md-lime-100: #f0f4c3;\n --md-lime-200: #e6ee9c;\n --md-lime-300: #dce775;\n --md-lime-400: #d4e157;\n --md-lime-500: #cddc39;\n --md-lime-600: #c0ca33;\n --md-lime-700: #afb42b;\n --md-lime-800: #9e9d24;\n --md-lime-900: #827717;\n --md-lime-A100: #f4ff81;\n --md-lime-A200: #eeff41;\n --md-lime-A400: #c6ff00;\n --md-lime-A700: #aeea00;\n --md-yellow-50: #fffde7;\n --md-yellow-100: #fff9c4;\n --md-yellow-200: #fff59d;\n --md-yellow-300: #fff176;\n --md-yellow-400: #ffee58;\n --md-yellow-500: #ffeb3b;\n --md-yellow-600: #fdd835;\n --md-yellow-700: #fbc02d;\n --md-yellow-800: #f9a825;\n --md-yellow-900: #f57f17;\n --md-yellow-A100: #ffff8d;\n --md-yellow-A200: #ff0;\n --md-yellow-A400: #ffea00;\n --md-yellow-A700: #ffd600;\n --md-amber-50: #fff8e1;\n --md-amber-100: #ffecb3;\n --md-amber-200: #ffe082;\n --md-amber-300: #ffd54f;\n --md-amber-400: #ffca28;\n --md-amber-500: #ffc107;\n --md-amber-600: #ffb300;\n --md-amber-700: #ffa000;\n --md-amber-800: #ff8f00;\n --md-amber-900: #ff6f00;\n --md-amber-A100: #ffe57f;\n --md-amber-A200: #ffd740;\n --md-amber-A400: #ffc400;\n --md-amber-A700: #ffab00;\n --md-orange-50: #fff3e0;\n --md-orange-100: #ffe0b2;\n --md-orange-200: #ffcc80;\n --md-orange-300: #ffb74d;\n --md-orange-400: #ffa726;\n --md-orange-500: #ff9800;\n --md-orange-600: #fb8c00;\n --md-orange-700: #f57c00;\n --md-orange-800: #ef6c00;\n --md-orange-900: #e65100;\n --md-orange-A100: #ffd180;\n --md-orange-A200: #ffab40;\n --md-orange-A400: #ff9100;\n --md-orange-A700: #ff6d00;\n --md-deep-orange-50: #fbe9e7;\n --md-deep-orange-100: #ffccbc;\n --md-deep-orange-200: #ffab91;\n --md-deep-orange-300: #ff8a65;\n --md-deep-orange-400: #ff7043;\n --md-deep-orange-500: #ff5722;\n --md-deep-orange-600: #f4511e;\n --md-deep-orange-700: #e64a19;\n --md-deep-orange-800: #d84315;\n --md-deep-orange-900: #bf360c;\n --md-deep-orange-A100: #ff9e80;\n --md-deep-orange-A200: #ff6e40;\n --md-deep-orange-A400: #ff3d00;\n --md-deep-orange-A700: #dd2c00;\n --md-brown-50: #efebe9;\n --md-brown-100: #d7ccc8;\n --md-brown-200: #bcaaa4;\n --md-brown-300: #a1887f;\n --md-brown-400: #8d6e63;\n --md-brown-500: #795548;\n --md-brown-600: #6d4c41;\n --md-brown-700: #5d4037;\n --md-brown-800: #4e342e;\n --md-brown-900: #3e2723;\n --md-grey-50: #fafafa;\n --md-grey-100: #f5f5f5;\n --md-grey-200: #eee;\n --md-grey-300: #e0e0e0;\n --md-grey-400: #bdbdbd;\n --md-grey-500: #9e9e9e;\n --md-grey-600: #757575;\n --md-grey-700: #616161;\n --md-grey-800: #424242;\n --md-grey-900: #212121;\n --md-blue-grey-50: #eceff1;\n --md-blue-grey-100: #cfd8dc;\n --md-blue-grey-200: #b0bec5;\n --md-blue-grey-300: #90a4ae;\n --md-blue-grey-400: #78909c;\n --md-blue-grey-500: #607d8b;\n --md-blue-grey-600: #546e7a;\n --md-blue-grey-700: #455a64;\n --md-blue-grey-800: #37474f;\n --md-blue-grey-900: #263238;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2017, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| RenderedText\n|----------------------------------------------------------------------------*\/\n\n:root {\n \/* This is the padding value to fill the gaps between lines containing spans with background color. *\/\n --jp-private-code-span-padding: calc(\n (var(--jp-code-line-height) - 1) * var(--jp-code-font-size) \/ 2\n );\n}\n\n.jp-RenderedText {\n text-align: left;\n padding-left: var(--jp-code-padding);\n line-height: var(--jp-code-line-height);\n font-family: var(--jp-code-font-family);\n}\n\n.jp-RenderedText pre,\n.jp-RenderedJavaScript pre,\n.jp-RenderedHTMLCommon pre {\n color: var(--jp-content-font-color1);\n font-size: var(--jp-code-font-size);\n border: none;\n margin: 0;\n padding: 0;\n}\n\n.jp-RenderedText pre a:link {\n text-decoration: none;\n color: var(--jp-content-link-color);\n}\n\n.jp-RenderedText pre a:hover {\n text-decoration: underline;\n color: var(--jp-content-link-color);\n}\n\n.jp-RenderedText pre a:visited {\n text-decoration: none;\n color: var(--jp-content-link-color);\n}\n\n\/* console foregrounds and backgrounds *\/\n.jp-RenderedText pre .ansi-black-fg {\n color: #3e424d;\n}\n\n.jp-RenderedText pre .ansi-red-fg {\n color: #e75c58;\n}\n\n.jp-RenderedText pre .ansi-green-fg {\n color: #00a250;\n}\n\n.jp-RenderedText pre .ansi-yellow-fg {\n color: #ddb62b;\n}\n\n.jp-RenderedText pre .ansi-blue-fg {\n color: #208ffb;\n}\n\n.jp-RenderedText pre .ansi-magenta-fg {\n color: #d160c4;\n}\n\n.jp-RenderedText pre .ansi-cyan-fg {\n color: #60c6c8;\n}\n\n.jp-RenderedText pre .ansi-white-fg {\n color: #c5c1b4;\n}\n\n.jp-RenderedText pre .ansi-black-bg {\n background-color: #3e424d;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-red-bg {\n background-color: #e75c58;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-green-bg {\n background-color: #00a250;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-yellow-bg {\n background-color: #ddb62b;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-blue-bg {\n background-color: #208ffb;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-magenta-bg {\n background-color: #d160c4;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-cyan-bg {\n background-color: #60c6c8;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-white-bg {\n background-color: #c5c1b4;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-black-intense-fg {\n color: #282c36;\n}\n\n.jp-RenderedText pre .ansi-red-intense-fg {\n color: #b22b31;\n}\n\n.jp-RenderedText pre .ansi-green-intense-fg {\n color: #007427;\n}\n\n.jp-RenderedText pre .ansi-yellow-intense-fg {\n color: #b27d12;\n}\n\n.jp-RenderedText pre .ansi-blue-intense-fg {\n color: #0065ca;\n}\n\n.jp-RenderedText pre .ansi-magenta-intense-fg {\n color: #a03196;\n}\n\n.jp-RenderedText pre .ansi-cyan-intense-fg {\n color: #258f8f;\n}\n\n.jp-RenderedText pre .ansi-white-intense-fg {\n color: #a1a6b2;\n}\n\n.jp-RenderedText pre .ansi-black-intense-bg {\n background-color: #282c36;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-red-intense-bg {\n background-color: #b22b31;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-green-intense-bg {\n background-color: #007427;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-yellow-intense-bg {\n background-color: #b27d12;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-blue-intense-bg {\n background-color: #0065ca;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-magenta-intense-bg {\n background-color: #a03196;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-cyan-intense-bg {\n background-color: #258f8f;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-white-intense-bg {\n background-color: #a1a6b2;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-default-inverse-fg {\n color: var(--jp-ui-inverse-font-color0);\n}\n\n.jp-RenderedText pre .ansi-default-inverse-bg {\n background-color: var(--jp-inverse-layout-color0);\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-bold {\n font-weight: bold;\n}\n\n.jp-RenderedText pre .ansi-underline {\n text-decoration: underline;\n}\n\n.jp-RenderedText[data-mime-type='application\/vnd.jupyter.stderr'] {\n background: var(--jp-rendermime-error-background);\n padding-top: var(--jp-code-padding);\n}\n\n\/*-----------------------------------------------------------------------------\n| RenderedLatex\n|----------------------------------------------------------------------------*\/\n\n.jp-RenderedLatex {\n color: var(--jp-content-font-color1);\n font-size: var(--jp-content-font-size1);\n line-height: var(--jp-content-line-height);\n}\n\n\/* Left-justify outputs.*\/\n.jp-OutputArea-output.jp-RenderedLatex {\n padding: var(--jp-code-padding);\n text-align: left;\n}\n\n\/*-----------------------------------------------------------------------------\n| RenderedHTML\n|----------------------------------------------------------------------------*\/\n\n.jp-RenderedHTMLCommon {\n color: var(--jp-content-font-color1);\n font-family: var(--jp-content-font-family);\n font-size: var(--jp-content-font-size1);\n line-height: var(--jp-content-line-height);\n\n \/* Give a bit more R padding on Markdown text to keep line lengths reasonable *\/\n padding-right: 20px;\n}\n\n.jp-RenderedHTMLCommon em {\n font-style: italic;\n}\n\n.jp-RenderedHTMLCommon strong {\n font-weight: bold;\n}\n\n.jp-RenderedHTMLCommon u {\n text-decoration: underline;\n}\n\n.jp-RenderedHTMLCommon a:link {\n text-decoration: none;\n color: var(--jp-content-link-color);\n}\n\n.jp-RenderedHTMLCommon a:hover {\n text-decoration: underline;\n color: var(--jp-content-link-color);\n}\n\n.jp-RenderedHTMLCommon a:visited {\n text-decoration: none;\n color: var(--jp-content-link-color);\n}\n\n\/* Headings *\/\n\n.jp-RenderedHTMLCommon h1,\n.jp-RenderedHTMLCommon h2,\n.jp-RenderedHTMLCommon h3,\n.jp-RenderedHTMLCommon h4,\n.jp-RenderedHTMLCommon h5,\n.jp-RenderedHTMLCommon h6 {\n line-height: var(--jp-content-heading-line-height);\n font-weight: var(--jp-content-heading-font-weight);\n font-style: normal;\n margin: var(--jp-content-heading-margin-top) 0\n var(--jp-content-heading-margin-bottom) 0;\n}\n\n.jp-RenderedHTMLCommon h1:first-child,\n.jp-RenderedHTMLCommon h2:first-child,\n.jp-RenderedHTMLCommon h3:first-child,\n.jp-RenderedHTMLCommon h4:first-child,\n.jp-RenderedHTMLCommon h5:first-child,\n.jp-RenderedHTMLCommon h6:first-child {\n margin-top: calc(0.5 * var(--jp-content-heading-margin-top));\n}\n\n.jp-RenderedHTMLCommon h1:last-child,\n.jp-RenderedHTMLCommon h2:last-child,\n.jp-RenderedHTMLCommon h3:last-child,\n.jp-RenderedHTMLCommon h4:last-child,\n.jp-RenderedHTMLCommon h5:last-child,\n.jp-RenderedHTMLCommon h6:last-child {\n margin-bottom: calc(0.5 * var(--jp-content-heading-margin-bottom));\n}\n\n.jp-RenderedHTMLCommon h1 {\n font-size: var(--jp-content-font-size5);\n}\n\n.jp-RenderedHTMLCommon h2 {\n font-size: var(--jp-content-font-size4);\n}\n\n.jp-RenderedHTMLCommon h3 {\n font-size: var(--jp-content-font-size3);\n}\n\n.jp-RenderedHTMLCommon h4 {\n font-size: var(--jp-content-font-size2);\n}\n\n.jp-RenderedHTMLCommon h5 {\n font-size: var(--jp-content-font-size1);\n}\n\n.jp-RenderedHTMLCommon h6 {\n font-size: var(--jp-content-font-size0);\n}\n\n\/* Lists *\/\n\n\/* stylelint-disable selector-max-type, selector-max-compound-selectors *\/\n\n.jp-RenderedHTMLCommon ul:not(.list-inline),\n.jp-RenderedHTMLCommon ol:not(.list-inline) {\n padding-left: 2em;\n}\n\n.jp-RenderedHTMLCommon ul {\n list-style: disc;\n}\n\n.jp-RenderedHTMLCommon ul ul {\n list-style: square;\n}\n\n.jp-RenderedHTMLCommon ul ul ul {\n list-style: circle;\n}\n\n.jp-RenderedHTMLCommon ol {\n list-style: decimal;\n}\n\n.jp-RenderedHTMLCommon ol ol {\n list-style: upper-alpha;\n}\n\n.jp-RenderedHTMLCommon ol ol ol {\n list-style: lower-alpha;\n}\n\n.jp-RenderedHTMLCommon ol ol ol ol {\n list-style: lower-roman;\n}\n\n.jp-RenderedHTMLCommon ol ol ol ol ol {\n list-style: decimal;\n}\n\n.jp-RenderedHTMLCommon ol,\n.jp-RenderedHTMLCommon ul {\n margin-bottom: 1em;\n}\n\n.jp-RenderedHTMLCommon ul ul,\n.jp-RenderedHTMLCommon ul ol,\n.jp-RenderedHTMLCommon ol ul,\n.jp-RenderedHTMLCommon ol ol {\n margin-bottom: 0;\n}\n\n\/* stylelint-enable selector-max-type, selector-max-compound-selectors *\/\n\n.jp-RenderedHTMLCommon hr {\n color: var(--jp-border-color2);\n background-color: var(--jp-border-color1);\n margin-top: 1em;\n margin-bottom: 1em;\n}\n\n.jp-RenderedHTMLCommon > pre {\n margin: 1.5em 2em;\n}\n\n.jp-RenderedHTMLCommon pre,\n.jp-RenderedHTMLCommon code {\n border: 0;\n background-color: var(--jp-layout-color0);\n color: var(--jp-content-font-color1);\n font-family: var(--jp-code-font-family);\n font-size: inherit;\n line-height: var(--jp-code-line-height);\n padding: 0;\n white-space: pre-wrap;\n}\n\n.jp-RenderedHTMLCommon :not(pre) > code {\n background-color: var(--jp-layout-color2);\n padding: 1px 5px;\n}\n\n\/* Tables *\/\n\n.jp-RenderedHTMLCommon table {\n border-collapse: collapse;\n border-spacing: 0;\n border: none;\n color: var(--jp-ui-font-color1);\n font-size: var(--jp-ui-font-size1);\n table-layout: fixed;\n margin-left: auto;\n margin-bottom: 1em;\n margin-right: auto;\n}\n\n.jp-RenderedHTMLCommon thead {\n border-bottom: var(--jp-border-width) solid var(--jp-border-color1);\n vertical-align: bottom;\n}\n\n.jp-RenderedHTMLCommon td,\n.jp-RenderedHTMLCommon th,\n.jp-RenderedHTMLCommon tr {\n vertical-align: middle;\n padding: 0.5em;\n line-height: normal;\n white-space: normal;\n max-width: none;\n border: none;\n}\n\n.jp-RenderedMarkdown.jp-RenderedHTMLCommon td,\n.jp-RenderedMarkdown.jp-RenderedHTMLCommon th {\n max-width: none;\n}\n\n:not(.jp-RenderedMarkdown).jp-RenderedHTMLCommon td,\n:not(.jp-RenderedMarkdown).jp-RenderedHTMLCommon th,\n:not(.jp-RenderedMarkdown).jp-RenderedHTMLCommon tr {\n text-align: right;\n}\n\n.jp-RenderedHTMLCommon th {\n font-weight: bold;\n}\n\n.jp-RenderedHTMLCommon tbody tr:nth-child(odd) {\n background: var(--jp-layout-color0);\n}\n\n.jp-RenderedHTMLCommon tbody tr:nth-child(even) {\n background: var(--jp-rendermime-table-row-background);\n}\n\n.jp-RenderedHTMLCommon tbody tr:hover {\n background: var(--jp-rendermime-table-row-hover-background);\n}\n\n.jp-RenderedHTMLCommon p {\n text-align: left;\n margin: 0;\n margin-bottom: 1em;\n}\n\n.jp-RenderedHTMLCommon img {\n -moz-force-broken-image-icon: 1;\n}\n\n\/* Restrict to direct children as other images could be nested in other content. *\/\n.jp-RenderedHTMLCommon > img {\n display: block;\n margin-left: 0;\n margin-right: 0;\n margin-bottom: 1em;\n}\n\n\/* Change color behind transparent images if they need it... *\/\n[data-jp-theme-light='false'] .jp-RenderedImage img.jp-needs-light-background {\n background-color: var(--jp-inverse-layout-color1);\n}\n\n[data-jp-theme-light='true'] .jp-RenderedImage img.jp-needs-dark-background {\n background-color: var(--jp-inverse-layout-color1);\n}\n\n.jp-RenderedHTMLCommon img,\n.jp-RenderedImage img,\n.jp-RenderedHTMLCommon svg,\n.jp-RenderedSVG svg {\n max-width: 100%;\n height: auto;\n}\n\n.jp-RenderedHTMLCommon img.jp-mod-unconfined,\n.jp-RenderedImage img.jp-mod-unconfined,\n.jp-RenderedHTMLCommon svg.jp-mod-unconfined,\n.jp-RenderedSVG svg.jp-mod-unconfined {\n max-width: none;\n}\n\n.jp-RenderedHTMLCommon .alert {\n padding: var(--jp-notebook-padding);\n border: var(--jp-border-width) solid transparent;\n border-radius: var(--jp-border-radius);\n margin-bottom: 1em;\n}\n\n.jp-RenderedHTMLCommon .alert-info {\n color: var(--jp-info-color0);\n background-color: var(--jp-info-color3);\n border-color: var(--jp-info-color2);\n}\n\n.jp-RenderedHTMLCommon .alert-info hr {\n border-color: var(--jp-info-color3);\n}\n\n.jp-RenderedHTMLCommon .alert-info > p:last-child,\n.jp-RenderedHTMLCommon .alert-info > ul:last-child {\n margin-bottom: 0;\n}\n\n.jp-RenderedHTMLCommon .alert-warning {\n color: var(--jp-warn-color0);\n background-color: var(--jp-warn-color3);\n border-color: var(--jp-warn-color2);\n}\n\n.jp-RenderedHTMLCommon .alert-warning hr {\n border-color: var(--jp-warn-color3);\n}\n\n.jp-RenderedHTMLCommon .alert-warning > p:last-child,\n.jp-RenderedHTMLCommon .alert-warning > ul:last-child {\n margin-bottom: 0;\n}\n\n.jp-RenderedHTMLCommon .alert-success {\n color: var(--jp-success-color0);\n background-color: var(--jp-success-color3);\n border-color: var(--jp-success-color2);\n}\n\n.jp-RenderedHTMLCommon .alert-success hr {\n border-color: var(--jp-success-color3);\n}\n\n.jp-RenderedHTMLCommon .alert-success > p:last-child,\n.jp-RenderedHTMLCommon .alert-success > ul:last-child {\n margin-bottom: 0;\n}\n\n.jp-RenderedHTMLCommon .alert-danger {\n color: var(--jp-error-color0);\n background-color: var(--jp-error-color3);\n border-color: var(--jp-error-color2);\n}\n\n.jp-RenderedHTMLCommon .alert-danger hr {\n border-color: var(--jp-error-color3);\n}\n\n.jp-RenderedHTMLCommon .alert-danger > p:last-child,\n.jp-RenderedHTMLCommon .alert-danger > ul:last-child {\n margin-bottom: 0;\n}\n\n.jp-RenderedHTMLCommon blockquote {\n margin: 1em 2em;\n padding: 0 1em;\n border-left: 5px solid var(--jp-border-color2);\n}\n\na.jp-InternalAnchorLink {\n visibility: hidden;\n margin-left: 8px;\n color: var(--md-blue-800);\n}\n\nh1:hover .jp-InternalAnchorLink,\nh2:hover .jp-InternalAnchorLink,\nh3:hover .jp-InternalAnchorLink,\nh4:hover .jp-InternalAnchorLink,\nh5:hover .jp-InternalAnchorLink,\nh6:hover .jp-InternalAnchorLink {\n visibility: visible;\n}\n\n.jp-RenderedHTMLCommon kbd {\n background-color: var(--jp-rendermime-table-row-background);\n border: 1px solid var(--jp-border-color0);\n border-bottom-color: var(--jp-border-color2);\n border-radius: 3px;\n box-shadow: inset 0 -1px 0 rgba(0, 0, 0, 0.25);\n display: inline-block;\n font-size: var(--jp-ui-font-size0);\n line-height: 1em;\n padding: 0.2em 0.5em;\n}\n\n\/* Most direct children of .jp-RenderedHTMLCommon have a margin-bottom of 1.0.\n * At the bottom of cells this is a bit too much as there is also spacing\n * between cells. Going all the way to 0 gets too tight between markdown and\n * code cells.\n *\/\n.jp-RenderedHTMLCommon > *:last-child {\n margin-bottom: 0.5em;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Copyright (c) 2014-2017, PhosphorJS Contributors\n|\n| Distributed under the terms of the BSD 3-Clause License.\n|\n| The full license is in the file LICENSE, distributed with this software.\n|----------------------------------------------------------------------------*\/\n\n.lm-cursor-backdrop {\n position: fixed;\n width: 200px;\n height: 200px;\n margin-top: -100px;\n margin-left: -100px;\n will-change: transform;\n z-index: 100;\n}\n\n.lm-mod-drag-image {\n will-change: transform;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n.jp-lineFormSearch {\n padding: 4px 12px;\n background-color: var(--jp-layout-color2);\n box-shadow: var(--jp-toolbar-box-shadow);\n z-index: 2;\n font-size: var(--jp-ui-font-size1);\n}\n\n.jp-lineFormCaption {\n font-size: var(--jp-ui-font-size0);\n line-height: var(--jp-ui-font-size1);\n margin-top: 4px;\n color: var(--jp-ui-font-color0);\n}\n\n.jp-baseLineForm {\n border: none;\n border-radius: 0;\n position: absolute;\n background-size: 16px;\n background-repeat: no-repeat;\n background-position: center;\n outline: none;\n}\n\n.jp-lineFormButtonContainer {\n top: 4px;\n right: 8px;\n height: 24px;\n padding: 0 12px;\n width: 12px;\n}\n\n.jp-lineFormButtonIcon {\n top: 0;\n right: 0;\n background-color: var(--jp-brand-color1);\n height: 100%;\n width: 100%;\n box-sizing: border-box;\n padding: 4px 6px;\n}\n\n.jp-lineFormButton {\n top: 0;\n right: 0;\n background-color: transparent;\n height: 100%;\n width: 100%;\n box-sizing: border-box;\n}\n\n.jp-lineFormWrapper {\n overflow: hidden;\n padding: 0 8px;\n border: 1px solid var(--jp-border-color0);\n background-color: var(--jp-input-active-background);\n height: 22px;\n}\n\n.jp-lineFormWrapperFocusWithin {\n border: var(--jp-border-width) solid var(--md-blue-500);\n box-shadow: inset 0 0 4px var(--md-blue-300);\n}\n\n.jp-lineFormInput {\n background: transparent;\n width: 200px;\n height: 100%;\n border: none;\n outline: none;\n color: var(--jp-ui-font-color0);\n line-height: 28px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2016, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-JSONEditor {\n display: flex;\n flex-direction: column;\n width: 100%;\n}\n\n.jp-JSONEditor-host {\n flex: 1 1 auto;\n border: var(--jp-border-width) solid var(--jp-input-border-color);\n border-radius: 0;\n background: var(--jp-layout-color0);\n min-height: 50px;\n padding: 1px;\n}\n\n.jp-JSONEditor.jp-mod-error .jp-JSONEditor-host {\n border-color: red;\n outline-color: red;\n}\n\n.jp-JSONEditor-header {\n display: flex;\n flex: 1 0 auto;\n padding: 0 0 0 12px;\n}\n\n.jp-JSONEditor-header label {\n flex: 0 0 auto;\n}\n\n.jp-JSONEditor-commitButton {\n height: 16px;\n width: 16px;\n background-size: 18px;\n background-repeat: no-repeat;\n background-position: center;\n}\n\n.jp-JSONEditor-host.jp-mod-focused {\n background-color: var(--jp-input-active-background);\n border: 1px solid var(--jp-input-active-border-color);\n box-shadow: var(--jp-input-box-shadow);\n}\n\n.jp-Editor.jp-mod-dropTarget {\n border: var(--jp-border-width) solid var(--jp-input-active-border-color);\n box-shadow: var(--jp-input-box-shadow);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n.jp-DocumentSearch-input {\n border: none;\n outline: none;\n color: var(--jp-ui-font-color0);\n font-size: var(--jp-ui-font-size1);\n background-color: var(--jp-layout-color0);\n font-family: var(--jp-ui-font-family);\n padding: 2px 1px;\n resize: none;\n}\n\n.jp-DocumentSearch-overlay {\n position: absolute;\n background-color: var(--jp-toolbar-background);\n border-bottom: var(--jp-border-width) solid var(--jp-toolbar-border-color);\n border-left: var(--jp-border-width) solid var(--jp-toolbar-border-color);\n top: 0;\n right: 0;\n z-index: 7;\n min-width: 405px;\n padding: 2px;\n font-size: var(--jp-ui-font-size1);\n\n --jp-private-document-search-button-height: 20px;\n}\n\n.jp-DocumentSearch-overlay button {\n background-color: var(--jp-toolbar-background);\n outline: 0;\n}\n\n.jp-DocumentSearch-overlay button:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-DocumentSearch-overlay button:active {\n background-color: var(--jp-layout-color3);\n}\n\n.jp-DocumentSearch-overlay-row {\n display: flex;\n align-items: center;\n margin-bottom: 2px;\n}\n\n.jp-DocumentSearch-button-content {\n display: inline-block;\n cursor: pointer;\n box-sizing: border-box;\n width: 100%;\n height: 100%;\n}\n\n.jp-DocumentSearch-button-content svg {\n width: 100%;\n height: 100%;\n}\n\n.jp-DocumentSearch-input-wrapper {\n border: var(--jp-border-width) solid var(--jp-border-color0);\n display: flex;\n background-color: var(--jp-layout-color0);\n margin: 2px;\n}\n\n.jp-DocumentSearch-input-wrapper:focus-within {\n border-color: var(--jp-cell-editor-active-border-color);\n}\n\n.jp-DocumentSearch-toggle-wrapper,\n.jp-DocumentSearch-button-wrapper {\n all: initial;\n overflow: hidden;\n display: inline-block;\n border: none;\n box-sizing: border-box;\n}\n\n.jp-DocumentSearch-toggle-wrapper {\n width: 14px;\n height: 14px;\n}\n\n.jp-DocumentSearch-button-wrapper {\n width: var(--jp-private-document-search-button-height);\n height: var(--jp-private-document-search-button-height);\n}\n\n.jp-DocumentSearch-toggle-wrapper:focus,\n.jp-DocumentSearch-button-wrapper:focus {\n outline: var(--jp-border-width) solid\n var(--jp-cell-editor-active-border-color);\n outline-offset: -1px;\n}\n\n.jp-DocumentSearch-toggle-wrapper,\n.jp-DocumentSearch-button-wrapper,\n.jp-DocumentSearch-button-content:focus {\n outline: none;\n}\n\n.jp-DocumentSearch-toggle-placeholder {\n width: 5px;\n}\n\n.jp-DocumentSearch-input-button::before {\n display: block;\n padding-top: 100%;\n}\n\n.jp-DocumentSearch-input-button-off {\n opacity: var(--jp-search-toggle-off-opacity);\n}\n\n.jp-DocumentSearch-input-button-off:hover {\n opacity: var(--jp-search-toggle-hover-opacity);\n}\n\n.jp-DocumentSearch-input-button-on {\n opacity: var(--jp-search-toggle-on-opacity);\n}\n\n.jp-DocumentSearch-index-counter {\n padding-left: 10px;\n padding-right: 10px;\n user-select: none;\n min-width: 35px;\n display: inline-block;\n}\n\n.jp-DocumentSearch-up-down-wrapper {\n display: inline-block;\n padding-right: 2px;\n margin-left: auto;\n white-space: nowrap;\n}\n\n.jp-DocumentSearch-spacer {\n margin-left: auto;\n}\n\n.jp-DocumentSearch-up-down-wrapper button {\n outline: 0;\n border: none;\n width: var(--jp-private-document-search-button-height);\n height: var(--jp-private-document-search-button-height);\n vertical-align: middle;\n margin: 1px 5px 2px;\n}\n\n.jp-DocumentSearch-up-down-button:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-DocumentSearch-up-down-button:active {\n background-color: var(--jp-layout-color3);\n}\n\n.jp-DocumentSearch-filter-button {\n border-radius: var(--jp-border-radius);\n}\n\n.jp-DocumentSearch-filter-button:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-DocumentSearch-filter-button-enabled {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-DocumentSearch-filter-button-enabled:hover {\n background-color: var(--jp-layout-color3);\n}\n\n.jp-DocumentSearch-search-options {\n padding: 0 8px;\n margin-left: 3px;\n width: 100%;\n display: grid;\n justify-content: start;\n grid-template-columns: 1fr 1fr;\n align-items: center;\n justify-items: stretch;\n}\n\n.jp-DocumentSearch-search-filter-disabled {\n color: var(--jp-ui-font-color2);\n}\n\n.jp-DocumentSearch-search-filter {\n display: flex;\n align-items: center;\n user-select: none;\n}\n\n.jp-DocumentSearch-regex-error {\n color: var(--jp-error-color0);\n}\n\n.jp-DocumentSearch-replace-button-wrapper {\n overflow: hidden;\n display: inline-block;\n box-sizing: border-box;\n border: var(--jp-border-width) solid var(--jp-border-color0);\n margin: auto 2px;\n padding: 1px 4px;\n height: calc(var(--jp-private-document-search-button-height) + 2px);\n}\n\n.jp-DocumentSearch-replace-button-wrapper:focus {\n border: var(--jp-border-width) solid var(--jp-cell-editor-active-border-color);\n}\n\n.jp-DocumentSearch-replace-button {\n display: inline-block;\n text-align: center;\n cursor: pointer;\n box-sizing: border-box;\n color: var(--jp-ui-font-color1);\n\n \/* height - 2 * (padding of wrapper) *\/\n line-height: calc(var(--jp-private-document-search-button-height) - 2px);\n width: 100%;\n height: 100%;\n}\n\n.jp-DocumentSearch-replace-button:focus {\n outline: none;\n}\n\n.jp-DocumentSearch-replace-wrapper-class {\n margin-left: 14px;\n display: flex;\n}\n\n.jp-DocumentSearch-replace-toggle {\n border: none;\n background-color: var(--jp-toolbar-background);\n border-radius: var(--jp-border-radius);\n}\n\n.jp-DocumentSearch-replace-toggle:hover {\n background-color: var(--jp-layout-color2);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.cm-editor {\n line-height: var(--jp-code-line-height);\n font-size: var(--jp-code-font-size);\n font-family: var(--jp-code-font-family);\n border: 0;\n border-radius: 0;\n height: auto;\n\n \/* Changed to auto to autogrow *\/\n}\n\n.cm-editor pre {\n padding: 0 var(--jp-code-padding);\n}\n\n.jp-CodeMirrorEditor[data-type='inline'] .cm-dialog {\n background-color: var(--jp-layout-color0);\n color: var(--jp-content-font-color1);\n}\n\n.jp-CodeMirrorEditor {\n cursor: text;\n}\n\n\/* When zoomed out 67% and 33% on a screen of 1440 width x 900 height *\/\n@media screen and (min-width: 2138px) and (max-width: 4319px) {\n .jp-CodeMirrorEditor[data-type='inline'] .cm-cursor {\n border-left: var(--jp-code-cursor-width1) solid\n var(--jp-editor-cursor-color);\n }\n}\n\n\/* When zoomed out less than 33% *\/\n@media screen and (min-width: 4320px) {\n .jp-CodeMirrorEditor[data-type='inline'] .cm-cursor {\n border-left: var(--jp-code-cursor-width2) solid\n var(--jp-editor-cursor-color);\n }\n}\n\n.cm-editor.jp-mod-readOnly .cm-cursor {\n display: none;\n}\n\n.jp-CollaboratorCursor {\n border-left: 5px solid transparent;\n border-right: 5px solid transparent;\n border-top: none;\n border-bottom: 3px solid;\n background-clip: content-box;\n margin-left: -5px;\n margin-right: -5px;\n}\n\n.cm-searching,\n.cm-searching span {\n \/* `.cm-searching span`: we need to override syntax highlighting *\/\n background-color: var(--jp-search-unselected-match-background-color);\n color: var(--jp-search-unselected-match-color);\n}\n\n.cm-searching::selection,\n.cm-searching span::selection {\n background-color: var(--jp-search-unselected-match-background-color);\n color: var(--jp-search-unselected-match-color);\n}\n\n.jp-current-match > .cm-searching,\n.jp-current-match > .cm-searching span,\n.cm-searching > .jp-current-match,\n.cm-searching > .jp-current-match span {\n background-color: var(--jp-search-selected-match-background-color);\n color: var(--jp-search-selected-match-color);\n}\n\n.jp-current-match > .cm-searching::selection,\n.cm-searching > .jp-current-match::selection,\n.jp-current-match > .cm-searching span::selection {\n background-color: var(--jp-search-selected-match-background-color);\n color: var(--jp-search-selected-match-color);\n}\n\n.cm-trailingspace {\n background-image: url(data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAFCAYAAAB4ka1VAAAAsElEQVQIHQGlAFr\/AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA7+r3zKmT0\/+pk9P\/7+r3zAAAAAAAAAAABAAAAAAAAAAA6OPzM+\/q9wAAAAAA6OPzMwAAAAAAAAAAAgAAAAAAAAAAGR8NiRQaCgAZIA0AGR8NiQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQyoYJ\/SY80UAAAAASUVORK5CYII=);\n background-position: center left;\n background-repeat: repeat-x;\n}\n\n.jp-CollaboratorCursor-hover {\n position: absolute;\n z-index: 1;\n transform: translateX(-50%);\n color: white;\n border-radius: 3px;\n padding-left: 4px;\n padding-right: 4px;\n padding-top: 1px;\n padding-bottom: 1px;\n text-align: center;\n font-size: var(--jp-ui-font-size1);\n white-space: nowrap;\n}\n\n.jp-CodeMirror-ruler {\n border-left: 1px dashed var(--jp-border-color2);\n}\n\n\/* Styles for shared cursors (remote cursor locations and selected ranges) *\/\n.jp-CodeMirrorEditor .cm-ySelectionCaret {\n position: relative;\n border-left: 1px solid black;\n margin-left: -1px;\n margin-right: -1px;\n box-sizing: border-box;\n}\n\n.jp-CodeMirrorEditor .cm-ySelectionCaret > .cm-ySelectionInfo {\n white-space: nowrap;\n position: absolute;\n top: -1.15em;\n padding-bottom: 0.05em;\n left: -1px;\n font-size: 0.95em;\n font-family: var(--jp-ui-font-family);\n font-weight: bold;\n line-height: normal;\n user-select: none;\n color: white;\n padding-left: 2px;\n padding-right: 2px;\n z-index: 101;\n transition: opacity 0.3s ease-in-out;\n}\n\n.jp-CodeMirrorEditor .cm-ySelectionInfo {\n transition-delay: 0.7s;\n opacity: 0;\n}\n\n.jp-CodeMirrorEditor .cm-ySelectionCaret:hover > .cm-ySelectionInfo {\n opacity: 1;\n transition-delay: 0s;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-MimeDocument {\n outline: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Variables\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-private-filebrowser-button-height: 28px;\n --jp-private-filebrowser-button-width: 48px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-FileBrowser .jp-SidePanel-content {\n display: flex;\n flex-direction: column;\n}\n\n.jp-FileBrowser-toolbar.jp-Toolbar {\n flex-wrap: wrap;\n row-gap: 12px;\n border-bottom: none;\n height: auto;\n margin: 8px 12px 0;\n box-shadow: none;\n padding: 0;\n justify-content: flex-start;\n}\n\n.jp-FileBrowser-Panel {\n flex: 1 1 auto;\n display: flex;\n flex-direction: column;\n}\n\n.jp-BreadCrumbs {\n flex: 0 0 auto;\n margin: 8px 12px;\n}\n\n.jp-BreadCrumbs-item {\n margin: 0 2px;\n padding: 0 2px;\n border-radius: var(--jp-border-radius);\n cursor: pointer;\n}\n\n.jp-BreadCrumbs-item:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-BreadCrumbs-item:first-child {\n margin-left: 0;\n}\n\n.jp-BreadCrumbs-item.jp-mod-dropTarget {\n background-color: var(--jp-brand-color2);\n opacity: 0.7;\n}\n\n\/*-----------------------------------------------------------------------------\n| Buttons\n|----------------------------------------------------------------------------*\/\n\n.jp-FileBrowser-toolbar > .jp-Toolbar-item {\n flex: 0 0 auto;\n padding-left: 0;\n padding-right: 2px;\n align-items: center;\n height: unset;\n}\n\n.jp-FileBrowser-toolbar > .jp-Toolbar-item .jp-ToolbarButtonComponent {\n width: 40px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Other styles\n|----------------------------------------------------------------------------*\/\n\n.jp-FileDialog.jp-mod-conflict input {\n color: var(--jp-error-color1);\n}\n\n.jp-FileDialog .jp-new-name-title {\n margin-top: 12px;\n}\n\n.jp-LastModified-hidden {\n display: none;\n}\n\n.jp-FileSize-hidden {\n display: none;\n}\n\n.jp-FileBrowser .lm-AccordionPanel > h3:first-child {\n display: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| DirListing\n|----------------------------------------------------------------------------*\/\n\n.jp-DirListing {\n flex: 1 1 auto;\n display: flex;\n flex-direction: column;\n outline: 0;\n}\n\n.jp-DirListing-header {\n flex: 0 0 auto;\n display: flex;\n flex-direction: row;\n align-items: center;\n overflow: hidden;\n border-top: var(--jp-border-width) solid var(--jp-border-color2);\n border-bottom: var(--jp-border-width) solid var(--jp-border-color1);\n box-shadow: var(--jp-toolbar-box-shadow);\n z-index: 2;\n}\n\n.jp-DirListing-headerItem {\n padding: 4px 12px 2px;\n font-weight: 500;\n}\n\n.jp-DirListing-headerItem:hover {\n background: var(--jp-layout-color2);\n}\n\n.jp-DirListing-headerItem.jp-id-name {\n flex: 1 0 84px;\n}\n\n.jp-DirListing-headerItem.jp-id-modified {\n flex: 0 0 112px;\n border-left: var(--jp-border-width) solid var(--jp-border-color2);\n text-align: right;\n}\n\n.jp-DirListing-headerItem.jp-id-filesize {\n flex: 0 0 75px;\n border-left: var(--jp-border-width) solid var(--jp-border-color2);\n text-align: right;\n}\n\n.jp-id-narrow {\n display: none;\n flex: 0 0 5px;\n padding: 4px;\n border-left: var(--jp-border-width) solid var(--jp-border-color2);\n text-align: right;\n color: var(--jp-border-color2);\n}\n\n.jp-DirListing-narrow .jp-id-narrow {\n display: block;\n}\n\n.jp-DirListing-narrow .jp-id-modified,\n.jp-DirListing-narrow .jp-DirListing-itemModified {\n display: none;\n}\n\n.jp-DirListing-headerItem.jp-mod-selected {\n font-weight: 600;\n}\n\n\/* increase specificity to override bundled default *\/\n.jp-DirListing-content {\n flex: 1 1 auto;\n margin: 0;\n padding: 0;\n list-style-type: none;\n overflow: auto;\n background-color: var(--jp-layout-color1);\n}\n\n.jp-DirListing-content mark {\n color: var(--jp-ui-font-color0);\n background-color: transparent;\n font-weight: bold;\n}\n\n.jp-DirListing-content .jp-DirListing-item.jp-mod-selected mark {\n color: var(--jp-ui-inverse-font-color0);\n}\n\n\/* Style the directory listing content when a user drops a file to upload *\/\n.jp-DirListing.jp-mod-native-drop .jp-DirListing-content {\n outline: 5px dashed rgba(128, 128, 128, 0.5);\n outline-offset: -10px;\n cursor: copy;\n}\n\n.jp-DirListing-item {\n display: flex;\n flex-direction: row;\n align-items: center;\n padding: 4px 12px;\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n.jp-DirListing-checkboxWrapper {\n \/* Increases hit area of checkbox. *\/\n padding: 4px;\n}\n\n.jp-DirListing-header\n .jp-DirListing-checkboxWrapper\n + .jp-DirListing-headerItem {\n padding-left: 4px;\n}\n\n.jp-DirListing-content .jp-DirListing-checkboxWrapper {\n position: relative;\n left: -4px;\n margin: -4px 0 -4px -8px;\n}\n\n.jp-DirListing-checkboxWrapper.jp-mod-visible {\n visibility: visible;\n}\n\n\/* For devices that support hovering, hide checkboxes until hovered, selected...\n*\/\n@media (hover: hover) {\n .jp-DirListing-checkboxWrapper {\n visibility: hidden;\n }\n\n .jp-DirListing-item:hover .jp-DirListing-checkboxWrapper,\n .jp-DirListing-item.jp-mod-selected .jp-DirListing-checkboxWrapper {\n visibility: visible;\n }\n}\n\n.jp-DirListing-item[data-is-dot] {\n opacity: 75%;\n}\n\n.jp-DirListing-item.jp-mod-selected {\n color: var(--jp-ui-inverse-font-color1);\n background: var(--jp-brand-color1);\n}\n\n.jp-DirListing-item.jp-mod-dropTarget {\n background: var(--jp-brand-color3);\n}\n\n.jp-DirListing-item:hover:not(.jp-mod-selected) {\n background: var(--jp-layout-color2);\n}\n\n.jp-DirListing-itemIcon {\n flex: 0 0 20px;\n margin-right: 4px;\n}\n\n.jp-DirListing-itemText {\n flex: 1 0 64px;\n white-space: nowrap;\n overflow: hidden;\n text-overflow: ellipsis;\n user-select: none;\n}\n\n.jp-DirListing-itemText:focus {\n outline-width: 2px;\n outline-color: var(--jp-inverse-layout-color1);\n outline-style: solid;\n outline-offset: 1px;\n}\n\n.jp-DirListing-item.jp-mod-selected .jp-DirListing-itemText:focus {\n outline-color: var(--jp-layout-color1);\n}\n\n.jp-DirListing-itemModified {\n flex: 0 0 125px;\n text-align: right;\n}\n\n.jp-DirListing-itemFileSize {\n flex: 0 0 90px;\n text-align: right;\n}\n\n.jp-DirListing-editor {\n flex: 1 0 64px;\n outline: none;\n border: none;\n color: var(--jp-ui-font-color1);\n background-color: var(--jp-layout-color1);\n}\n\n.jp-DirListing-item.jp-mod-running .jp-DirListing-itemIcon::before {\n color: var(--jp-success-color1);\n content: '\\25CF';\n font-size: 8px;\n position: absolute;\n left: -8px;\n}\n\n.jp-DirListing-item.jp-mod-running.jp-mod-selected\n .jp-DirListing-itemIcon::before {\n color: var(--jp-ui-inverse-font-color1);\n}\n\n.jp-DirListing-item.lm-mod-drag-image,\n.jp-DirListing-item.jp-mod-selected.lm-mod-drag-image {\n font-size: var(--jp-ui-font-size1);\n padding-left: 4px;\n margin-left: 4px;\n width: 160px;\n background-color: var(--jp-ui-inverse-font-color2);\n box-shadow: var(--jp-elevation-z2);\n border-radius: 0;\n color: var(--jp-ui-font-color1);\n transform: translateX(-40%) translateY(-58%);\n}\n\n.jp-Document {\n min-width: 120px;\n min-height: 120px;\n outline: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Main OutputArea\n| OutputArea has a list of Outputs\n|----------------------------------------------------------------------------*\/\n\n.jp-OutputArea {\n overflow-y: auto;\n}\n\n.jp-OutputArea-child {\n display: table;\n table-layout: fixed;\n width: 100%;\n overflow: hidden;\n}\n\n.jp-OutputPrompt {\n width: var(--jp-cell-prompt-width);\n color: var(--jp-cell-outprompt-font-color);\n font-family: var(--jp-cell-prompt-font-family);\n padding: var(--jp-code-padding);\n letter-spacing: var(--jp-cell-prompt-letter-spacing);\n line-height: var(--jp-code-line-height);\n font-size: var(--jp-code-font-size);\n border: var(--jp-border-width) solid transparent;\n opacity: var(--jp-cell-prompt-opacity);\n\n \/* Right align prompt text, don't wrap to handle large prompt numbers *\/\n text-align: right;\n white-space: nowrap;\n overflow: hidden;\n text-overflow: ellipsis;\n\n \/* Disable text selection *\/\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n.jp-OutputArea-prompt {\n display: table-cell;\n vertical-align: top;\n}\n\n.jp-OutputArea-output {\n display: table-cell;\n width: 100%;\n height: auto;\n overflow: auto;\n user-select: text;\n -moz-user-select: text;\n -webkit-user-select: text;\n -ms-user-select: text;\n}\n\n.jp-OutputArea .jp-RenderedText {\n padding-left: 1ch;\n}\n\n\/**\n * Prompt overlay.\n *\/\n\n.jp-OutputArea-promptOverlay {\n position: absolute;\n top: 0;\n width: var(--jp-cell-prompt-width);\n height: 100%;\n opacity: 0.5;\n}\n\n.jp-OutputArea-promptOverlay:hover {\n background: var(--jp-layout-color2);\n box-shadow: inset 0 0 1px var(--jp-inverse-layout-color0);\n cursor: zoom-out;\n}\n\n.jp-mod-outputsScrolled .jp-OutputArea-promptOverlay:hover {\n cursor: zoom-in;\n}\n\n\/**\n * Isolated output.\n *\/\n.jp-OutputArea-output.jp-mod-isolated {\n width: 100%;\n display: block;\n}\n\n\/*\nWhen drag events occur, `lm-mod-override-cursor` is added to the body.\nBecause iframes steal all cursor events, the following two rules are necessary\nto suppress pointer events while resize drags are occurring. There may be a\nbetter solution to this problem.\n*\/\nbody.lm-mod-override-cursor .jp-OutputArea-output.jp-mod-isolated {\n position: relative;\n}\n\nbody.lm-mod-override-cursor .jp-OutputArea-output.jp-mod-isolated::before {\n content: '';\n position: absolute;\n top: 0;\n left: 0;\n right: 0;\n bottom: 0;\n background: transparent;\n}\n\n\/* pre *\/\n\n.jp-OutputArea-output pre {\n border: none;\n margin: 0;\n padding: 0;\n overflow-x: auto;\n overflow-y: auto;\n word-break: break-all;\n word-wrap: break-word;\n white-space: pre-wrap;\n}\n\n\/* tables *\/\n\n.jp-OutputArea-output.jp-RenderedHTMLCommon table {\n margin-left: 0;\n margin-right: 0;\n}\n\n\/* description lists *\/\n\n.jp-OutputArea-output dl,\n.jp-OutputArea-output dt,\n.jp-OutputArea-output dd {\n display: block;\n}\n\n.jp-OutputArea-output dl {\n width: 100%;\n overflow: hidden;\n padding: 0;\n margin: 0;\n}\n\n.jp-OutputArea-output dt {\n font-weight: bold;\n float: left;\n width: 20%;\n padding: 0;\n margin: 0;\n}\n\n.jp-OutputArea-output dd {\n float: left;\n width: 80%;\n padding: 0;\n margin: 0;\n}\n\n.jp-TrimmedOutputs pre {\n background: var(--jp-layout-color3);\n font-size: calc(var(--jp-code-font-size) * 1.4);\n text-align: center;\n text-transform: uppercase;\n}\n\n\/* Hide the gutter in case of\n * - nested output areas (e.g. in the case of output widgets)\n * - mirrored output areas\n *\/\n.jp-OutputArea .jp-OutputArea .jp-OutputArea-prompt {\n display: none;\n}\n\n\/* Hide empty lines in the output area, for instance due to cleared widgets *\/\n.jp-OutputArea-prompt:empty {\n padding: 0;\n border: 0;\n}\n\n\/*-----------------------------------------------------------------------------\n| executeResult is added to any Output-result for the display of the object\n| returned by a cell\n|----------------------------------------------------------------------------*\/\n\n.jp-OutputArea-output.jp-OutputArea-executeResult {\n margin-left: 0;\n width: 100%;\n}\n\n\/* Text output with the Out[] prompt needs a top padding to match the\n * alignment of the Out[] prompt itself.\n *\/\n.jp-OutputArea-executeResult .jp-RenderedText.jp-OutputArea-output {\n padding-top: var(--jp-code-padding);\n border-top: var(--jp-border-width) solid transparent;\n}\n\n\/*-----------------------------------------------------------------------------\n| The Stdin output\n|----------------------------------------------------------------------------*\/\n\n.jp-Stdin-prompt {\n color: var(--jp-content-font-color0);\n padding-right: var(--jp-code-padding);\n vertical-align: baseline;\n flex: 0 0 auto;\n}\n\n.jp-Stdin-input {\n font-family: var(--jp-code-font-family);\n font-size: inherit;\n color: inherit;\n background-color: inherit;\n width: 42%;\n min-width: 200px;\n\n \/* make sure input baseline aligns with prompt *\/\n vertical-align: baseline;\n\n \/* padding + margin = 0.5em between prompt and cursor *\/\n padding: 0 0.25em;\n margin: 0 0.25em;\n flex: 0 0 70%;\n}\n\n.jp-Stdin-input::placeholder {\n opacity: 0;\n}\n\n.jp-Stdin-input:focus {\n box-shadow: none;\n}\n\n.jp-Stdin-input:focus::placeholder {\n opacity: 1;\n}\n\n\/*-----------------------------------------------------------------------------\n| Output Area View\n|----------------------------------------------------------------------------*\/\n\n.jp-LinkedOutputView .jp-OutputArea {\n height: 100%;\n display: block;\n}\n\n.jp-LinkedOutputView .jp-OutputArea-output:only-child {\n height: 100%;\n}\n\n\/*-----------------------------------------------------------------------------\n| Printing\n|----------------------------------------------------------------------------*\/\n\n@media print {\n .jp-OutputArea-child {\n break-inside: avoid-page;\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Mobile\n|----------------------------------------------------------------------------*\/\n@media only screen and (max-width: 760px) {\n .jp-OutputPrompt {\n display: table-row;\n text-align: left;\n }\n\n .jp-OutputArea-child .jp-OutputArea-output {\n display: table-row;\n margin-left: var(--jp-notebook-padding);\n }\n}\n\n\/* Trimmed outputs warning *\/\n.jp-TrimmedOutputs > a {\n margin: 10px;\n text-decoration: none;\n cursor: pointer;\n}\n\n.jp-TrimmedOutputs > a:hover {\n text-decoration: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Table of Contents\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-private-toc-active-width: 4px;\n}\n\n.jp-TableOfContents {\n display: flex;\n flex-direction: column;\n background: var(--jp-layout-color1);\n color: var(--jp-ui-font-color1);\n font-size: var(--jp-ui-font-size1);\n height: 100%;\n}\n\n.jp-TableOfContents-placeholder {\n text-align: center;\n}\n\n.jp-TableOfContents-placeholderContent {\n color: var(--jp-content-font-color2);\n padding: 8px;\n}\n\n.jp-TableOfContents-placeholderContent > h3 {\n margin-bottom: var(--jp-content-heading-margin-bottom);\n}\n\n.jp-TableOfContents .jp-SidePanel-content {\n overflow-y: auto;\n}\n\n.jp-TableOfContents-tree {\n margin: 4px;\n}\n\n.jp-TableOfContents ol {\n list-style-type: none;\n}\n\n\/* stylelint-disable-next-line selector-max-type *\/\n.jp-TableOfContents li > ol {\n \/* Align left border with triangle icon center *\/\n padding-left: 11px;\n}\n\n.jp-TableOfContents-content {\n \/* left margin for the active heading indicator *\/\n margin: 0 0 0 var(--jp-private-toc-active-width);\n padding: 0;\n background-color: var(--jp-layout-color1);\n}\n\n.jp-tocItem {\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n.jp-tocItem-heading {\n display: flex;\n cursor: pointer;\n}\n\n.jp-tocItem-heading:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-tocItem-content {\n display: block;\n padding: 4px 0;\n white-space: nowrap;\n text-overflow: ellipsis;\n overflow-x: hidden;\n}\n\n.jp-tocItem-collapser {\n height: 20px;\n margin: 2px 2px 0;\n padding: 0;\n background: none;\n border: none;\n cursor: pointer;\n}\n\n.jp-tocItem-collapser:hover {\n background-color: var(--jp-layout-color3);\n}\n\n\/* Active heading indicator *\/\n\n.jp-tocItem-heading::before {\n content: ' ';\n background: transparent;\n width: var(--jp-private-toc-active-width);\n height: 24px;\n position: absolute;\n left: 0;\n border-radius: var(--jp-border-radius);\n}\n\n.jp-tocItem-heading.jp-tocItem-active::before {\n background-color: var(--jp-brand-color1);\n}\n\n.jp-tocItem-heading:hover.jp-tocItem-active::before {\n background: var(--jp-brand-color0);\n opacity: 1;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-Collapser {\n flex: 0 0 var(--jp-cell-collapser-width);\n padding: 0;\n margin: 0;\n border: none;\n outline: none;\n background: transparent;\n border-radius: var(--jp-border-radius);\n opacity: 1;\n}\n\n.jp-Collapser-child {\n display: block;\n width: 100%;\n box-sizing: border-box;\n\n \/* height: 100% doesn't work because the height of its parent is computed from content *\/\n position: absolute;\n top: 0;\n bottom: 0;\n}\n\n\/*-----------------------------------------------------------------------------\n| Printing\n|----------------------------------------------------------------------------*\/\n\n\/*\nHiding collapsers in print mode.\n\nNote: input and output wrappers have \"display: block\" propery in print mode.\n*\/\n\n@media print {\n .jp-Collapser {\n display: none;\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Header\/Footer\n|----------------------------------------------------------------------------*\/\n\n\/* Hidden by zero height by default *\/\n.jp-CellHeader,\n.jp-CellFooter {\n height: 0;\n width: 100%;\n padding: 0;\n margin: 0;\n border: none;\n outline: none;\n background: transparent;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Input\n|----------------------------------------------------------------------------*\/\n\n\/* All input areas *\/\n.jp-InputArea {\n display: table;\n table-layout: fixed;\n width: 100%;\n overflow: hidden;\n}\n\n.jp-InputArea-editor {\n display: table-cell;\n overflow: hidden;\n vertical-align: top;\n\n \/* This is the non-active, default styling *\/\n border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);\n border-radius: 0;\n background: var(--jp-cell-editor-background);\n}\n\n.jp-InputPrompt {\n display: table-cell;\n vertical-align: top;\n width: var(--jp-cell-prompt-width);\n color: var(--jp-cell-inprompt-font-color);\n font-family: var(--jp-cell-prompt-font-family);\n padding: var(--jp-code-padding);\n letter-spacing: var(--jp-cell-prompt-letter-spacing);\n opacity: var(--jp-cell-prompt-opacity);\n line-height: var(--jp-code-line-height);\n font-size: var(--jp-code-font-size);\n border: var(--jp-border-width) solid transparent;\n\n \/* Right align prompt text, don't wrap to handle large prompt numbers *\/\n text-align: right;\n white-space: nowrap;\n overflow: hidden;\n text-overflow: ellipsis;\n\n \/* Disable text selection *\/\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Mobile\n|----------------------------------------------------------------------------*\/\n@media only screen and (max-width: 760px) {\n .jp-InputArea-editor {\n display: table-row;\n margin-left: var(--jp-notebook-padding);\n }\n\n .jp-InputPrompt {\n display: table-row;\n text-align: left;\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Placeholder\n|----------------------------------------------------------------------------*\/\n\n.jp-Placeholder {\n display: table;\n table-layout: fixed;\n width: 100%;\n}\n\n.jp-Placeholder-prompt {\n display: table-cell;\n box-sizing: border-box;\n}\n\n.jp-Placeholder-content {\n display: table-cell;\n padding: 4px 6px;\n border: 1px solid transparent;\n border-radius: 0;\n background: none;\n box-sizing: border-box;\n cursor: pointer;\n}\n\n.jp-Placeholder-contentContainer {\n display: flex;\n}\n\n.jp-Placeholder-content:hover,\n.jp-InputPlaceholder > .jp-Placeholder-content:hover {\n border-color: var(--jp-layout-color3);\n}\n\n.jp-Placeholder-content .jp-MoreHorizIcon {\n width: 32px;\n height: 16px;\n border: 1px solid transparent;\n border-radius: var(--jp-border-radius);\n}\n\n.jp-Placeholder-content .jp-MoreHorizIcon:hover {\n border: 1px solid var(--jp-border-color1);\n box-shadow: 0 0 2px 0 rgba(0, 0, 0, 0.25);\n background-color: var(--jp-layout-color0);\n}\n\n.jp-PlaceholderText {\n white-space: nowrap;\n overflow-x: hidden;\n color: var(--jp-inverse-layout-color3);\n font-family: var(--jp-code-font-family);\n}\n\n.jp-InputPlaceholder > .jp-Placeholder-content {\n border-color: var(--jp-cell-editor-border-color);\n background: var(--jp-cell-editor-background);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Private CSS variables\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-private-cell-scrolling-output-offset: 5px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Cell\n|----------------------------------------------------------------------------*\/\n\n.jp-Cell {\n padding: var(--jp-cell-padding);\n margin: 0;\n border: none;\n outline: none;\n background: transparent;\n}\n\n\/*-----------------------------------------------------------------------------\n| Common input\/output\n|----------------------------------------------------------------------------*\/\n\n.jp-Cell-inputWrapper,\n.jp-Cell-outputWrapper {\n display: flex;\n flex-direction: row;\n padding: 0;\n margin: 0;\n\n \/* Added to reveal the box-shadow on the input and output collapsers. *\/\n overflow: visible;\n}\n\n\/* Only input\/output areas inside cells *\/\n.jp-Cell-inputArea,\n.jp-Cell-outputArea {\n flex: 1 1 auto;\n}\n\n\/*-----------------------------------------------------------------------------\n| Collapser\n|----------------------------------------------------------------------------*\/\n\n\/* Make the output collapser disappear when there is not output, but do so\n * in a manner that leaves it in the layout and preserves its width.\n *\/\n.jp-Cell.jp-mod-noOutputs .jp-Cell-outputCollapser {\n border: none !important;\n background: transparent !important;\n}\n\n.jp-Cell:not(.jp-mod-noOutputs) .jp-Cell-outputCollapser {\n min-height: var(--jp-cell-collapser-min-height);\n}\n\n\/*-----------------------------------------------------------------------------\n| Output\n|----------------------------------------------------------------------------*\/\n\n\/* Put a space between input and output when there IS output *\/\n.jp-Cell:not(.jp-mod-noOutputs) .jp-Cell-outputWrapper {\n margin-top: 5px;\n}\n\n.jp-CodeCell.jp-mod-outputsScrolled .jp-Cell-outputArea {\n overflow-y: auto;\n max-height: 24em;\n margin-left: var(--jp-private-cell-scrolling-output-offset);\n resize: vertical;\n}\n\n.jp-CodeCell.jp-mod-outputsScrolled .jp-Cell-outputArea[style*='height'] {\n max-height: unset;\n}\n\n.jp-CodeCell.jp-mod-outputsScrolled .jp-Cell-outputArea::after {\n content: ' ';\n box-shadow: inset 0 0 6px 2px rgb(0 0 0 \/ 30%);\n width: 100%;\n height: 100%;\n position: sticky;\n bottom: 0;\n top: 0;\n margin-top: -50%;\n float: left;\n display: block;\n pointer-events: none;\n}\n\n.jp-CodeCell.jp-mod-outputsScrolled .jp-OutputArea-child {\n padding-top: 6px;\n}\n\n.jp-CodeCell.jp-mod-outputsScrolled .jp-OutputArea-prompt {\n width: calc(\n var(--jp-cell-prompt-width) - var(--jp-private-cell-scrolling-output-offset)\n );\n}\n\n.jp-CodeCell.jp-mod-outputsScrolled .jp-OutputArea-promptOverlay {\n left: calc(-1 * var(--jp-private-cell-scrolling-output-offset));\n}\n\n\/*-----------------------------------------------------------------------------\n| CodeCell\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| MarkdownCell\n|----------------------------------------------------------------------------*\/\n\n.jp-MarkdownOutput {\n display: table-cell;\n width: 100%;\n margin-top: 0;\n margin-bottom: 0;\n padding-left: var(--jp-code-padding);\n}\n\n.jp-MarkdownOutput.jp-RenderedHTMLCommon {\n overflow: auto;\n}\n\n\/* collapseHeadingButton (show always if hiddenCellsButton is _not_ shown) *\/\n.jp-collapseHeadingButton {\n display: flex;\n min-height: var(--jp-cell-collapser-min-height);\n font-size: var(--jp-code-font-size);\n position: absolute;\n background-color: transparent;\n background-size: 25px;\n background-repeat: no-repeat;\n background-position-x: center;\n background-position-y: top;\n background-image: var(--jp-icon-caret-down);\n right: 0;\n top: 0;\n bottom: 0;\n}\n\n.jp-collapseHeadingButton.jp-mod-collapsed {\n background-image: var(--jp-icon-caret-right);\n}\n\n\/*\n set the container font size to match that of content\n so that the nested collapse buttons have the right size\n*\/\n.jp-MarkdownCell .jp-InputPrompt {\n font-size: var(--jp-content-font-size1);\n}\n\n\/*\n Align collapseHeadingButton with cell top header\n The font sizes are identical to the ones in packages\/rendermime\/style\/base.css\n*\/\n.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='1'] {\n font-size: var(--jp-content-font-size5);\n background-position-y: calc(0.3 * var(--jp-content-font-size5));\n}\n\n.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='2'] {\n font-size: var(--jp-content-font-size4);\n background-position-y: calc(0.3 * var(--jp-content-font-size4));\n}\n\n.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='3'] {\n font-size: var(--jp-content-font-size3);\n background-position-y: calc(0.3 * var(--jp-content-font-size3));\n}\n\n.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='4'] {\n font-size: var(--jp-content-font-size2);\n background-position-y: calc(0.3 * var(--jp-content-font-size2));\n}\n\n.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='5'] {\n font-size: var(--jp-content-font-size1);\n background-position-y: top;\n}\n\n.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='6'] {\n font-size: var(--jp-content-font-size0);\n background-position-y: top;\n}\n\n\/* collapseHeadingButton (show only on (hover,active) if hiddenCellsButton is shown) *\/\n.jp-Notebook.jp-mod-showHiddenCellsButton .jp-collapseHeadingButton {\n display: none;\n}\n\n.jp-Notebook.jp-mod-showHiddenCellsButton\n :is(.jp-MarkdownCell:hover, .jp-mod-active)\n .jp-collapseHeadingButton {\n display: flex;\n}\n\n\/* showHiddenCellsButton (only show if jp-mod-showHiddenCellsButton is set, which\nis a consequence of the showHiddenCellsButton option in Notebook Settings)*\/\n.jp-Notebook.jp-mod-showHiddenCellsButton .jp-showHiddenCellsButton {\n margin-left: calc(var(--jp-cell-prompt-width) + 2 * var(--jp-code-padding));\n margin-top: var(--jp-code-padding);\n border: 1px solid var(--jp-border-color2);\n background-color: var(--jp-border-color3) !important;\n color: var(--jp-content-font-color0) !important;\n display: flex;\n}\n\n.jp-Notebook.jp-mod-showHiddenCellsButton .jp-showHiddenCellsButton:hover {\n background-color: var(--jp-border-color2) !important;\n}\n\n.jp-showHiddenCellsButton {\n display: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Printing\n|----------------------------------------------------------------------------*\/\n\n\/*\nUsing block instead of flex to allow the use of the break-inside CSS property for\ncell outputs.\n*\/\n\n@media print {\n .jp-Cell-inputWrapper,\n .jp-Cell-outputWrapper {\n display: block;\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Variables\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-notebook-toolbar-padding: 2px 5px 2px 2px;\n}\n\n\/*-----------------------------------------------------------------------------\n\n\/*-----------------------------------------------------------------------------\n| Styles\n|----------------------------------------------------------------------------*\/\n\n.jp-NotebookPanel-toolbar {\n padding: var(--jp-notebook-toolbar-padding);\n\n \/* disable paint containment from lumino 2.0 default strict CSS containment *\/\n contain: style size !important;\n}\n\n.jp-Toolbar-item.jp-Notebook-toolbarCellType .jp-select-wrapper.jp-mod-focused {\n border: none;\n box-shadow: none;\n}\n\n.jp-Notebook-toolbarCellTypeDropdown select {\n height: 24px;\n font-size: var(--jp-ui-font-size1);\n line-height: 14px;\n border-radius: 0;\n display: block;\n}\n\n.jp-Notebook-toolbarCellTypeDropdown span {\n top: 5px !important;\n}\n\n.jp-Toolbar-responsive-popup {\n position: absolute;\n height: fit-content;\n display: flex;\n flex-direction: row;\n flex-wrap: wrap;\n justify-content: flex-end;\n border-bottom: var(--jp-border-width) solid var(--jp-toolbar-border-color);\n box-shadow: var(--jp-toolbar-box-shadow);\n background: var(--jp-toolbar-background);\n min-height: var(--jp-toolbar-micro-height);\n padding: var(--jp-notebook-toolbar-padding);\n z-index: 1;\n right: 0;\n top: 0;\n}\n\n.jp-Toolbar > .jp-Toolbar-responsive-opener {\n margin-left: auto;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Variables\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n\n\/*-----------------------------------------------------------------------------\n| Styles\n|----------------------------------------------------------------------------*\/\n\n.jp-Notebook-ExecutionIndicator {\n position: relative;\n display: inline-block;\n height: 100%;\n z-index: 9997;\n}\n\n.jp-Notebook-ExecutionIndicator-tooltip {\n visibility: hidden;\n height: auto;\n width: max-content;\n width: -moz-max-content;\n background-color: var(--jp-layout-color2);\n color: var(--jp-ui-font-color1);\n text-align: justify;\n border-radius: 6px;\n padding: 0 5px;\n position: fixed;\n display: table;\n}\n\n.jp-Notebook-ExecutionIndicator-tooltip.up {\n transform: translateX(-50%) translateY(-100%) translateY(-32px);\n}\n\n.jp-Notebook-ExecutionIndicator-tooltip.down {\n transform: translateX(calc(-100% + 16px)) translateY(5px);\n}\n\n.jp-Notebook-ExecutionIndicator-tooltip.hidden {\n display: none;\n}\n\n.jp-Notebook-ExecutionIndicator:hover .jp-Notebook-ExecutionIndicator-tooltip {\n visibility: visible;\n}\n\n.jp-Notebook-ExecutionIndicator span {\n font-size: var(--jp-ui-font-size1);\n font-family: var(--jp-ui-font-family);\n color: var(--jp-ui-font-color1);\n line-height: 24px;\n display: block;\n}\n\n.jp-Notebook-ExecutionIndicator-progress-bar {\n display: flex;\n justify-content: center;\n height: 100%;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*\n * Execution indicator\n *\/\n.jp-tocItem-content::after {\n content: '';\n\n \/* Must be identical to form a circle *\/\n width: 12px;\n height: 12px;\n background: none;\n border: none;\n position: absolute;\n right: 0;\n}\n\n.jp-tocItem-content[data-running='0']::after {\n border-radius: 50%;\n border: var(--jp-border-width) solid var(--jp-inverse-layout-color3);\n background: none;\n}\n\n.jp-tocItem-content[data-running='1']::after {\n border-radius: 50%;\n border: var(--jp-border-width) solid var(--jp-inverse-layout-color3);\n background-color: var(--jp-inverse-layout-color3);\n}\n\n.jp-tocItem-content[data-running='0'],\n.jp-tocItem-content[data-running='1'] {\n margin-right: 12px;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n.jp-Notebook-footer {\n height: 27px;\n margin-left: calc(\n var(--jp-cell-prompt-width) + var(--jp-cell-collapser-width) +\n var(--jp-cell-padding)\n );\n width: calc(\n 100% -\n (\n var(--jp-cell-prompt-width) + var(--jp-cell-collapser-width) +\n var(--jp-cell-padding) + var(--jp-cell-padding)\n )\n );\n border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);\n color: var(--jp-ui-font-color3);\n margin-top: 6px;\n background: none;\n cursor: pointer;\n}\n\n.jp-Notebook-footer:focus {\n border-color: var(--jp-cell-editor-active-border-color);\n}\n\n\/* For devices that support hovering, hide footer until hover *\/\n@media (hover: hover) {\n .jp-Notebook-footer {\n opacity: 0;\n }\n\n .jp-Notebook-footer:focus,\n .jp-Notebook-footer:hover {\n opacity: 1;\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Imports\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| CSS variables\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-side-by-side-output-size: 1fr;\n --jp-side-by-side-resized-cell: var(--jp-side-by-side-output-size);\n --jp-private-notebook-dragImage-width: 304px;\n --jp-private-notebook-dragImage-height: 36px;\n --jp-private-notebook-selected-color: var(--md-blue-400);\n --jp-private-notebook-active-color: var(--md-green-400);\n}\n\n\/*-----------------------------------------------------------------------------\n| Notebook\n|----------------------------------------------------------------------------*\/\n\n\/* stylelint-disable selector-max-class *\/\n\n.jp-NotebookPanel {\n display: block;\n height: 100%;\n}\n\n.jp-NotebookPanel.jp-Document {\n min-width: 240px;\n min-height: 120px;\n}\n\n.jp-Notebook {\n padding: var(--jp-notebook-padding);\n outline: none;\n overflow: auto;\n background: var(--jp-layout-color0);\n}\n\n.jp-Notebook.jp-mod-scrollPastEnd::after {\n display: block;\n content: '';\n min-height: var(--jp-notebook-scroll-padding);\n}\n\n.jp-MainAreaWidget-ContainStrict .jp-Notebook * {\n contain: strict;\n}\n\n.jp-Notebook .jp-Cell {\n overflow: visible;\n}\n\n.jp-Notebook .jp-Cell .jp-InputPrompt {\n cursor: move;\n}\n\n\/*-----------------------------------------------------------------------------\n| Notebook state related styling\n|\n| The notebook and cells each have states, here are the possibilities:\n|\n| - Notebook\n| - Command\n| - Edit\n| - Cell\n| - None\n| - Active (only one can be active)\n| - Selected (the cells actions are applied to)\n| - Multiselected (when multiple selected, the cursor)\n| - No outputs\n|----------------------------------------------------------------------------*\/\n\n\/* Command or edit modes *\/\n\n.jp-Notebook .jp-Cell:not(.jp-mod-active) .jp-InputPrompt {\n opacity: var(--jp-cell-prompt-not-active-opacity);\n color: var(--jp-cell-prompt-not-active-font-color);\n}\n\n.jp-Notebook .jp-Cell:not(.jp-mod-active) .jp-OutputPrompt {\n opacity: var(--jp-cell-prompt-not-active-opacity);\n color: var(--jp-cell-prompt-not-active-font-color);\n}\n\n\/* cell is active *\/\n.jp-Notebook .jp-Cell.jp-mod-active .jp-Collapser {\n background: var(--jp-brand-color1);\n}\n\n\/* cell is dirty *\/\n.jp-Notebook .jp-Cell.jp-mod-dirty .jp-InputPrompt {\n color: var(--jp-warn-color1);\n}\n\n.jp-Notebook .jp-Cell.jp-mod-dirty .jp-InputPrompt::before {\n color: var(--jp-warn-color1);\n content: '\u2022';\n}\n\n.jp-Notebook .jp-Cell.jp-mod-active.jp-mod-dirty .jp-Collapser {\n background: var(--jp-warn-color1);\n}\n\n\/* collapser is hovered *\/\n.jp-Notebook .jp-Cell .jp-Collapser:hover {\n box-shadow: var(--jp-elevation-z2);\n background: var(--jp-brand-color1);\n opacity: var(--jp-cell-collapser-not-active-hover-opacity);\n}\n\n\/* cell is active and collapser is hovered *\/\n.jp-Notebook .jp-Cell.jp-mod-active .jp-Collapser:hover {\n background: var(--jp-brand-color0);\n opacity: 1;\n}\n\n\/* Command mode *\/\n\n.jp-Notebook.jp-mod-commandMode .jp-Cell.jp-mod-selected {\n background: var(--jp-notebook-multiselected-color);\n}\n\n.jp-Notebook.jp-mod-commandMode\n .jp-Cell.jp-mod-active.jp-mod-selected:not(.jp-mod-multiSelected) {\n background: transparent;\n}\n\n\/* Edit mode *\/\n\n.jp-Notebook.jp-mod-editMode .jp-Cell.jp-mod-active .jp-InputArea-editor {\n border: var(--jp-border-width) solid var(--jp-cell-editor-active-border-color);\n box-shadow: var(--jp-input-box-shadow);\n background-color: var(--jp-cell-editor-active-background);\n}\n\n\/*-----------------------------------------------------------------------------\n| Notebook drag and drop\n|----------------------------------------------------------------------------*\/\n\n.jp-Notebook-cell.jp-mod-dropSource {\n opacity: 0.5;\n}\n\n.jp-Notebook-cell.jp-mod-dropTarget,\n.jp-Notebook.jp-mod-commandMode\n .jp-Notebook-cell.jp-mod-active.jp-mod-selected.jp-mod-dropTarget {\n border-top-color: var(--jp-private-notebook-selected-color);\n border-top-style: solid;\n border-top-width: 2px;\n}\n\n.jp-dragImage {\n display: block;\n flex-direction: row;\n width: var(--jp-private-notebook-dragImage-width);\n height: var(--jp-private-notebook-dragImage-height);\n border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);\n background: var(--jp-cell-editor-background);\n overflow: visible;\n}\n\n.jp-dragImage-singlePrompt {\n box-shadow: 2px 2px 4px 0 rgba(0, 0, 0, 0.12);\n}\n\n.jp-dragImage .jp-dragImage-content {\n flex: 1 1 auto;\n z-index: 2;\n font-size: var(--jp-code-font-size);\n font-family: var(--jp-code-font-family);\n line-height: var(--jp-code-line-height);\n padding: var(--jp-code-padding);\n border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);\n background: var(--jp-cell-editor-background-color);\n color: var(--jp-content-font-color3);\n text-align: left;\n margin: 4px 4px 4px 0;\n}\n\n.jp-dragImage .jp-dragImage-prompt {\n flex: 0 0 auto;\n min-width: 36px;\n color: var(--jp-cell-inprompt-font-color);\n padding: var(--jp-code-padding);\n padding-left: 12px;\n font-family: var(--jp-cell-prompt-font-family);\n letter-spacing: var(--jp-cell-prompt-letter-spacing);\n line-height: 1.9;\n font-size: var(--jp-code-font-size);\n border: var(--jp-border-width) solid transparent;\n}\n\n.jp-dragImage-multipleBack {\n z-index: -1;\n position: absolute;\n height: 32px;\n width: 300px;\n top: 8px;\n left: 8px;\n background: var(--jp-layout-color2);\n border: var(--jp-border-width) solid var(--jp-input-border-color);\n box-shadow: 2px 2px 4px 0 rgba(0, 0, 0, 0.12);\n}\n\n\/*-----------------------------------------------------------------------------\n| Cell toolbar\n|----------------------------------------------------------------------------*\/\n\n.jp-NotebookTools {\n display: block;\n min-width: var(--jp-sidebar-min-width);\n color: var(--jp-ui-font-color1);\n background: var(--jp-layout-color1);\n\n \/* This is needed so that all font sizing of children done in ems is\n * relative to this base size *\/\n font-size: var(--jp-ui-font-size1);\n overflow: auto;\n}\n\n.jp-ActiveCellTool {\n padding: 12px 0;\n display: flex;\n}\n\n.jp-ActiveCellTool-Content {\n flex: 1 1 auto;\n}\n\n.jp-ActiveCellTool .jp-ActiveCellTool-CellContent {\n background: var(--jp-cell-editor-background);\n border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);\n border-radius: 0;\n min-height: 29px;\n}\n\n.jp-ActiveCellTool .jp-InputPrompt {\n min-width: calc(var(--jp-cell-prompt-width) * 0.75);\n}\n\n.jp-ActiveCellTool-CellContent > pre {\n padding: 5px 4px;\n margin: 0;\n white-space: normal;\n}\n\n.jp-MetadataEditorTool {\n flex-direction: column;\n padding: 12px 0;\n}\n\n.jp-RankedPanel > :not(:first-child) {\n margin-top: 12px;\n}\n\n.jp-KeySelector select.jp-mod-styled {\n font-size: var(--jp-ui-font-size1);\n color: var(--jp-ui-font-color0);\n border: var(--jp-border-width) solid var(--jp-border-color1);\n}\n\n.jp-KeySelector label,\n.jp-MetadataEditorTool label,\n.jp-NumberSetter label {\n line-height: 1.4;\n}\n\n.jp-NotebookTools .jp-select-wrapper {\n margin-top: 4px;\n margin-bottom: 0;\n}\n\n.jp-NumberSetter input {\n width: 100%;\n margin-top: 4px;\n}\n\n.jp-NotebookTools .jp-Collapse {\n margin-top: 16px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Presentation Mode (.jp-mod-presentationMode)\n|----------------------------------------------------------------------------*\/\n\n.jp-mod-presentationMode .jp-Notebook {\n --jp-content-font-size1: var(--jp-content-presentation-font-size1);\n --jp-code-font-size: var(--jp-code-presentation-font-size);\n}\n\n.jp-mod-presentationMode .jp-Notebook .jp-Cell .jp-InputPrompt,\n.jp-mod-presentationMode .jp-Notebook .jp-Cell .jp-OutputPrompt {\n flex: 0 0 110px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Side-by-side Mode (.jp-mod-sideBySide)\n|----------------------------------------------------------------------------*\/\n.jp-mod-sideBySide.jp-Notebook .jp-Notebook-cell {\n margin-top: 3em;\n margin-bottom: 3em;\n margin-left: 5%;\n margin-right: 5%;\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell {\n display: grid;\n grid-template-columns: minmax(0, 1fr) min-content minmax(\n 0,\n var(--jp-side-by-side-output-size)\n );\n grid-template-rows: auto minmax(0, 1fr) auto;\n grid-template-areas:\n 'header header header'\n 'input handle output'\n 'footer footer footer';\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell.jp-mod-resizedCell {\n grid-template-columns: minmax(0, 1fr) min-content minmax(\n 0,\n var(--jp-side-by-side-resized-cell)\n );\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-CellHeader {\n grid-area: header;\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-Cell-inputWrapper {\n grid-area: input;\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-Cell-outputWrapper {\n \/* overwrite the default margin (no vertical separation needed in side by side move *\/\n margin-top: 0;\n grid-area: output;\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-CellFooter {\n grid-area: footer;\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-CellResizeHandle {\n grid-area: handle;\n user-select: none;\n display: block;\n height: 100%;\n cursor: ew-resize;\n padding: 0 var(--jp-cell-padding);\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-CellResizeHandle::after {\n content: '';\n display: block;\n background: var(--jp-border-color2);\n height: 100%;\n width: 5px;\n}\n\n.jp-mod-sideBySide.jp-Notebook\n .jp-CodeCell.jp-mod-resizedCell\n .jp-CellResizeHandle::after {\n background: var(--jp-border-color0);\n}\n\n.jp-CellResizeHandle {\n display: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Placeholder\n|----------------------------------------------------------------------------*\/\n\n.jp-Cell-Placeholder {\n padding-left: 55px;\n}\n\n.jp-Cell-Placeholder-wrapper {\n background: #fff;\n border: 1px solid;\n border-color: #e5e6e9 #dfe0e4 #d0d1d5;\n border-radius: 4px;\n -webkit-border-radius: 4px;\n margin: 10px 15px;\n}\n\n.jp-Cell-Placeholder-wrapper-inner {\n padding: 15px;\n position: relative;\n}\n\n.jp-Cell-Placeholder-wrapper-body {\n background-repeat: repeat;\n background-size: 50% auto;\n}\n\n.jp-Cell-Placeholder-wrapper-body div {\n background: #f6f7f8;\n background-image: -webkit-linear-gradient(\n left,\n #f6f7f8 0%,\n #edeef1 20%,\n #f6f7f8 40%,\n #f6f7f8 100%\n );\n background-repeat: no-repeat;\n background-size: 800px 104px;\n height: 104px;\n position: absolute;\n right: 15px;\n left: 15px;\n top: 15px;\n}\n\ndiv.jp-Cell-Placeholder-h1 {\n top: 20px;\n height: 20px;\n left: 15px;\n width: 150px;\n}\n\ndiv.jp-Cell-Placeholder-h2 {\n left: 15px;\n top: 50px;\n height: 10px;\n width: 100px;\n}\n\ndiv.jp-Cell-Placeholder-content-1,\ndiv.jp-Cell-Placeholder-content-2,\ndiv.jp-Cell-Placeholder-content-3 {\n left: 15px;\n right: 15px;\n height: 10px;\n}\n\ndiv.jp-Cell-Placeholder-content-1 {\n top: 100px;\n}\n\ndiv.jp-Cell-Placeholder-content-2 {\n top: 120px;\n}\n\ndiv.jp-Cell-Placeholder-content-3 {\n top: 140px;\n}\n\n<\/style>\n<style type=\"text\/css\">\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*\nThe following CSS variables define the main, public API for styling JupyterLab.\nThese variables should be used by all plugins wherever possible. In other\nwords, plugins should not define custom colors, sizes, etc unless absolutely\nnecessary. This enables users to change the visual theme of JupyterLab\nby changing these variables.\n\nMany variables appear in an ordered sequence (0,1,2,3). These sequences\nare designed to work well together, so for example, `--jp-border-color1` should\nbe used with `--jp-layout-color1`. The numbers have the following meanings:\n\n* 0: super-primary, reserved for special emphasis\n* 1: primary, most important under normal situations\n* 2: secondary, next most important under normal situations\n* 3: tertiary, next most important under normal situations\n\nThroughout JupyterLab, we are mostly following principles from Google's\nMaterial Design when selecting colors. We are not, however, following\nall of MD as it is not optimized for dense, information rich UIs.\n*\/\n\n:root {\n \/* Elevation\n *\n * We style box-shadows using Material Design's idea of elevation. These particular numbers are taken from here:\n *\n * https:\/\/github.com\/material-components\/material-components-web\n * https:\/\/material-components-web.appspot.com\/elevation.html\n *\/\n\n --jp-shadow-base-lightness: 0;\n --jp-shadow-umbra-color: rgba(\n var(--jp-shadow-base-lightness),\n var(--jp-shadow-base-lightness),\n var(--jp-shadow-base-lightness),\n 0.2\n );\n --jp-shadow-penumbra-color: rgba(\n var(--jp-shadow-base-lightness),\n var(--jp-shadow-base-lightness),\n var(--jp-shadow-base-lightness),\n 0.14\n );\n --jp-shadow-ambient-color: rgba(\n var(--jp-shadow-base-lightness),\n var(--jp-shadow-base-lightness),\n var(--jp-shadow-base-lightness),\n 0.12\n );\n --jp-elevation-z0: none;\n --jp-elevation-z1: 0 2px 1px -1px var(--jp-shadow-umbra-color),\n 0 1px 1px 0 var(--jp-shadow-penumbra-color),\n 0 1px 3px 0 var(--jp-shadow-ambient-color);\n --jp-elevation-z2: 0 3px 1px -2px var(--jp-shadow-umbra-color),\n 0 2px 2px 0 var(--jp-shadow-penumbra-color),\n 0 1px 5px 0 var(--jp-shadow-ambient-color);\n --jp-elevation-z4: 0 2px 4px -1px var(--jp-shadow-umbra-color),\n 0 4px 5px 0 var(--jp-shadow-penumbra-color),\n 0 1px 10px 0 var(--jp-shadow-ambient-color);\n --jp-elevation-z6: 0 3px 5px -1px var(--jp-shadow-umbra-color),\n 0 6px 10px 0 var(--jp-shadow-penumbra-color),\n 0 1px 18px 0 var(--jp-shadow-ambient-color);\n --jp-elevation-z8: 0 5px 5px -3px var(--jp-shadow-umbra-color),\n 0 8px 10px 1px var(--jp-shadow-penumbra-color),\n 0 3px 14px 2px var(--jp-shadow-ambient-color);\n --jp-elevation-z12: 0 7px 8px -4px var(--jp-shadow-umbra-color),\n 0 12px 17px 2px var(--jp-shadow-penumbra-color),\n 0 5px 22px 4px var(--jp-shadow-ambient-color);\n --jp-elevation-z16: 0 8px 10px -5px var(--jp-shadow-umbra-color),\n 0 16px 24px 2px var(--jp-shadow-penumbra-color),\n 0 6px 30px 5px var(--jp-shadow-ambient-color);\n --jp-elevation-z20: 0 10px 13px -6px var(--jp-shadow-umbra-color),\n 0 20px 31px 3px var(--jp-shadow-penumbra-color),\n 0 8px 38px 7px var(--jp-shadow-ambient-color);\n --jp-elevation-z24: 0 11px 15px -7px var(--jp-shadow-umbra-color),\n 0 24px 38px 3px var(--jp-shadow-penumbra-color),\n 0 9px 46px 8px var(--jp-shadow-ambient-color);\n\n \/* Borders\n *\n * The following variables, specify the visual styling of borders in JupyterLab.\n *\/\n\n --jp-border-width: 1px;\n --jp-border-color0: var(--md-grey-400);\n --jp-border-color1: var(--md-grey-400);\n --jp-border-color2: var(--md-grey-300);\n --jp-border-color3: var(--md-grey-200);\n --jp-inverse-border-color: var(--md-grey-600);\n --jp-border-radius: 2px;\n\n \/* UI Fonts\n *\n * The UI font CSS variables are used for the typography all of the JupyterLab\n * user interface elements that are not directly user generated content.\n *\n * The font sizing here is done assuming that the body font size of --jp-ui-font-size1\n * is applied to a parent element. When children elements, such as headings, are sized\n * in em all things will be computed relative to that body size.\n *\/\n\n --jp-ui-font-scale-factor: 1.2;\n --jp-ui-font-size0: 0.83333em;\n --jp-ui-font-size1: 13px; \/* Base font size *\/\n --jp-ui-font-size2: 1.2em;\n --jp-ui-font-size3: 1.44em;\n --jp-ui-font-family: system-ui, -apple-system, blinkmacsystemfont, 'Segoe UI',\n helvetica, arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji',\n 'Segoe UI Symbol';\n\n \/*\n * Use these font colors against the corresponding main layout colors.\n * In a light theme, these go from dark to light.\n *\/\n\n \/* Defaults use Material Design specification *\/\n --jp-ui-font-color0: rgba(0, 0, 0, 1);\n --jp-ui-font-color1: rgba(0, 0, 0, 0.87);\n --jp-ui-font-color2: rgba(0, 0, 0, 0.54);\n --jp-ui-font-color3: rgba(0, 0, 0, 0.38);\n\n \/*\n * Use these against the brand\/accent\/warn\/error colors.\n * These will typically go from light to darker, in both a dark and light theme.\n *\/\n\n --jp-ui-inverse-font-color0: rgba(255, 255, 255, 1);\n --jp-ui-inverse-font-color1: rgba(255, 255, 255, 1);\n --jp-ui-inverse-font-color2: rgba(255, 255, 255, 0.7);\n --jp-ui-inverse-font-color3: rgba(255, 255, 255, 0.5);\n\n \/* Content Fonts\n *\n * Content font variables are used for typography of user generated content.\n *\n * The font sizing here is done assuming that the body font size of --jp-content-font-size1\n * is applied to a parent element. When children elements, such as headings, are sized\n * in em all things will be computed relative to that body size.\n *\/\n\n --jp-content-line-height: 1.6;\n --jp-content-font-scale-factor: 1.2;\n --jp-content-font-size0: 0.83333em;\n --jp-content-font-size1: 14px; \/* Base font size *\/\n --jp-content-font-size2: 1.2em;\n --jp-content-font-size3: 1.44em;\n --jp-content-font-size4: 1.728em;\n --jp-content-font-size5: 2.0736em;\n\n \/* This gives a magnification of about 125% in presentation mode over normal. *\/\n --jp-content-presentation-font-size1: 17px;\n --jp-content-heading-line-height: 1;\n --jp-content-heading-margin-top: 1.2em;\n --jp-content-heading-margin-bottom: 0.8em;\n --jp-content-heading-font-weight: 500;\n\n \/* Defaults use Material Design specification *\/\n --jp-content-font-color0: rgba(0, 0, 0, 1);\n --jp-content-font-color1: rgba(0, 0, 0, 0.87);\n --jp-content-font-color2: rgba(0, 0, 0, 0.54);\n --jp-content-font-color3: rgba(0, 0, 0, 0.38);\n --jp-content-link-color: var(--md-blue-900);\n --jp-content-font-family: system-ui, -apple-system, blinkmacsystemfont,\n 'Segoe UI', helvetica, arial, sans-serif, 'Apple Color Emoji',\n 'Segoe UI Emoji', 'Segoe UI Symbol';\n\n \/*\n * Code Fonts\n *\n * Code font variables are used for typography of code and other monospaces content.\n *\/\n\n --jp-code-font-size: 13px;\n --jp-code-line-height: 1.3077; \/* 17px for 13px base *\/\n --jp-code-padding: 5px; \/* 5px for 13px base, codemirror highlighting needs integer px value *\/\n --jp-code-font-family-default: menlo, consolas, 'DejaVu Sans Mono', monospace;\n --jp-code-font-family: var(--jp-code-font-family-default);\n\n \/* This gives a magnification of about 125% in presentation mode over normal. *\/\n --jp-code-presentation-font-size: 16px;\n\n \/* may need to tweak cursor width if you change font size *\/\n --jp-code-cursor-width0: 1.4px;\n --jp-code-cursor-width1: 2px;\n --jp-code-cursor-width2: 4px;\n\n \/* Layout\n *\n * The following are the main layout colors use in JupyterLab. In a light\n * theme these would go from light to dark.\n *\/\n\n --jp-layout-color0: white;\n --jp-layout-color1: white;\n --jp-layout-color2: var(--md-grey-200);\n --jp-layout-color3: var(--md-grey-400);\n --jp-layout-color4: var(--md-grey-600);\n\n \/* Inverse Layout\n *\n * The following are the inverse layout colors use in JupyterLab. In a light\n * theme these would go from dark to light.\n *\/\n\n --jp-inverse-layout-color0: #111;\n --jp-inverse-layout-color1: var(--md-grey-900);\n --jp-inverse-layout-color2: var(--md-grey-800);\n --jp-inverse-layout-color3: var(--md-grey-700);\n --jp-inverse-layout-color4: var(--md-grey-600);\n\n \/* Brand\/accent *\/\n\n --jp-brand-color0: var(--md-blue-900);\n --jp-brand-color1: var(--md-blue-700);\n --jp-brand-color2: var(--md-blue-300);\n --jp-brand-color3: var(--md-blue-100);\n --jp-brand-color4: var(--md-blue-50);\n --jp-accent-color0: var(--md-green-900);\n --jp-accent-color1: var(--md-green-700);\n --jp-accent-color2: var(--md-green-300);\n --jp-accent-color3: var(--md-green-100);\n\n \/* State colors (warn, error, success, info) *\/\n\n --jp-warn-color0: var(--md-orange-900);\n --jp-warn-color1: var(--md-orange-700);\n --jp-warn-color2: var(--md-orange-300);\n --jp-warn-color3: var(--md-orange-100);\n --jp-error-color0: var(--md-red-900);\n --jp-error-color1: var(--md-red-700);\n --jp-error-color2: var(--md-red-300);\n --jp-error-color3: var(--md-red-100);\n --jp-success-color0: var(--md-green-900);\n --jp-success-color1: var(--md-green-700);\n --jp-success-color2: var(--md-green-300);\n --jp-success-color3: var(--md-green-100);\n --jp-info-color0: var(--md-cyan-900);\n --jp-info-color1: var(--md-cyan-700);\n --jp-info-color2: var(--md-cyan-300);\n --jp-info-color3: var(--md-cyan-100);\n\n \/* Cell specific styles *\/\n\n --jp-cell-padding: 5px;\n --jp-cell-collapser-width: 8px;\n --jp-cell-collapser-min-height: 20px;\n --jp-cell-collapser-not-active-hover-opacity: 0.6;\n --jp-cell-editor-background: var(--md-grey-100);\n --jp-cell-editor-border-color: var(--md-grey-300);\n --jp-cell-editor-box-shadow: inset 0 0 2px var(--md-blue-300);\n --jp-cell-editor-active-background: var(--jp-layout-color0);\n --jp-cell-editor-active-border-color: var(--jp-brand-color1);\n --jp-cell-prompt-width: 64px;\n --jp-cell-prompt-font-family: var(--jp-code-font-family-default);\n --jp-cell-prompt-letter-spacing: 0;\n --jp-cell-prompt-opacity: 1;\n --jp-cell-prompt-not-active-opacity: 0.5;\n --jp-cell-prompt-not-active-font-color: var(--md-grey-700);\n\n \/* A custom blend of MD grey and blue 600\n * See https:\/\/meyerweb.com\/eric\/tools\/color-blend\/#546E7A:1E88E5:5:hex *\/\n --jp-cell-inprompt-font-color: #307fc1;\n\n \/* A custom blend of MD grey and orange 600\n * https:\/\/meyerweb.com\/eric\/tools\/color-blend\/#546E7A:F4511E:5:hex *\/\n --jp-cell-outprompt-font-color: #bf5b3d;\n\n \/* Notebook specific styles *\/\n\n --jp-notebook-padding: 10px;\n --jp-notebook-select-background: var(--jp-layout-color1);\n --jp-notebook-multiselected-color: var(--md-blue-50);\n\n \/* The scroll padding is calculated to fill enough space at the bottom of the\n notebook to show one single-line cell (with appropriate padding) at the top\n when the notebook is scrolled all the way to the bottom. We also subtract one\n pixel so that no scrollbar appears if we have just one single-line cell in the\n notebook. This padding is to enable a 'scroll past end' feature in a notebook.\n *\/\n --jp-notebook-scroll-padding: calc(\n 100% - var(--jp-code-font-size) * var(--jp-code-line-height) -\n var(--jp-code-padding) - var(--jp-cell-padding) - 1px\n );\n\n \/* Rendermime styles *\/\n\n --jp-rendermime-error-background: #fdd;\n --jp-rendermime-table-row-background: var(--md-grey-100);\n --jp-rendermime-table-row-hover-background: var(--md-light-blue-50);\n\n \/* Dialog specific styles *\/\n\n --jp-dialog-background: rgba(0, 0, 0, 0.25);\n\n \/* Console specific styles *\/\n\n --jp-console-padding: 10px;\n\n \/* Toolbar specific styles *\/\n\n --jp-toolbar-border-color: var(--jp-border-color1);\n --jp-toolbar-micro-height: 8px;\n --jp-toolbar-background: var(--jp-layout-color1);\n --jp-toolbar-box-shadow: 0 0 2px 0 rgba(0, 0, 0, 0.24);\n --jp-toolbar-header-margin: 4px 4px 0 4px;\n --jp-toolbar-active-background: var(--md-grey-300);\n\n \/* Statusbar specific styles *\/\n\n --jp-statusbar-height: 24px;\n\n \/* Input field styles *\/\n\n --jp-input-box-shadow: inset 0 0 2px var(--md-blue-300);\n --jp-input-active-background: var(--jp-layout-color1);\n --jp-input-hover-background: var(--jp-layout-color1);\n --jp-input-background: var(--md-grey-100);\n --jp-input-border-color: var(--jp-inverse-border-color);\n --jp-input-active-border-color: var(--jp-brand-color1);\n --jp-input-active-box-shadow-color: rgba(19, 124, 189, 0.3);\n\n \/* General editor styles *\/\n\n --jp-editor-selected-background: #d9d9d9;\n --jp-editor-selected-focused-background: #d7d4f0;\n --jp-editor-cursor-color: var(--jp-ui-font-color0);\n\n \/* Code mirror specific styles *\/\n\n --jp-mirror-editor-keyword-color: #008000;\n --jp-mirror-editor-atom-color: #88f;\n --jp-mirror-editor-number-color: #080;\n --jp-mirror-editor-def-color: #00f;\n --jp-mirror-editor-variable-color: var(--md-grey-900);\n --jp-mirror-editor-variable-2-color: rgb(0, 54, 109);\n --jp-mirror-editor-variable-3-color: #085;\n --jp-mirror-editor-punctuation-color: #05a;\n --jp-mirror-editor-property-color: #05a;\n --jp-mirror-editor-operator-color: #a2f;\n --jp-mirror-editor-comment-color: #408080;\n --jp-mirror-editor-string-color: #ba2121;\n --jp-mirror-editor-string-2-color: #708;\n --jp-mirror-editor-meta-color: #a2f;\n --jp-mirror-editor-qualifier-color: #555;\n --jp-mirror-editor-builtin-color: #008000;\n --jp-mirror-editor-bracket-color: #997;\n --jp-mirror-editor-tag-color: #170;\n --jp-mirror-editor-attribute-color: #00c;\n --jp-mirror-editor-header-color: blue;\n --jp-mirror-editor-quote-color: #090;\n --jp-mirror-editor-link-color: #00c;\n --jp-mirror-editor-error-color: #f00;\n --jp-mirror-editor-hr-color: #999;\n\n \/*\n RTC user specific colors.\n These colors are used for the cursor, username in the editor,\n and the icon of the user.\n *\/\n\n --jp-collaborator-color1: #ffad8e;\n --jp-collaborator-color2: #dac83d;\n --jp-collaborator-color3: #72dd76;\n --jp-collaborator-color4: #00e4d0;\n --jp-collaborator-color5: #45d4ff;\n --jp-collaborator-color6: #e2b1ff;\n --jp-collaborator-color7: #ff9de6;\n\n \/* Vega extension styles *\/\n\n --jp-vega-background: white;\n\n \/* Sidebar-related styles *\/\n\n --jp-sidebar-min-width: 250px;\n\n \/* Search-related styles *\/\n\n --jp-search-toggle-off-opacity: 0.5;\n --jp-search-toggle-hover-opacity: 0.8;\n --jp-search-toggle-on-opacity: 1;\n --jp-search-selected-match-background-color: rgb(245, 200, 0);\n --jp-search-selected-match-color: black;\n --jp-search-unselected-match-background-color: var(\n --jp-inverse-layout-color0\n );\n --jp-search-unselected-match-color: var(--jp-ui-inverse-font-color0);\n\n \/* Icon colors that work well with light or dark backgrounds *\/\n --jp-icon-contrast-color0: var(--md-purple-600);\n --jp-icon-contrast-color1: var(--md-green-600);\n --jp-icon-contrast-color2: var(--md-pink-600);\n --jp-icon-contrast-color3: var(--md-blue-600);\n\n \/* Button colors *\/\n --jp-accept-color-normal: var(--md-blue-700);\n --jp-accept-color-hover: var(--md-blue-800);\n --jp-accept-color-active: var(--md-blue-900);\n --jp-warn-color-normal: var(--md-red-700);\n --jp-warn-color-hover: var(--md-red-800);\n --jp-warn-color-active: var(--md-red-900);\n --jp-reject-color-normal: var(--md-grey-600);\n --jp-reject-color-hover: var(--md-grey-700);\n --jp-reject-color-active: var(--md-grey-800);\n\n \/* File or activity icons and switch semantic variables *\/\n --jp-jupyter-icon-color: #f37626;\n --jp-notebook-icon-color: #f37626;\n --jp-json-icon-color: var(--md-orange-700);\n --jp-console-icon-background-color: var(--md-blue-700);\n --jp-console-icon-color: white;\n --jp-terminal-icon-background-color: var(--md-grey-800);\n --jp-terminal-icon-color: var(--md-grey-200);\n --jp-text-editor-icon-color: var(--md-grey-700);\n --jp-inspector-icon-color: var(--md-grey-700);\n --jp-switch-color: var(--md-grey-400);\n --jp-switch-true-position-color: var(--md-orange-900);\n}\n<\/style>\n<style type=\"text\/css\">\n\/* Force rendering true colors when outputing to pdf *\/\n* {\n -webkit-print-color-adjust: exact;\n}\n\n\/* Misc *\/\na.anchor-link {\n display: none;\n}\n\n\/* Input area styling *\/\n.jp-InputArea {\n overflow: hidden;\n}\n\n.jp-InputArea-editor {\n overflow: hidden;\n}\n\n.cm-editor.cm-s-jupyter .highlight pre {\n\/* weird, but --jp-code-padding defined to be 5px but 4px horizontal padding is hardcoded for pre.cm-line *\/\n padding: var(--jp-code-padding) 4px;\n margin: 0;\n\n font-family: inherit;\n font-size: inherit;\n line-height: inherit;\n color: inherit;\n\n}\n\n.jp-OutputArea-output pre {\n line-height: inherit;\n font-family: inherit;\n}\n\n.jp-RenderedText pre {\n color: var(--jp-content-font-color1);\n font-size: var(--jp-code-font-size);\n}\n\n\/* Hiding the collapser by default *\/\n.jp-Collapser {\n display: none;\n}\n\n@page {\n margin: 0.5in; \/* Margin for each printed piece of paper *\/\n}\n\n@media print {\n .jp-Cell-inputWrapper,\n .jp-Cell-outputWrapper {\n display: block;\n }\n}\n<\/style>\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/latest.js?config=TeX-AMS_CHTML-full,Safe\"> <\/script>\n\n<script type=\"text\/x-mathjax-config\">\n init_mathjax = function() {\n if (window.MathJax) {\n \/\/ MathJax loaded\n MathJax.Hub.Config({\n TeX: {\n equationNumbers: {\n autoNumber: \"AMS\",\n useLabelIds: true\n }\n },\n tex2jax: {\n inlineMath: [ ['$','$'], [\"\\\$\",\"\\\$\"] ],\n displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ],\n processEscapes: true,\n processEnvironments: true\n },\n displayAlign: 'center',\n CommonHTML: {\n linebreaks: {\n automatic: true\n }\n }\n });\n\n MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n }\n }\n init_mathjax();\n <\/script>\n<script type=\"module\">\n document.addEventListener(\"DOMContentLoaded\", async () => {\n const diagrams = document.querySelectorAll(\".jp-Mermaid > pre.mermaid\");\n \/\/ do not load mermaidjs if not needed\n if (!diagrams.length) {\n return;\n }\n const mermaid = (await import(\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mermaid\/10.7.0\/mermaid.esm.min.mjs\")).default;\n const parser = new DOMParser();\n\n mermaid.initialize({\n maxTextSize: 100000,\n maxEdges: 100000,\n startOnLoad: false,\n fontFamily: window\n .getComputedStyle(document.body)\n .getPropertyValue(\"--jp-ui-font-family\"),\n theme: document.querySelector(\"body[data-jp-theme-light='true']\")\n ? \"default\"\n : \"dark\",\n });\n\n let _nextMermaidId = 0;\n\n function makeMermaidImage(svg) {\n const img = document.createElement(\"img\");\n const doc = parser.parseFromString(svg, \"image\/svg+xml\");\n const svgEl = doc.querySelector(\"svg\");\n const { maxWidth } = svgEl?.style || {};\n const firstTitle = doc.querySelector(\"title\");\n const firstDesc = doc.querySelector(\"desc\");\n\n img.setAttribute(\"src\", `data:image\/svg+xml,${encodeURIComponent(svg)}`);\n if (maxWidth) {\n img.width = parseInt(maxWidth);\n }\n if 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}\n\n async function renderOneMarmaid(src) {\n const id = `jp-mermaid-${_nextMermaidId++}`;\n const parent = src.parentNode;\n let raw = src.textContent.trim();\n const el = document.createElement(\"div\");\n el.style.visibility = \"hidden\";\n document.body.appendChild(el);\n let results = null;\n let output = null;\n try {\n let { svg } = await mermaid.render(id, raw, el);\n svg = cleanMermaidSvg(svg);\n results = makeMermaidImage(svg);\n output = document.createElement(\"figure\");\n results.map(output.appendChild, output);\n } catch (err) {\n parent.classList.add(\"jp-mod-warning\");\n results = await makeMermaidError(raw);\n output = results[0];\n } finally {\n el.remove();\n }\n parent.classList.add(\"jp-RenderedMermaid\");\n parent.appendChild(output);\n }\n\n\n \/**\n * Post-process to ensure mermaid diagrams contain only valid SVG and XHTML.\n *\/\n function cleanMermaidSvg(svg) {\n return svg.replace(RE_VOID_ELEMENT, replaceVoidElement);\n }\n\n\n \/**\n * A regular expression for all void elements, which may include attributes and\n * a slash.\n *\n * @see https:\/\/developer.mozilla.org\/en-US\/docs\/Glossary\/Void_element\n *\n * Of these, only `<br>` is generated by Mermaid in place of `\\n`,\n * but _any_ \"malformed\" tag will break the SVG rendering entirely.\n *\/\n const RE_VOID_ELEMENT =\n \/<\\s*(area|base|br|col|embed|hr|img|input|link|meta|param|source|track|wbr)\\s*([^>]*?)\\s*>\/gi;\n\n \/**\n * Ensure a void element is closed with a slash, preserving any attributes.\n *\/\n function replaceVoidElement(match, tag, rest) {\n rest = rest.trim();\n if (!rest.endsWith('\/')) {\n rest = `${rest} \/`;\n }\n return `<${tag} ${rest}>`;\n }\n\n void Promise.all([...diagrams].map(renderOneMarmaid));\n });\n<\/script>\n<style>\n .jp-Mermaid:not(.jp-RenderedMermaid) {\n display: none;\n }\n\n .jp-RenderedMermaid {\n overflow: auto;\n display: flex;\n }\n\n .jp-RenderedMermaid.jp-mod-warning {\n width: auto;\n padding: 0.5em;\n margin-top: 0.5em;\n border: var(--jp-border-width) solid var(--jp-warn-color2);\n border-radius: var(--jp-border-radius);\n color: var(--jp-ui-font-color1);\n font-size: var(--jp-ui-font-size1);\n white-space: pre-wrap;\n word-wrap: break-word;\n }\n\n .jp-RenderedMermaid figure {\n margin: 0;\n overflow: auto;\n max-width: 100%;\n }\n\n .jp-RenderedMermaid img {\n max-width: 100%;\n }\n\n .jp-RenderedMermaid-Details > pre {\n margin-top: 1em;\n }\n\n .jp-RenderedMermaid-Summary {\n color: var(--jp-warn-color2);\n }\n\n .jp-RenderedMermaid:not(.jp-mod-warning) pre {\n display: none;\n }\n\n .jp-RenderedMermaid-Summary > pre {\n display: inline-block;\n white-space: normal;\n }\n<\/style>\n<\/head>\n<body class=\"jp-Notebook\" data-jp-theme-light=\"true\" data-jp-theme-name=\"JupyterLab Light\">\n<main>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<h1 id=\"Logarithms-and-heteroskedasticity\">Logarithms and heteroskedasticity<a class=\"anchor-link\" href=\"#Logarithms-and-heteroskedasticity\">\u00b6<\/a><\/h1><p>Here’s a <a href=\"https:\/\/www.reddit.com\/r\/statistics\/comments\/1czsban\/eq_is_it_correct_to_use_logarithmic\/\">question from the Reddit statistics forum<\/a>.<\/p>\n<blockquote>\n<p>Is it correct to use logarithmic transformation in order to mitigate heteroskedasticity?<\/p>\n<p>For my studies I gathered data on certain preferences across a group of people. I am trying to figure out if I can pinpoint preferences to factors such as gender in this case.<\/p>\n<p>I used mixed ANOVA analysis with good success however one of my hypothesis came up with heteroskedasticity when doing Levene’s test. [I’ve been] breaking my head all day on how to solve this. I’ve now used logarithmic transformation to all 3 test results and run another Levene’s. When using the media value the test now results [in] homoskedasticity, however interaction is no longer significant?<\/p>\n<p>Is this the correct way to deal with this problem or is there something I am missing? Thanks in advance to everyone taking their time to help.<\/p>\n<\/blockquote>\n<p>Although the question is about ANOVA, I’m going to reframe it in terms of regression, for two reasons:<\/p>\n<ul>\n<li><p>Discussion of heteroskedasticity is clearer in the context of regression.<\/p>\n<\/li>\n<li><p>For many problems, a regression model is better than ANOVA anyway.<\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput celltag_remove-print\" data-mime-type=\"text\/markdown\">\n<p><a href=\"https:\/\/colab.research.google.com\/github\/AllenDowney\/DataQnA\/blob\/main\/nb\/log_heterosked.ipynb\">Click here to run this notebook on Colab<\/a>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput celltag_hide-cell\" data-mime-type=\"text\/markdown\">\n<p>I’ll download a utilities module with some of my frequently-used functions, and then import the usual libraries.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs celltag_hide-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [1]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"kn\">from<\/span> <span class=\"nn\">os.path<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">basename<\/span><span class=\"p\">,<\/span> <span class=\"n\">exists<\/span>\n\n<span class=\"k\">def<\/span> <span class=\"nf\">download<\/span><span class=\"p\">(<\/span><span class=\"n\">url<\/span><span class=\"p\">):<\/span>\n <span class=\"n\">filename<\/span> <span class=\"o\">=<\/span> <span class=\"n\">basename<\/span><span class=\"p\">(<\/span><span class=\"n\">url<\/span><span class=\"p\">)<\/span>\n <span class=\"k\">if<\/span> <span class=\"ow\">not<\/span> <span class=\"n\">exists<\/span><span class=\"p\">(<\/span><span class=\"n\">filename<\/span><span class=\"p\">):<\/span>\n <span class=\"kn\">from<\/span> <span class=\"nn\">urllib.request<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">urlretrieve<\/span>\n\n <span class=\"n\">local<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">urlretrieve<\/span><span class=\"p\">(<\/span><span class=\"n\">url<\/span><span class=\"p\">,<\/span> <span class=\"n\">filename<\/span><span class=\"p\">)<\/span>\n <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"Downloaded \"<\/span> <span class=\"o\">+<\/span> <span class=\"nb\">str<\/span><span class=\"p\">(<\/span><span class=\"n\">local<\/span><span class=\"p\">))<\/span>\n <span class=\"k\">return<\/span> <span class=\"n\">filename<\/span>\n\n<span class=\"n\">download<\/span><span class=\"p\">(<\/span><span class=\"s1\">'https:\/\/github.com\/AllenDowney\/DataQnA\/raw\/main\/nb\/utils.py'<\/span><span class=\"p\">)<\/span>\n\n<span class=\"kn\">import<\/span> <span class=\"nn\">numpy<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">np<\/span>\n<span class=\"kn\">import<\/span> <span class=\"nn\">matplotlib.pyplot<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">plt<\/span>\n<span class=\"kn\">import<\/span> <span class=\"nn\">pandas<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">pd<\/span>\n<span class=\"kn\">import<\/span> <span class=\"nn\">seaborn<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">sns<\/span>\n\n<span class=\"kn\">from<\/span> <span class=\"nn\">utils<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">decorate<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs celltag_hide-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [2]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"c1\"># install the empiricaldist library, if necessary<\/span>\n\n<span class=\"k\">try<\/span><span class=\"p\">:<\/span>\n <span class=\"kn\">import<\/span> <span class=\"nn\">empiricaldist<\/span>\n<span class=\"k\">except<\/span> <span class=\"ne\">ImportError<\/span><span class=\"p\">:<\/span>\n <span class=\"o\">!<\/span>pip<span class=\"w\"> <\/span>install<span class=\"w\"> <\/span>empiricaldist\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<h2 id=\"What-is-heteroskedasticity?\">What is heteroskedasticity?<a class=\"anchor-link\" href=\"#What-is-heteroskedasticity?\">\u00b6<\/a><\/h2><p>Linear regression is based on a model of the data-generating process where the independent variable <code>y<\/code> is the sum of<\/p>\n<ul>\n<li><p>A linear function of <code>x<\/code> with an unknown slope and intercept, and<\/p>\n<\/li>\n<li><p>Random values drawn from a Gaussian distribution with mean 0 and unknown standard deviation, <code>sigma<\/code>, that does not depend on <code>x<\/code>.<\/p>\n<\/li>\n<\/ul>\n<p>If, contrary to the second assumption, <code>sigma<\/code> depends on <code>x<\/code>, the data-generating process is heteroskedastic.\nSome amount of heteroskedasticity is common in real data, but most of the time it’s not a problem, because:<\/p>\n<ul>\n<li><p>Heteroskedasticity doesn’t bias the estimated parameters of the model, only the standard errors,<\/p>\n<\/li>\n<li><p>Even very strong heteroskedasticity doesn’t affect the standard errors by much, and<\/p>\n<\/li>\n<li><p>For practical purposes we don’t need standard errors to be particularly precise.<\/p>\n<\/li>\n<\/ul>\n<p>To demonstrate, let’s generate some data.\nFirst, we’ll draw <code>xs<\/code> from a normal distribution.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [3]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">seed<\/span><span class=\"p\">(<\/span><span class=\"mi\">17<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">n<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">200<\/span>\n<span class=\"n\">xs<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mi\">30<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"n\">n<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">xs<\/span><span class=\"o\">.<\/span><span class=\"n\">sort<\/span><span class=\"p\">()<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>To generate heteroskedastic data, I’ll use <code>interpolate<\/code> to construct a function where <code>sigma<\/code> depends on <code>x<\/code>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [4]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"kn\">from<\/span> <span class=\"nn\">scipy.interpolate<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">interp1d<\/span>\n\n<span class=\"k\">def<\/span> <span class=\"nf\">interpolate<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigma_seq<\/span><span class=\"p\">):<\/span>\n <span class=\"k\">return<\/span> <span class=\"n\">interp1d<\/span><span class=\"p\">([<\/span><span class=\"n\">xs<\/span><span class=\"o\">.<\/span><span class=\"n\">min<\/span><span class=\"p\">(),<\/span> <span class=\"n\">xs<\/span><span class=\"o\">.<\/span><span class=\"n\">max<\/span><span class=\"p\">()],<\/span> <span class=\"n\">sigma_seq<\/span><span class=\"p\">)(<\/span><span class=\"n\">xs<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>To generate strong heteroskedasticity, I’ll vary sigma over a wide range.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [5]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">sigmas<\/span> <span class=\"o\">=<\/span> <span class=\"n\">interpolate<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"p\">[<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"mf\">6.0<\/span><span class=\"p\">])<\/span>\n<span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">mean<\/span><span class=\"p\">(<\/span><span class=\"n\">sigmas<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[5]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>3.126391153924031<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Here’s what <code>sigma<\/code> looks like as a function of <code>x<\/code>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [6]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigmas<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span>\n <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'sigma'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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aP3++nn322ZBbd33\/+983rTAgngSGKN+tPa5QI5ROhzQq7Qr5DIPF3kAvixh0Fy5ckKQOp4qzVyXQUXl1oxav3SmP1x\/2mm9fzzM4wCoRg+6BBx6Q9FnQfe9739OAAQM0a9Ysbd++XcuXL++VAoFYVV7dqMp9J1T36dmIIcdEE8BaUT2j27Rpk5555hmVlZUpNTVVVVVVuuWWW\/TNb37T7PqAmNJ+w+Xaoy264DPkcjrUJ8mhC76Og5ac7A3EhqiCLnAG3dtvv63i4mKNGDHC1KKAWLOsrFavf\/CJWjy+Tp95\/YZm5gxR5pX9dLTZo09OtGpGzlB6cUCMiCroxo4dq0WLFuntt9\/WU089pXPnzqkX94IGLNXVhsspLqfu\/AILvYFYFVXQrVmzRmVlZXrsscc0YMAAHTp0SD\/72c\/Mrg2wVFdLBRySZrCbCRDzogq6K664QrNnzw6+Tk9PV3p6umlFAVZaVlar322v06etFyJet4hJJkBciCrogEQQ7WLv1L4uPXdHPr04IE4QdEh4i1Z\/rK21x9Tm9Ydc7B3AqQJAfCLokLCWldXq\/\/xlvy5E2m1Z0uf7J2vuF0YxTAnEKYIOCae8ulHPbqnRwZPnQn7ukHRl\/z4amdZPi2dmM0QJxDmCDgmlvLpRD67ZIW+EXhyTTAB7IeiQENpv1xUu5JhkAtgTQQfbCoRbv2SXXn7\/gDxev1xOh5Kckq\/d1pQDUpL0retG04sDbIqggy2VVzdq0Zod8l3Uewts1yVJMsRibyABEHSwlUAv7t3a4x1CziHJENt1AYmIoINtLFr9scr2NIZcC3dl\/z66LX+kCrMGE3JAgiHoEPei2dFk7hcyeQYHJCiCDnEp1EST9hySbpownCNzAJgXdPX19brvvvt0+PBhOZ1OzZo1Sz\/96U\/Nuh0SyJzfVGhH3SlJktMhhVotcNOE4WzVBUCSiUHncrn085\/\/XAUFBWpra9ONN96oTZs26fbbbzfrlrCxwIkCzee8Hbbs8htSktMhn9+Q0yGNHNhXsyal04MDEGRa0I0YMSJ4EnlycrImT56suro6s24HG+vq4NMHpo\/V2TYvE00AhNQrz+hOnjypjRs3qry8vDduB5sIPIf7v38\/EvaaKZlp9N4ARGR60LW1tam4uFhLlixRTk7nv5BKS0tVWloafN3U1GR2SYgD5dWNWrx2Z6dJJgEcmQMgWg7DMCKfUXIZfD6f5s6dq8zMTL3wwgtRfY\/b7VZNTY1ZJSFOPL15j16tPBh8HVjwLUk3M9EEwEUiZYepPbr7779fAwYM0PPPP2\/mbWADgWHKwHO2wqzBWvtRvTxev1JcTi2YNobncAAuiWk9uoqKCk2bNk0TJkxQUlKSJGn+\/Pn6zne+E\/H76NEllvLqRq3bXqdt\/zqhCz5DKS6nlt81WUW5wzuFHwCEY0mPburUqTJxVBQ2EOo5nMfrV+W+EyrKHR78AoDL4bS6ACSuyn0nOk02SXE5VZg12KKKANgRQQfLFGYNVorrs9+CLqdDM8cNCQ5bAkBPYa9LWKYod7iW3zWZ53AATEXQwVI8hwNgNoYuAQC2Ro8OPYKlAABiFUGHy7KsrFabqw7pSLNHPr+htR\/VM6EEQExh6BKXLHCqQMOp8\/L9\/6NzAuvgACBW0KNDt7Qfony39linz1kHByDWEHSIysVbda39qF4zc4bqH40twWvy0gdq8cxshi0BxBSCDhFdHHABHq9fw1JT9OANWXq39phm5AzlXDgAMYmgQ0jhAi4gMERZlDucgAMQ0wg6dBLp0FOX06HpVw\/WnV\/MZIgSQFwg6CCp4ySTUJstE3AA4hVBhw49uLUf1WvBtDFKcTnl8foJOABxj6BLUOF6cB6vX2fbvGy2DMA2CLoEFKkH136SCQEHwA4IugQS6MXVfXqWHhyAhEHQJYj2vTiX06E+SQ5d8Bn04ADYHkGXINo\/h\/P6Dc3MGaLMK\/vRgwNgewRdgijMGqy1H9UHn8Pd+QVmUQJIDARdgijKHc5zOAAJiaBLIDyHA5CITD2PbsmSJcrIyJDLRZ4CAKxhatDdcccd+tvf\/mbmLQAAiMjUrta0adPM\/PEAAHTJ1B4dAABWs\/zhWWlpqUpLS4Ovm5qaLKwGAGA3DsMwOp+q2cNcLpe8Xm9U17rdbtXU1JhcEQDATiJlB0OXAABbMzXoHnjgAWVkZMjn8ykjI0MlJSVm3g4AgE5MfUa3YsUKM388AABdYugSAGBrBB0AwNYIOgCArRF0AABbI+gAALZG0AEAbI2gAwDYGkEHALA1gg4AYGuWn14Qb8qrG1W574QKswarKHe41eUAALpAj64byqsbtXjtTr1aeVCL1+5UeXWj1SUBALpA0HVD5b4T8nj9kiSP16\/KfScsrggA0BWCrhsKswYrxfXZL1mKy6nCrMEWVwQA6ArP6LqhKHe4lt81mWd0ABBHCLpuKsodTsABQBxh6BIAYGsEHQDA1gg6AICtEXQAAFsj6AAAtkbQAQBsjaADANiaLdfRsfEyACDA1B7de++9p9zcXGVnZ2vhwoXy+Xxm3k4SGy8DADoyLej8fr8WLlyo3\/\/+9\/r3v\/+t5uZmrV692qzbBbHxMgCgPdOCbvv27Ro5cqTcbrckacGCBXrzzTfNul0QGy8DANoz7RldQ0ODRo0aFXydmZmp+vp6s24XxMbLAID2TAs6wzCiuq60tFSlpaXB101NTZd9bzZeBgAEmDZ0OWrUqA49uLq6OmVkZHS6rqSkRDU1NcGvQYMGmVUSACABmRZ0BQUFamhoUE1NjSTp5Zdf1pw5c8y6HQAAIZkWdElJSVq5cqWKi4uVlZWlz33uc\/rWt75l1u0AAAjJ1AXjM2fODPboAACwAluAAQBszWFEOz2yl6SmpoactBILmpqabDlZhnbFF9oVP+zYJik229XQ0KDm5uaQn8Vc0MUyt9tty6FY2hVfaFf8sGObpPhrF0OXAABbI+gAALZG0HVDSUmJ1SWYgnbFF9oVP+zYJin+2sUzOgCArdGjAwDYGkEXQn19vW688UaNHz9eubm5euKJJyRJK1eu1KRJk4JfycnJ2rRpk8XVRi9cuzwej+655x7l5eVp\/Pjxeuihh+T3+y2uNnrh2tXc3Ky5c+cqLy9PEydO1ObNmy2utPuKioo0adIk5eXlqbi4ODh9eunSpcrOztY111zTK8df9bRQ7aqrq9P06dPVv39\/LVy40OoSL0modq1Zs0b5+fmaOHGiCgoKtHXrVqvL7JZQbfrggw+Cfw\/m5uZ22Jg\/Jhno5PDhw8b27dsNwzAMj8djTJs2zdi4cWOHa+rq6oy0tDTj3LlzVpR4ScK166WXXjLuuusuwzAMw+v1GlOnTjX++Mc\/Wllqt4Rr1+OPP2488sgjhmEYRlNTk5GXl2e0tLRYWWq3nTp1KvjfS5YsMZ566injrbfeMr785S8bXq\/XaGhoMEaNGmWLdp08edKoqKgwXnzxRWPBggUWVnfpQrWroqLCOHHihGEYhrFr1y5j6NChhs\/ns6rEbgvVptbWVuPChQuGYRjG6dOnjczMTOPAgQMWVdg1enQhjBgxQgUFBZKk5ORkTZ48WXV1dR2ueeONNzRnzhz17dvXihIvSaR2tba2yuv1yuPxyOPxaPjw+DnmKFy79uzZo5tuukmSlJaWppycHP3pT3+ystRuGzhwoCTJ7\/fr\/PnzcjgcevPNN3XfffcpKSlJ6enpmjp1qsrLyy2utHtCtWvQoEEqLCyMqz9TFwvVrsLCQn3+85+XJE2YMEEej0etra1WltktodrUr18\/uVyf7SDp8Xjk8\/msLLFLBF0XTp48qY0bN+orX\/lKh\/fXrFkT15tUt2\/XPffco+TkZA0bNkzDhg1TUVGRrr32WqtLvCTt2zV58mStX79efr9fhw4d0vvvv98rh\/\/2tNmzZ2vo0KHau3evHn30UcsONe5pF7fLLiK1a926dcrLy9OAAQMsqu7ShGrT7t27lZeXp8zMTD3++OMaPXq0tUVGQNBF0NbWpuLiYi1ZskQ5OTnB9\/\/+97\/r1KlTuv766y2s7tJd3K6PPvpIXq9Xhw8fVn19vbZs2aLKykqry+y2i9v1xBNPyOl0asqUKbr\/\/vt1\/fXXKykpyeoyu23Dhg06fPiwMjIy9Ic\/\/CHqQ41j3cXtsotw7dq5c6eWLl2qVatWWVjdpQnVpry8PO3evVs1NTVauXKljh07ZnGV4RF0Yfh8Ps2bN0+TJk3q9K+y1atX6+6775bD4bCouksXql3r1q3TLbfcopSUFKWlpamoqEh\/\/etfLa60e0K1q3\/\/\/lqxYoWqqqq0ZcsWnT17tsM\/WOJJcnKy7rzzTm3YsCHqQ43jQft22cnF7frnP\/+pb3zjG1q3bp2uvvpqi6u7NOH+X40ZM0bjxo1TRUWFRZV1jaAL4\/7779eAAQP0\/PPPd3jf7\/dr7dq1cTtsGapdV111ld555x35\/X55PB5t27ZNbrfbwiq7L1S7Tp8+LY\/HI0mqqKjQgQMHOg1Bx7KWlhYdOXJE0me\/7zZv3qzc3FzNmTNHr776qnw+X3BItqioyOJqoxeuXfEuXLsaGhp066236sUXX9R1111ncZXdE65N+\/fvl9frlSQdPXpUH374ocaPH29lqZFZPRsmFr3\/\/vuGJGPChAlGfn6+kZ+fb\/z61782DMMw3nnnHWPy5MkWV3hpwrXrzJkzxty5c43x48cbOTk5xtKlS60utVvCtevDDz80srOzjZycHOOGG24wamtrrS61Ww4dOmQUFBQYeXl5Rm5urjF\/\/nyjtbXVMAzDeOyxx4yxY8ca2dnZxvr16y2utHvCtau1tdVIT083Bg0aZPTr189IT0833n33XavLjVq4di1cuNBITU0N\/t7Mz8+P6RmK7YVr0yuvvGK43W5j4sSJRn5+vvHaa69ZXWpE7IwCALA1hi4BALZG0AEAbI2gAwDYGkEHALA1gg4AYGsEHQDA1gg6AICtEXQAAFsj6IAYV1VVpauvvlqnT5+W3+\/XjBkztH79eqvLAuIGO6MAcWDZsmXatWuX8vPztXv3bv32t7+1uiQgbhB0QBzw+\/264YYb1NDQoKqqKqWmplpdEhA3GLoE4kBzc7OOHDkiwzDU3NxsdTlAXKFHB8SBefPm6dprr9WIESO0atUqvfXWW3F5HiJgBXp0QIx74403dOTIET3yyCOaN2+ehg4dql\/+8pdWlwXEDXp0AABbo0cHALA1gg4AYGsEHQDA1gg6AICtEXQAAFsj6AAAtkbQAQBsjaADANja\/wPS1n3BUQf8XwAAAABJRU5ErkJggg==\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Now we can generate <code>ys<\/code> with variable values of <code>sigma<\/code>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [7]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">ys<\/span> <span class=\"o\">=<\/span> <span class=\"n\">xs<\/span> <span class=\"o\">+<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigmas<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>If we make a scatter plot of the data, we see a cone shape that indicates heteroskedasticity.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [8]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">ys<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'y'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Now let’s fit a model to the data.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [9]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"kn\">import<\/span> <span class=\"nn\">statsmodels.api<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">sm<\/span>\n\n<span class=\"n\">X<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sm<\/span><span class=\"o\">.<\/span><span class=\"n\">add_constant<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ols_model<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sm<\/span><span class=\"o\">.<\/span><span class=\"n\">OLS<\/span><span class=\"p\">(<\/span><span class=\"n\">ys<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ols_results<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ols_model<\/span><span class=\"o\">.<\/span><span class=\"n\">fit<\/span><span class=\"p\">()<\/span>\n\n<span class=\"n\">intercept<\/span><span class=\"p\">,<\/span> <span class=\"n\">slope<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ols_results<\/span><span class=\"o\">.<\/span><span class=\"n\">params<\/span>\n<span class=\"n\">intercept<\/span><span class=\"p\">,<\/span> <span class=\"n\">slope<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[9]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>(0.7580177696902339, 0.9672433174107101)<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Here’s what the fitted line looks like.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [10]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">fys<\/span> <span class=\"o\">=<\/span> <span class=\"n\">intercept<\/span> <span class=\"o\">+<\/span> <span class=\"n\">slope<\/span> <span class=\"o\">*<\/span> <span class=\"n\">xs<\/span>\n\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">ys<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">fys<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'y'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>If we plot the absolute values of the residuals, we can see the heteroskedasticity more clearly.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [11]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">resid<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ys<\/span> <span class=\"o\">-<\/span> <span class=\"n\">fys<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">abs<\/span><span class=\"p\">(<\/span><span class=\"n\">resid<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'absolute residual'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<h2 id=\"Testing-for-heteroskedasticity\">Testing for heteroskedasticity<a class=\"anchor-link\" href=\"#Testing-for-heteroskedasticity\">\u00b6<\/a><\/h2><p>OP mentions using the Levene test for heteroskedasticity, which is used to test whether <code>sigma<\/code> is different between groups.\nFor continuous values of <code>x<\/code> and <code>y<\/code>, we can use the Breusch-Pagan Lagrange Multiplier test:<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [12]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"kn\">from<\/span> <span class=\"nn\">statsmodels.stats.diagnostic<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">het_breuschpagan<\/span>\n\n<span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">p_value<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">het_breuschpagan<\/span><span class=\"p\">(<\/span><span class=\"n\">resid<\/span><span class=\"p\">,<\/span> <span class=\"n\">ols_model<\/span><span class=\"o\">.<\/span><span class=\"n\">exog<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">p_value<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[12]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>0.0006411829020109725<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Or White’s Lagrange Multiplier test:<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [13]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"kn\">from<\/span> <span class=\"nn\">statsmodels.stats.diagnostic<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">het_white<\/span>\n\n<span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">p_value<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">het_white<\/span><span class=\"p\">(<\/span><span class=\"n\">resid<\/span><span class=\"p\">,<\/span> <span class=\"n\">ols_model<\/span><span class=\"o\">.<\/span><span class=\"n\">exog<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">p_value<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[13]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>0.0019263142806157931<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Both tests produce small p-values, which means that if we generate a dataset by a homoskedastic process, there is almost no chance it would have as much heteroskedasticity as the dataset we generated.<\/p>\n<p>If you have never heard of either of these tests, don’t panic — neither had I under I looked them up for this example.\nAnd don’t worry about remembering them, because you should never use them again.\nLike testing for normality, testing for heteroskedasticity is never useful.<\/p>\n<p>Why? Because in almost any real dataset, you will find some heteroskedasticity.\nSo if you test for it, there are only two possible results:<\/p>\n<ul>\n<li><p>If the heteroskedasticity is small and you don’t have much data, you will fail to reject the null hypothesis.<\/p>\n<\/li>\n<li><p>If the heteroskedasticity is large or you have a lot of data, you will reject the null hypothesis.<\/p>\n<\/li>\n<\/ul>\n<p>Either way, you learn nothing — and in particular, you don’t learn the answer to the question you actually care about, which is whether the heteroskedasticity is so large that the effect on the standard errors is large enough that you should care.<\/p>\n<p>And the answer to that question is almost always no.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<h2 id=\"Should-we-care?\">Should we care?<a class=\"anchor-link\" href=\"#Should-we-care?\">\u00b6<\/a><\/h2><p>The dataset we generated has very large heteroskedasticity.\nLet’s see how much effect that has on the results.\nHere are the standard errors from simple linear regression:<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [14]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">ols_results<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[14]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>array([6.06159018, 0.20152957])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Now, there are several ways to generate standard errors that are robust in the presence of heteroskedasticity.\nOne is the Huber-White estimator, which we can compute like this:<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [15]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">robust_se<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ols_results<\/span><span class=\"o\">.<\/span><span class=\"n\">get_robustcov_results<\/span><span class=\"p\">(<\/span><span class=\"n\">cov_type<\/span><span class=\"o\">=<\/span><span class=\"s1\">'HC3'<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">robust_se<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[15]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>array([6.73913518, 0.2268012 ])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Another is to use Huber regression.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [16]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">huber_model<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sm<\/span><span class=\"o\">.<\/span><span class=\"n\">RLM<\/span><span class=\"p\">(<\/span><span class=\"n\">ys<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"o\">=<\/span><span class=\"n\">sm<\/span><span class=\"o\">.<\/span><span class=\"n\">robust<\/span><span class=\"o\">.<\/span><span class=\"n\">norms<\/span><span class=\"o\">.<\/span><span class=\"n\">HuberT<\/span><span class=\"p\">())<\/span>\n<span class=\"n\">huber_results<\/span> <span class=\"o\">=<\/span> <span class=\"n\">huber_model<\/span><span class=\"o\">.<\/span><span class=\"n\">fit<\/span><span class=\"p\">()<\/span>\n<span class=\"n\">huber_results<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[16]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>array([5.92709031, 0.19705786])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Another is to use quantile regression.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [17]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">quantile_model<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sm<\/span><span class=\"o\">.<\/span><span class=\"n\">QuantReg<\/span><span class=\"p\">(<\/span><span class=\"n\">ys<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">quantile_results<\/span> <span class=\"o\">=<\/span> <span class=\"n\">quantile_model<\/span><span class=\"o\">.<\/span><span class=\"n\">fit<\/span><span class=\"p\">(<\/span><span class=\"n\">q<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">quantile_results<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[17]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>array([7.6449323 , 0.25417092])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>And one more option is a wild bootstrap, which resamples the residuals by multiplying them by a random sequence of <code>1<\/code> and <code>-1<\/code>.\nThis way of resampling preserves heteroskedasticity, because it only changes the sign of the residuals, not the magnitude, and it maintains the relationship between those magnitudes and <code>x<\/code>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [18]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"kn\">from<\/span> <span class=\"nn\">scipy.stats<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">linregress<\/span>\n\n<span class=\"k\">def<\/span> <span class=\"nf\">wild_bootstrap<\/span><span class=\"p\">():<\/span>\n <span class=\"n\">resampled<\/span> <span class=\"o\">=<\/span> <span class=\"n\">fys<\/span> <span class=\"o\">+<\/span> <span class=\"n\">ols_results<\/span><span class=\"o\">.<\/span><span class=\"n\">resid<\/span> <span class=\"o\">*<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">choice<\/span><span class=\"p\">([<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"n\">n<\/span><span class=\"p\">)<\/span>\n <span class=\"n\">res<\/span> <span class=\"o\">=<\/span> <span class=\"n\">linregress<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">resampled<\/span><span class=\"p\">)<\/span>\n <span class=\"k\">return<\/span> <span class=\"n\">res<\/span><span class=\"o\">.<\/span><span class=\"n\">intercept<\/span><span class=\"p\">,<\/span> <span class=\"n\">res<\/span><span class=\"o\">.<\/span><span class=\"n\">slope<\/span> \n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>We can use <code>wild_bootstrap<\/code> to generate a sample from the sampling distributions of the intercept and slope.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [19]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">sample<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">wild_bootstrap<\/span><span class=\"p\">()<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1001<\/span><span class=\"p\">)]<\/span> \n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>The standard deviation of the sampling distributions is the standard error.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [20]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">bootstrap_bse<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">std<\/span><span class=\"p\">(<\/span><span class=\"n\">sample<\/span><span class=\"p\">,<\/span> <span class=\"n\">axis<\/span><span class=\"o\">=<\/span><span class=\"mi\">0<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">bootstrap_bse<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[20]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>array([6.63622313, 0.22341784])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Now let’s put all of the result in a table.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [21]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">columns<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"s1\">'SE(intercept)'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'SE(slope)'<\/span><span class=\"p\">]<\/span>\n<span class=\"n\">index<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"s1\">'OLS'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'Huber-White'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'Huber'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'quantile'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'bootstrap'<\/span><span class=\"p\">]<\/span>\n<span class=\"n\">data<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">ols_results<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span><span class=\"p\">,<\/span> <span class=\"n\">robust_se<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span><span class=\"p\">,<\/span> <span class=\"n\">huber_results<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span><span class=\"p\">,<\/span> \n <span class=\"n\">quantile_results<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span><span class=\"p\">,<\/span> <span class=\"n\">bootstrap_bse<\/span><span class=\"p\">]<\/span>\n<span class=\"n\">df<\/span> <span class=\"o\">=<\/span> <span class=\"n\">pd<\/span><span class=\"o\">.<\/span><span class=\"n\">DataFrame<\/span><span class=\"p\">(<\/span><span class=\"n\">data<\/span><span class=\"p\">,<\/span> <span class=\"n\">columns<\/span><span class=\"o\">=<\/span><span class=\"n\">columns<\/span><span class=\"p\">,<\/span> <span class=\"n\">index<\/span><span class=\"o\">=<\/span><span class=\"n\">index<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">df<\/span><span class=\"o\">.<\/span><span class=\"n\">sort_values<\/span><span class=\"p\">(<\/span><span class=\"n\">by<\/span><span class=\"o\">=<\/span><span class=\"s1\">'SE(slope)'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[21]:<\/div>\n<div class=\"jp-RenderedHTMLCommon jp-RenderedHTML jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/html\" tabindex=\"0\">\n<div>\n<style scoped=\"\">\n .dataframe tbody tr th:only-of-type {\n vertical-align: middle;\n }\n\n .dataframe tbody tr th {\n vertical-align: top;\n }\n\n .dataframe thead th {\n text-align: right;\n }\n<\/style>\n<table border=\"1\" class=\"dataframe\">\n<thead>\n<tr style=\"text-align: right;\">\n<th><\/th>\n<th>SE(intercept)<\/th>\n<th>SE(slope)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>Huber<\/th>\n<td>5.927090<\/td>\n<td>0.197058<\/td>\n<\/tr>\n<tr>\n<th>OLS<\/th>\n<td>6.061590<\/td>\n<td>0.201530<\/td>\n<\/tr>\n<tr>\n<th>bootstrap<\/th>\n<td>6.636223<\/td>\n<td>0.223418<\/td>\n<\/tr>\n<tr>\n<th>Huber-White<\/th>\n<td>6.739135<\/td>\n<td>0.226801<\/td>\n<\/tr>\n<tr>\n<th>quantile<\/th>\n<td>7.644932<\/td>\n<td>0.254171<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>The standard errors we get from different methods are notably different, but the differences probably don’t matter.<\/p>\n<p>First, I am skeptical of the results from Huber regression.\nWith this kind of heteroskedasticity, the standard errors should be larger than what we get from OLS.\nI’m not sure what’s the problem is, and I haven’t bothered to find out, because I don’t think Huber regression is necessary in the first place.<\/p>\n<p>The results from bootstrapping and the Huber-White estimator are the most reliable — which suggests that the standard errors from quantile regression are too big.<\/p>\n<p>In my opinion, we don’t need esoteric methods to deal with heteroskedasticity.\nIf heteroskedasticity is extreme, consider using wild bootstrap.\nOtherwise, just use ordinary least squares.<\/p>\n<p>Now let’s address OP’s headline question, “Is it correct to use logarithmic transformation in order to mitigate heteroskedasticity?”<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<h2 id=\"Log-transform-help?\">Log transform help?<a class=\"anchor-link\" href=\"#Log-transform-help?\">\u00b6<\/a><\/h2><p>In some cases, a log transform can reduce or eliminate heteroskedasticity.\nHowever, there are several reasons this is not a good idea in general:<\/p>\n<ul>\n<li><p>As we’ve seen, heteroskedasticity is not a big problem, so it usually doesn’t require any mitigation.<\/p>\n<\/li>\n<li><p>Taking a log transform of one or more variables in a regression model changes the meaning of the model — it hypothesizes a relationship between the variables that might not make sense in context.<\/p>\n<\/li>\n<li><p>Anyway, taking a log transform doesn’t always help.<\/p>\n<\/li>\n<\/ul>\n<p>To demonstrate the last point, let’s see what happens if we apply a log transform to the dependent variable:<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [22]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">log_ys<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">log10<\/span><span class=\"p\">(<\/span><span class=\"n\">ys<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Here’s what the scatter plot looks like after the transform.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [23]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">log_ys<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'log10 y'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Here’s what we get if we fit a model to the data.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [24]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">ols_model_log<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sm<\/span><span class=\"o\">.<\/span><span class=\"n\">OLS<\/span><span class=\"p\">(<\/span><span class=\"n\">log_ys<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ols_results_log<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ols_model_log<\/span><span class=\"o\">.<\/span><span class=\"n\">fit<\/span><span class=\"p\">()<\/span>\n\n<span class=\"n\">intercept<\/span><span class=\"p\">,<\/span> <span class=\"n\">slope<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ols_results_log<\/span><span class=\"o\">.<\/span><span class=\"n\">params<\/span>\n<span class=\"n\">intercept<\/span><span class=\"p\">,<\/span> <span class=\"n\">slope<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[24]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>(1.072059757295944, 0.013315487289434717)<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>And here’s the fitted line.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [25]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">log_fys<\/span> <span class=\"o\">=<\/span> <span class=\"n\">intercept<\/span> <span class=\"o\">+<\/span> <span class=\"n\">slope<\/span> <span class=\"o\">*<\/span> <span class=\"n\">xs<\/span>\n\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">log_ys<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">log_fys<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'log10 y'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>If we plot the absolute values of the residuals, we can see that the log transform did not entirely remove the heteroskedasticity.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [26]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">log_resid<\/span> <span class=\"o\">=<\/span> <span class=\"n\">log_ys<\/span> <span class=\"o\">-<\/span> <span class=\"n\">log_fys<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">abs<\/span><span class=\"p\">(<\/span><span class=\"n\">log_resid<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'absolute residual on log y'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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ArFmzUFRUhPT0dACwz9W7evUqYmJiuOwYBZ0\/\/S3tee5XIP1TrmpD4fbatef3XslEJTpb4vGF2WyGTqez346Li0Ntba3XY0pKSgAAK1euxIMPPog\/\/\/nPqKurw3vvvYeOHTv6HAeRvwJZRLk9zv0KdNHp1Pju2PxFrb1\/K1xrQ+3xvVc6j02XHTp0aLWIs\/OPJ2LGuHg6ZsuWLZg6dSrMZjMqKiowb948XL16tc1xRqMRer3e\/lNXV+f1eYnEYH+LbwJ9vdrjEmcUHB5rdDdu3AAALF++HLfddhtmz54NQRDwzjvv4PLlyx4fWKfTtarBmUwmxMbGtjmmqqrK5TEbN27EBx98AAAYPHgwevXqhWPHjmHkyJGtHiMvLw95eXn227amUqJAqaWGESxSvF5y1YY45L+dE0QYNmyYqPscWSwWoX\/\/\/kJ1dbUgCILw8MMPC+vWrWt1zJUrV4TY2Fjh7Nmzwo0bN4TRo0cLe\/fuFQRBEB588EHhzTffFARBEEwmk9CzZ0\/h8uXLXmMdNGiQiBIRibPzm3PCsn8cFnZ+cy7UoYQFJb5eO785JyQu2SH0+38fColLdigqNpKOp2u\/qFGXERERrXYb37NnDyIiPJ+q1WqRn5+PnJwcxMfHo0uXLpg5cyaKi4thMBgA3FxS7NVXX0VaWhoGDhyI9PR0jB07FgDwpz\/9CVu2bMHQoUMxYcIEvPHGG+jWrZu\/+ZzIL5nJvbB88mBV1QLkHMIv5vUK9hQCNkGTqAnjhw4dwuzZs3H+\/M0\/zD59+mD9+vUYNmyY7AH6ihPGidwL9YTmUDx\/qMtMweHp2i9q1OXw4cNx6NAhNDQ0AACio6Oli46IJOOtLyrUQ\/hD8fwc8k8eE11VVRWGDh2K8vJyl79PTU2VJSgi8p2Y4f2doiKhjdCgxSqEZIBNqAb4cMh\/++Yx0b355ptYs2ZNq6W5bDQaDbfsIVIQb7WlXdXnsfbT02ixCojQALn39Q\/6xZ+1KwoFj4luzZo1AIB9+\/YFJRgi8p+32pJjIrQKQGOzJRRhsnZFQSdq1GVxcbF9nck\/\/vGPmDp1Kr755htZAyMi33ibcC31OozhvgAztR+iRl0OGTIEhw8fxldffYV58+bh6aefxptvvokDBw4EI0afcNQlBYs\/k5BDPXFZqufnSEZSmoC36bEt97V9+3bMmTMH06dPx48\/\/ihdhERhxp+V9pWwOr9U8wI5N43CiahE17FjR7z33nsoLCzEf\/7nfwIAmpubZQ2MSMn8udCrKTmEw3Y0bFolG1GJbv369SgvL8eLL76I2NhYnDx5Eo888ojcsREplj8X+nBIDmIpfQFmJdSeSTlE9dEBwJUrV3Dq1Kk2iyorDfvoKFjCsY+uvVhe\/A02lH9rvz07tR+WTx4cwohIbgH30b3\/\/vsYNWoUcnJyANxcEmzChAnSRUgUBpybwvzp71Lj2plKpKbaMwVO1BJgL730EiorK5GRkQHg5pJgJpNJzriIFCXQTUXDhVpqnJyYTo5EJbqoqCjExMS0us\/b7gVEahLqNSKDQW3JnBPTyUZUturfvz8+\/vhjaDQaNDQ0YPny5YrcuYBILqFoCuN2NoHjyEsCRCa6v\/zlL3jnnXdgNpsRHx+PU6dO4fXXX5c7NiLFCPYoQylGDfp6kQ9mMg9GAuLIS7Lx2nTZ0tKClStXYuPGjcGIh0ixgtkUFmhTqT\/NkMHq1wpWE2l7aG4mcbzW6LRaLcrKyvx68NLSUiQnJyMhIQEGgwEtLS1tjiksLERiYiLi4+Pb7JKwfv166PV6DB48GJmZmX7FQBSOAq1d+dsMGYxRocFqIuXIS7IRNRhlzJgxeOyxxzBjxgx07tzZfr+n\/eisVisMBgOKi4uh1+sxZcoUFBQUYNasWfZj6uvrsXDhQlRUVKBHjx5IS0tDWVkZ0tPT8dlnn2HNmjX4\/PPPER0dbd\/dnEjJpBq1GGjtKlT7vokRrNg48pJsRE0YHzt2bNsTvexHV1FRgeeeew6ffPIJAGDnzp0wGo0oLi62H\/Pee+9h+\/bt+Nvf\/gYAWL16Naqrq\/H6669j+vTpmDZtGn7xi1\/4VCBOGKdQCXShY6mH9it5qoCSY6Pw5OnaL6pG589+dGazGTqdzn47Li4OtbW1Xo8pKSkBABw5cgRfffUVfv\/738NisWDRokX2CetEShRIn5Ac\/VZKHl6v5NhsmIzVQ7bJcGJWFvN0jMViwbfffov9+\/dj27ZtWLBgAU6dOtXmOKPRCL1eb\/+pq6sLKG4ifwXSJ6TGof3uhMOQf47YVBfZEp1Op2tVgzOZTIiNjRV9jE6nw0MPPQStVou+ffvi3nvvRVVVVZvnycvLQ01Njf2nW7duMpWIyLNApiD4miTDIVm4Ei4JpD198WgPZEt0KSkpMJvN9jbTtWvXIjs7u9UxWVlZ2LdvH86dOweLxYKNGzfaj8nJycGePXsA3By08uWXX2LQoEFyhUskCTGjFl0lKV+SpBKShb+JNlwSCEdsqovoRLdz5068+eabAIDvv\/8ex44d83i8VqtFfn4+cnJyEB8fjy5dumDmzJkoLi6GwWAAAMTExODVV19FWloaBg4ciPT0dPvAl0cffRTXrl1DcnIyxowZg8WLF2PgwIH+lpNIETwlKbFD+0OdLAJJtIEkkGDWYpW+DRH5RtSoy6VLl+Lw4cM4cuQIjh49inPnzuGhhx5CeXl5MGL0CUddkpJJsX2Mp9GdwRi5GUgZdlWfx5ZKEyAA00bF+TVYx58RraR+AW\/T8+GHH+KDDz5Ap06dAAC9e\/fG1atXpYuQqJ2QoknMXW1DyibNXdXn8fiGL5C36as2j+dvGWzx7T3ybxw4ecmneEJdi6XwJmp6wS233AKNRmO\/3dTUJGpUJVF74EstKtBJzI7P5VyLkmrJK8fak43j4\/lbhkDiU\/IEeFI+UYnugQcewAsvvIDGxkYUFxfjrbfe4pw2Ivi\/pmSgCcjVc\/mbDJwTtWNCsnF+PH\/KEEiy4ionFAhRfXSCIGDDhg3YsWMHBEHAgw8+iNzc3GDE5zP20VEwSdHnJuVz+dpH56rvC4D9vsgIDdIGdPepP83b8zFZkRwCXhll27ZteOyxx\/DYY4\/Z73v\/\/ffbTBcgam+C2aTWKSoS2ggNWqyC2+fytablqjlx+eTBstWewmFFFFIfUYNRXnrppTb3vfzyy5IHQxRugjUMfVf1eaz99DRarAIiNEDuff0leS7HgSWRERqYLjViV\/X5oOxiIFa4To4n5fBYo9u\/fz8++eQTfP\/991ixYoX9\/vr6epdb7hApQbCbx4JRS3GseVkFoLHZIsnj2hL1lkoT9h+\/iL1Hb46IVMrw\/WDtXScnNteGnscandVqhcVigdVqxY0bN+w\/d9xxB4qKioIVI5FoSlg1RA5yrtSRmdwLcbd1wo2Wm931Shq+H+7TCtT69xhuPNbo0tPTkZ6ejunTpyMxMTFYMRH5Ta27Sss96lCpw\/eVGpdYav17DDeiBqNs2bLF5f0vvviipMEQBSrcL4yeyNlEqtTh+0qNSyw1\/z2GE1GJTqvV2v9\/\/fp17NixA0OHDpUtKCJ\/hduFUUn9N0oYEenq9VBCXP4Kt79HtRI1j85ZY2MjJk2aZN9dQEk4j44CFazkE4r1G5WUWJ1xPcufKPl9UqqA59E502q1MJlMAQVFJCd\/LxTBHOXnbqCFXBc4pY9gZH\/WTUp\/n8KRqEQ3fvx4+1qXVqsVR44cwezZs+WMi8hvni4U3hJgMC+2zv03naIiW8Wde19\/NDZbfEp6nsonV9mkqn2wP+smJnzpiUp0S5cu\/emEyEjceeed6Nu3r2xBEQXC3YVCzDflQC62vl7wnftvnONe\/ckptFgF0d\/q5VoLM5Dn9AX7s25iwpeeqESXnp4udxxEknF3oRDzTdnfi62\/F3zngRa2uCM0QIu19bw2fzdkdSyL1InE+Tm3VJoCetxwHngiFSZ86XmcMD5gwAAkJia2+bHd701paSmSk5ORkJAAg8HgcjWVwsJCJCYmIj4+HkuWLGnz+88\/\/xxarRYFBQU+FIvaM3fLcomddO3P8ldSTGx2jHtuerzPE8Sdy2drCnWcrCz10l6p8d0R8dMOXth\/\/CInRUtASUuwqYHHGt3HH3\/s9wNbrVYYDAYUFxdDr9djypQpKCgowKxZs+zH1NfXY+HChaioqECPHj2QlpaGsrIyew2yubkZixYtQlZWlt9xUHAobZSYq5qBnN+UpWpucox7uK6rpE2hcvX1WB3Gbd9oEfDG3uOK+lsg8pjo+vXrZ\/\/\/pUuXUFlZCQAYNWoUbrvtNo8PXFlZiT59+kCv1wMAcnNzYTQaWyW6kpISZGRkoHfv3gCAWbNmoaioyJ7oVqxYgdmzZ+OTTz7xo2gULEobJeYp6doSiW2hYKkuxnIkUX+a8dw1hUrZ1+P4+m75ou3o68PfNeDwdw1+D6ghkpqoProPP\/wQTzzxBH7+858DAObMmYPVq1djwoQJbs8xm83Q6XT223FxcaitrfV6TElJCQCguroa5eXlWLZsGROdwilplJiYpCtXYg52\/5K3WrQcydf5tUvs2cXtsf4MqPE1FrXVHNVYJiUQleheeOEFfPbZZ\/Yanslkwi9+8QuPiU7MPHR3x1itVsybNw+rV6+2T2twx2g0wmg02m\/X1dV5fV6SlpJGiYlJukpKzP4Sm6ylTr7Or12P6I6IPK+Bxdr2s+zPgBqxlNaKIAU1lkkpRCW6lpaWVs2YcXFxXrfp0el0rWpwJpMJsbGxbY6pqqpqc8wPP\/yA6upqe9\/cxYsXsX37djQ3N+Pxxx9v9Rh5eXnIy8uz37Y1lVLwKGmUmJikq6TEDPj3LT5Uydr5tZt2Txym3ROH8pMX0SkqEo3Nllb\/rv30tCyvsxq+rDhTY5mUQlSi0+v1WLBgAQwGAwBg\/fr1XhNKSkoKzGYzampqoNfrsXbt2jY7kmdlZWHhwoU4d+4cevTogY0bN+Lll19GTEwMLl78adTa7Nmz8cADD+B\/\/ud\/fC0fBYlShoWLSbpyNekFcyWWUCVrd6+du5h9GVDjy2uotC8rUlBjmZRC1FqXDQ0NWL58OUpLS6HRaJCRkYFly5YhOjra43l79+7FU089haamJqSnp2PNmjXYsWMHiouLkZ+fD+DmzggvvPACrFYrpkyZgpUrV7Z5HF8SHde6JG9cXVAD6RsJZI3G5cXfYEP5t\/bbs1P7YfnkwX6XQ2pKXvdTjf1ZtjLZasVqKpvcPF37\/VrUWcmY6MgTVxdUAAEtJuycrLp16oDpo+KwKCvJ53gcRykC8q17KUYwF1kOJOGrDRe39o+na7\/HCeM2L7zwAurr62G1WvFf\/\/VfuOOOO7B161ZJg6T2wTasP1STil31gwQ62dtxojYA1DXewF9KT+KVkiNez3WcJJ57X3+s\/fQ0NpR\/i3nvfoW8TV9JujO1r699MHf3lnMH9XAT7ruqK5GoRPePf\/wDMTEx2LVrF2699VYcOnQIK1askDs2CkPOF1PH27ZvqlJevH3VKSqyze1AL7K2ZNWtU4dW9+87ckH0+csnD0Zjs8V+gbNYBdxoaT1i0Reu3gdfX\/tgJh93q9m0R0z60hM1GCUi4uaL\/vHHH+Phhx+2T\/AmcuQ8sMJWQ7HdHhN\/e9BHlTn34zQ2W1r9vrHZIsnglMzkXjhUewV\/KT1pv29sUk+fHsNxMEJkhAYazc2VRiI0bRO0J64GuPgzos\/T6yJH\/5i\/A5rU1lenpFHMaiHq03PXXXfhySefxO7du7Fs2TL8+OOPoubJUfvifDHdd+RCq9vQ3PyGGqxRZa4u+O5GtkkxatTWJ7fvyAWMTeopqo\/OkfMF7lDtFfuE67WfnsZwXVdRMbpKav6O6HP1uihpvpeSYpGSUkYxq4Wopst3330XmZmZ9qbLy5cv43e\/+53csVGYcW5yGZvUs9XtaffEBbV5yl0tRs4YFmUl4aNfpfmc5GwcF\/NtbLa0mXAthqumLynLraQ+JCXFQsolqkb3s5\/9DImJidi5cycAIC0tjQsttxO+NAu5anJxNY8qWN9U5ay9BYOnWpi39TzfmD4CWypNgIeGF3+b\/JQ030tJsZByiZpesGrVKhiNRkyePBkA8M9\/\/hNPPfUUnn76adkD9BWnF0hHjmHOwe5PCff+G3dz\/ry9L66mLTiuUuJ829f3Vkmvq5JiodDxdO0XVaN7++238eWXXyImJgYAsGzZMowaNUqRiY6kI\/WSRKHoTwmX2ps7ruL3Zz1P5\/5S59u+vrdKeF0dE1x7nXNH4ojqo+vatSu6dPlplfLOnTuja9eucsVECiH1MOf20J8SjHmCYt4Xb\/2lzrfDrclPCVNVKHx4rNFt2rQJADBy5EiMHTsW06dPh0ajwZYtW3D33XcHJUAKHamHOau9PyVYNVZ\/1\/N07i\/1dWNXJeECyOQLj310jz32mPsTNRqsW7dOlqACwT46ZVNzfwqXsZKP898Nl8kKjnD6vHKtS6Ig4MW3Nakuku5e13C6CIejcPt7DngwCgDs3r0bhw8fxvXr1+33\/frXvw48OiKV4IoWrVffd1wVJ5CLpLtmSiUMiFEzNTUPi0p0CxYswKlTp1BRUYEZM2agqKgI6enpcsdGFDC5v\/WzVvETxxpAhAawbToe6EVS7X27SqWm111U0+XQoUPx9ddfY\/jw4fj6669x6dIlTJkyBXv27AlGjD5h0yXZyN304m2umtKbeqTm3EepjdCgxSp4fS3EfFlwPuaVkiN+L7VG4oXTF7mAmy5vueUWaDQaaLVaNDY24vbbb8fZs2clDZJIalI1vbj7sG\/5wiTp3LRw5PjaONcAHPfW85TAnBcCdzzH1Vy5V0qO2BfP\/tf5HwCAyU4mamkeFjWPrl+\/fqirq8PDDz+MjIwMZGZmIinJ+x9WaWkpkpOTkZCQAIPBgJaWljbHFBYWIjExEfHx8ViyZIn9\/kWLFiEpKQnDhg3D+PHj8e2337Y5l8jG1fw1KeYBupuvtav6PD45\/tM8wA5ajSxz00K9f58nzq8NgFbraS7KSrKv2+mO85eR1Z+csj\/eKyVHXL72ztsfid0OidovUYlu69at6NatG55\/\/nn84Q9\/wPz581FYWOjxHKvVCoPBgK1bt+LEiRNoaGhAQUFBq2Pq6+uxcOFClJWV4ejRo9i3bx\/KysoAAOPGjcPhw4fx9ddfIzs7G7\/61a\/8KyGpnrtkJMVCxu4muZefvAiL9adW\/\/sHdMeirCRJF4yWY1K0lInTXY3ZW3Jz5PhlJEKDVotYu6ohA223P\/J1OyRqf0QlOkdpaWmYNGkSOnTo4PG4yspK9OnTB3q9HgCQm5uLoqKiVseUlJQgIyMDvXv3RmRkJGbNmmU\/Jisry\/4c9957L0wmk6+hUjvhacUVXy+8ztzVCp3vn3ZPnMvzA0ksgawk4+p5pUicjo8rRY3Z8cvI3PR4Uau3LMpKwryMeAzqdSvmZcSz2ZK8Er+bo4\/MZjN0Op39dlxcHGpra70eU1JS0uaxVq9ejQkTJsgVKoU5f1f5F8PdlAFX93vbeNbXWp6\/o97crdASaJ+lq8eVYjqFYz+Q2NVbFmUlMcGRaLIlOjHz0MUc89e\/\/hUHDx60N2k6MxqNMBqN9tt1dXXigyRVcJeMpFqSy3YhttVmOkVF2gdMOK584m0hZX8WTvYnkTgPkrHVBE2XG9FBq8GNFsFl4vT2pcBVogyktuyK8+AHtQyGoNCSLdHpdLpWNTiTyYTY2Ng2x1RVVbk9pqioCK+99hpKS0vxs5\/9zOXz5OXlIS8vz37b1lRK7Yu\/q\/yL5Zg0bZyTp3MNbGxST5y6eM1tjUxMbdPXC72rQTKdoiLtsUdGaDBuYA9MGxXX6nHFfClwV8MMpyHoUmhv5VUD2RJdSkoKzGYzampqoNfrsXbtWmRnZ7c6JisrCwsXLsS5c+fQo0cPbNy4ES+\/\/DIA4OOPP8bixYuxZ88e9OjRQ64wKYz4eoGRcsKrYy3Jxjl5it141lYWORaAdjVIprHZYo\/dYhUADey1PNtzivlSIKa5VmlzB6VOSkovL7nm82AUsbRaLfLz85GTk4P4+Hh06dIFM2fORHFxMQwGAwAgJiYGr776KtLS0jBw4ECkp6dj7NixAIAnn3wSjY2NmDx5MoYPH44HHnhArlApDPgzkEKKUZe253asJdm4Sp7Og19cDYbZVX0eq3Yfk2XLIleDZBzvi4zQYP\/xi21eR7EDS5zLI8fWS1KNDJVj1Gp72GpKjWSr0QE3pwg4z1SfPHmyfadyAJg2bRqmTZvW5tzjx4\/LGRr5IZRNNv42Q4pp+hPTN+VYS7q9cwcMi+3apvlPDFdNoO4Siz+vt7t+Pdt9pkuN2Hv03wDarhvpT3+g1MtESVljkmOtRjUti9WeyJroSD1cXYAA+J34QtkM6RyHmL6pdytMuNFyM9ldunYDB05ewrRRrqcUeOJ48QWAQb1uxTPjE9s8p2Ncf\/vsW8xNFz+M3lVydxxQc+DkJZevoz8DP6ReyFrK5CTH3wwX7g5PTHQkivMFaEulCQdOXPLrm7c\/39rlusCIvbA6DxB2PNaXpN0pqvVHbmxST68jHK0CsPqTUxiu6xpwueV4HaUcGSllcpLrb0aK8iplQItS4pCbbH10pC7OfTgQ4Hdfhb\/9HLb+IQCSre6RGt8dkREaADf7r1xdWJ2bLoGfmhs9LRHmKsbGZovH245x\/V9YAG6uGCJVf1Cgk+jlJGW\/6vLibwBAcWWVo+8wnOMIBiY6EsX5AjRtVJzfq2IEsqKGHB9Ojab1v86cB3OMG9jD4yRsTzH6Muhjbno8tP+X7eTuD1LSmpqBJmKlX8CVMqBFKXEEA5suSTTnJht\/m4UCaVLytQ9HzEATW9\/bjRZB9LB6G1dNbZ5i9KXsi7KS3E5PkJLahswrfcNQpQxoUUocwcBER34LpK\/C33N9+XAGMglabLzuEpenx\/Sl7MFYGUTpicFXgSydFoz+qmAMaBG7GEF7GVgjauPVcMKNV9VP7AXJeSPQ2an9Wi3Z5evjyRGjEjjvDO5phGe4lMvXOOXepDeY1FQWXwS88SpJI1wuEkontpYTaG3Nxt\/5bOHyHmcm90Luff3xdtlJWAXgr\/tdj\/AMVhOn8+sdjNdfTbVaNZVFKkx0QaK2fpBwIEXTjL\/vm7eLs9K+9Bw51wDbwNIbLQJ++89qAGgVWzAuoIHuAOHv66qm\/io1lUUqHHUZJO1phJMSSDW83J\/3zduov0BHBUq5RJb9cZxGnJqvXPd7xGggxOwA4U4gr6tU0xqUQE1lkQoTXZAE4yJBN0k5vNx5grfzbVe8JcdAN1SVomzOj5PUK9o+n9DG1Sa2ni6g3hKwmATt\/Dlxt\/mqK4F+mVTy\/EJfqaksUmDTZZC0pxFOoSZlE5vYCd6OvDUdBdK0JFXZnB+nsdmCvzwyElsqTdh\/\/GKbPescmwTdDejx1MQrtgnY1edE7BQLNtmRO0x0QRROAxQCFco+KCkveI6PFRmhgelSI3ZVn\/dYJm9fagL50iNV2VzVVG1\/n64Gg3hLUt4SsC8J2vlz4u5z4xin7Tly7+tv3xS3vXzWyDsmOpJcqAfeSFl7tj2Wraaz9+i\/ceDkJa9l8valxt8vPf6UzVVCMF1qbHWMY03VOTbnJLVq9zH7cTZy1mLdlcn2N1bwuQkaDey1UPZLkTMmOpJcKIc3e2ti80dmcq9WK6hIVSYxtV5Xx\/iSJN0lhMgIDTpoNW2aKF1xTFIA8K\/zP2D+5oNtdrCQqxbriuPfmOM6pO4ScaCUNkqWfMPBKCS5UA28kXONQ6nLJCZWXxeMdsU5IdiStcUq4P4B3UWNzLMlqUG9brXfZ9vBwjE+wPMIVykHSDivP9pB+9NAGlsilur9V\/rameSd7ImutLQUycnJSEhIgMFgQEtLS5tjCgsLkZiYiPj4eCxZssR+f0NDAyZNmoQBAwYgJSUF\/\/rXv+QOV1GL24arUA1vlnMKh9RlEhOrrwtGu9IpKtK+C4I2AvaEYNt9XGziyUzuhWfGJ\/q0g4WcnyXH9+Mvj4yEccbINolYqvefU4PCn6yJzmq1wmAwYOvWrThx4gQaGhpQUFDQ6pj6+nosXLgQZWVlOHr0KPbt24eysjIAwCuvvIIhQ4bg+PHj+O1vf4t58+bJGS6\/uUkoFMOb5a5JylUjcRerq2PEXnR3VZ\/HpDf2463Sk3DcYWjO\/Xf5naydk72nHSyC8VmyvR\/AzWTky1QEX3BqUPiTtY+usrISffr0gV6vBwDk5ubCaDRi1qxZ9mNKSkqQkZGB3r17AwBmzZqFoqIipKeno6ioCNu3bwcATJgwAXPmzMGlS5dw++23yxIvl84Jb+E0hUNMrO6O8TaoY1f1ecx796s2e+i1WIEj5xuwbvaogOJ2jNVdGYL1WXJe11GOUZfh9HdFrsma6MxmM3Q6nf12XFwcamtrvR5TUlLi8nexsbEwm82yJTrOwwl\/4TSFQ0ysrobae7voutoo1mb\/8Ytep0f4wl0ZgvVZcjUfUKpBSI7C6e+K2pI10YnZGCHQzROMRiOMRqP9dl1dnd+PxW9uFA68XXRT47uj4HOTy2Tnbs89qQXrs8QvpySGrIlOp9O1qsGZTCbExsa2OaaqqsrlMbGxsaitrcVdd90F4GYNr2\/fvq3Oz8vLQ15env22rZnUX\/zmRuEuM7mXfZUTCEBS72j7wsjBTAbB+CzxyymJIWuiS0lJgdlsRk1NDfR6PdauXYvs7OxWx2RlZWHhwoU4d+4cevTogY0bN+Lll18GAGRnZyM\/Px8rVqzAjh07kJCQgO7d+Y2NyBvnJBOMncpDhV9OyRtZE51Wq0V+fj5ycnLQ1NSE9PR0zJw5E8XFxSguLkZ+fj5iYmLw6quvIi0tDVarFVOmTMHYsWMBAIsWLcIjjzyCAQMG4NZbb8U777wjZ7hEqsVkQO0ZdxgnIqKw5+naz5VRiIhI1ZjoiIhI1ZjoiIhI1ZjoiIhI1VQ3GCU6OrrNXD0lqKurQ7du3UIdhmTUVB41lQVgeZRMTWUBlFUes9mMhoYGl79TXaJTKrWNBlVTedRUFoDlUTI1lQUIn\/Kw6ZKIiFSNiY6IiFSNiS5IHNfjVAM1lUdNZQFYHiVTU1mA8CkP++iIiEjVWKMjIiJVY6KTWG1tLf7jP\/4DgwYNQnJyMp5\/\/nkAQH5+PoYPH27\/iYqKwj\/+8Y8QR+udu\/I0NTXh0UcfxZAhQzBo0CA89dRTsFqtIY7WM3dlaWhowNSpUzFkyBAMHToUxcXFIY5UvMzMTAwfPhxDhgxBTk6OfXj14sWLkZCQgMTERBQVFYU4SvFclcdkMiEtLQ2dO3eGwWAIdYiiuSrLu+++i2HDhmHo0KFISUnB3r17Qx2maK7K89lnn9mvacnJya32BlUUgSR19uxZobKyUhAEQWhqahLuu+8+4YMPPmh1jMlkErp27Sr8+OOPoQjRJ+7Ks2bNGmH69OmCIAiCxWIRxowZI3z44YehDNUrd2VZtGiR8OyzzwqCIAh1dXXCkCFDhB9++CGUoYp25coV+\/+ffvppYdmyZcLu3buF+++\/X7BYLILZbBZ0Ol1Yl+fy5cvCgQMHhLfeekvIzc0NYXS+cVWWAwcOCBcvXhQEQRCqqqqEnj17Ci0tLaEK0SeuynPt2jXhxo0bgiAIQn19vRAXFyecPn06RBG6xxqdxHr37o2UlBQAQFRUFEaMGAGTydTqmE2bNiE7Oxu33HJLKEL0iafyXLt2DRaLBU1NTWhqakKvXsreBsZdWb755htkZWUBALp27YqkpCR89NFHoQxVtJiYGACA1WrF9evXodFoUFRUhNmzZ0Or1aJv374YM2YMdu3aFeJIxXFVnm7duiE1NTUsPi+OXJUlNTUVt99+OwBg8ODBaGpqwrVr10IZpmiuytOpUydERt7c7a2pqQktLS2hDNEtJjoZXb58GR988AHGjx\/f6v53330XM2fODFFU\/nMsz6OPPoqoqCjccccduOOOO5CZmYm777471CGK5liWESNGoLCwEFarFd999x0+\/fRT1NbWhjpE0f77v\/8bPXv2xNGjR7FgwQKYzWbodDr77+Pi4sK6POHMU1m2bNmCIUOG4NZbbw1RdL5zVZ7Dhw9jyJAhiIuLw6JFi3DnnXeGNkgXmOhk0tzcjJycHDz99NNISkqy3\/\/111\/jypUrSE9PD2F0vnMuzxdffAGLxYKzZ8+itrYW27dvR3l5eajDFMW5LM8\/\/zwiIiIwcuRIPPHEE0hPT4dWqw11mKJt27YNZ8+eRWxsLP7+979DCPOB1M7lCWfuynLw4EEsXrwY69atC2F0vnNVniFDhuDw4cOoqalBfn4+Lly4EOIo22Kik0FLSwtmzJiB4cOHt\/kWV1BQgEceeQQajSZE0fnOVXm2bNmCCRMmoGPHjujatSsyMzPx+eefhzhS71yVpXPnzli9ejUOHTqE7du3o7GxsdWXk3AQFRWFadOmYdu2bdDpdK1qcCaTSZHrv3riWJ5w51yWY8eO4aGHHsKWLVswYMCAEEfnO3fvTf\/+\/TFw4EAcOHAgRJG5x0QngyeeeAK33nor\/vjHP7a632q1YvPmzWHXbOmqPP369cOePXtgtVrR1NSE\/fv3Q6\/XhzBKcVyVpb6+Hk1NTQCAAwcO4PTp022am5Xohx9+wLlz5wDc\/NsqLi5GcnIysrOzsWHDBrS0tNibYjMzM0McrXfuyhOO3JXFbDZj4sSJeOuttzB69OgQRymeu\/KcOnUKFosFAPD999+joqICgwYNCmWoroV6NIzafPrppwIAYfDgwcKwYcOEYcOGCX\/+858FQRCEPXv2CCNGjAhxhL5xV56rV68KU6dOFQYNGiQkJSUJixcvDnWoXrkrS0VFhZCQkCAkJSUJGRkZwpEjR0IdqijfffedkJKSIgwZMkRITk4WHn\/8ceHatWuCIAjCc889J9x1111CQkKCUFhYGOJIxXFXnmvXrgl9+\/YVunXrJnTq1Eno27evsG\/fvlCH65G7shgMBiE6Otr+9zds2DBFjlJ05q4869evF\/R6vTB06FBh2LBhwsaNG0MdqktcGYWIiFSNTZdERKRqTHRERKRqTHRERKRqTHRERKRqTHRERKRqTHRERKRqTHRERKRqTHRERKRqTHREYe7QoUMYMGAA6uvrYbVaMXbsWBQWFoY6LCLF4MooRCrwyiuvoKqqCsOGDcPhw4fxt7\/9LdQhESkGEx2RClitVmRkZMBsNuPQoUOIjo4OdUhEisGmSyIVaGhowLlz5yAIAhoaGkIdDpGisEZHpAIzZszA3Xffjd69e2PdunXYvXt3WO15SCQn1uiIwtymTZtw7tw5PPvss5gxYwZ69uyJVatWhTosIsVgjY6IiFSNNToiIlI1JjoiIlI1JjoiIlI1JjoiIlI1JjoiIlI1JjoiIlI1JjoiIlI1JjoiIlK1\/w\/Jodue1T9F9gAAAABJRU5ErkJggg==\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Which we can confirm by running the tests again (which we should never do).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [27]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">p_value<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">het_breuschpagan<\/span><span class=\"p\">(<\/span><span class=\"n\">log_resid<\/span><span class=\"p\">,<\/span> <span class=\"n\">ols_model_log<\/span><span class=\"o\">.<\/span><span class=\"n\">exog<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">p_value<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[27]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>0.002154782205265498<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [28]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">p_value<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">het_white<\/span><span class=\"p\">(<\/span><span class=\"n\">log_resid<\/span><span class=\"p\">,<\/span> <span class=\"n\">ols_model_log<\/span><span class=\"o\">.<\/span><span class=\"n\">exog<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">p_value<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[28]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>0.006069762292696221<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>The p-values are bigger, which suggests that the log transform mitigated the heteroskedasticity a little.\nBut if the goal was to eliminate heteroskedasticity, the log transform didn’t do it.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<h2 id=\"Discussion\">Discussion<a class=\"anchor-link\" href=\"#Discussion\">\u00b6<\/a><\/h2><p>To summarize:<\/p>\n<ul>\n<li><p>Heteroskedasticity is common in real datasets — if you test for it, you will often find it, provided you have enough data.<\/p>\n<\/li>\n<li><p>Either way, testing does not answer the question you really care about, which is whether the heteroskedasticity is extreme enough to be a problem.<\/p>\n<\/li>\n<li><p>Plain old linear regression is robust to heteroskedasticity, so unless it is really extreme, it is probably not a problem.<\/p>\n<\/li>\n<li><p>Even in the worst case, heteroskedasticity does not bias the estimated parameters — it only affects the standard errors — and we don’t need standard errors to be particularly precise anyway.<\/p>\n<\/li>\n<li><p>Although a log transform can sometimes mitigate heteroskedasticity, it doesn’t always succeed, and even if it does, it’s usually not necessary.<\/p>\n<\/li>\n<li><p>A log transform changes the meaning of the regression model in ways that might not make sense in context.<\/p>\n<\/li>\n<\/ul>\n<p>So, use a log transform if it makes sense in context, not to mitigate a problem that’s not much of a problem in the first place.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p><a href=\"https:\/\/allendowney.github.io\/DataQnA\/index.html\"><em>Data Q&A: Answering the real questions with Python<\/em><\/a><\/p>\n<p>Copyright 2024 <a href=\"https:\/\/allendowney.com\">Allen B. Downey<\/a><\/p>\n<p>License: <a href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/\">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [ ]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span> \n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/main>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Here’s another installment in Data Q&A: Answering the real questions with Python. Previous installments are available from the Data Q&A landing page. log_heterosked Logarithms and heteroskedasticity\u00b6 Here’s a question from the Reddit statistics forum. Is it correct to use logarithmic transformation in order to mitigate heteroskedasticity? For my studies I gathered data on certain preferences across a group of people. I am trying to figure out if I can pinpoint preferences to factors such as gender in this case. I…<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/www.allendowney.com\/blog\/2024\/05\/26\/logarithms-and-heteroskedasticity\/\"> Read More<span class=\"screen-reader-text\"> Read More<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-1292","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"\n<title>Logarithms and Heteroskedasticity - Probably Overthinking It<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.allendowney.com\/blog\/2024\/05\/26\/logarithms-and-heteroskedasticity\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Logarithms and Heteroskedasticity - Probably Overthinking It\" \/>\n<meta property=\"og:description\" content=\"Here’s another installment in Data Q&A: Answering the real questions with Python. 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Previous installments are available from the Data Q&A landing page. low_percentile Bootstrapping percentiles\u00b6Here's a question from the Reddit statistics forum. I'm trying to figure out how to determine the confidence interval for the .2 percentile temperature for specific\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1262,"url":"https:\/\/www.allendowney.com\/blog\/2024\/04\/09\/data-qa\/","url_meta":{"origin":1292,"position":1},"title":"Data Q&A","author":"AllenDowney","date":"April 9, 2024","format":false,"excerpt":"Today I'm starting a new project with the working title Data Q&A: Answering the real questions with Python. In each installment, I'll take a question from Reddit's statistics forum and answer it, using Python code to demonstrate. The first installment is a question about the harmonic mean, which is a\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1271,"url":"https:\/\/www.allendowney.com\/blog\/2024\/04\/21\/what-does-strength-mean\/","url_meta":{"origin":1292,"position":2},"title":"What does “strength” mean?","author":"AllenDowney","date":"April 21, 2024","format":false,"excerpt":"Here's another installment in Data Q&A: Answering the real questions with Python. Previous installments are available from the Data Q&A landing page. corr_trend What does \"strength\" mean?\u00b6Here's a question from the Reddit statistics forum. 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I have two different samples (about 100 observations per sample) drawn from the same population (or that's what\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1278,"url":"https:\/\/www.allendowney.com\/blog\/2024\/05\/03\/the-mean-of-a-likert-scale\/","url_meta":{"origin":1292,"position":4},"title":"The mean of a Likert scale?","author":"AllenDowney","date":"May 3, 2024","format":false,"excerpt":"Here's another installment in Data Q&A: Answering the real questions with Python. Previous installments are available from the Data Q&A landing page. likert_mean Likert scale analysis\u00b6Here's a question from the Reddit statistics forum. I have collected data regarding how individuals feel about a particular program. They reported their feelings on\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1281,"url":"https:\/\/www.allendowney.com\/blog\/2024\/05\/07\/destructive-testing\/","url_meta":{"origin":1292,"position":5},"title":"Destructive Testing","author":"AllenDowney","date":"May 7, 2024","format":false,"excerpt":"Here's another installment in Data Q&A: Answering the real questions with Python. Previous installments are available from the Data Q&A landing page. sample_size Sample Size Selection\u00b6Here's a question from the Reddit statistics forum. Hi Redditors, I am a civil engineer trying to solve a statistical problem for a current project\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/1292","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/comments?post=1292"}],"version-history":[{"count":2,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/1292\/revisions"}],"predecessor-version":[{"id":1294,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/1292\/revisions\/1294"}],"wp:attachment":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/media?parent=1292"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/categories?post=1292"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/tags?post=1292"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":1292,"date":"2024-05-26T18:54:09","date_gmt":"2024-05-26T18:54:09","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=1292"},"modified":"2024-05-26T19:01:11","modified_gmt":"2024-05-26T19:01:11","slug":"logarithms-and-heteroskedasticity","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2024\/05\/26\/logarithms-and-heteroskedasticity\/","title":{"rendered":"Logarithms and Heteroskedasticity"},"content":{"rendered":"\n

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align-items: center;\n font-size: var(--jp-ui-font-size0);\n font-weight: 600;\n text-transform: uppercase;\n user-select: none;\n}\n\n.jp-Collapser-icon {\n height: 16px;\n}\n\n.jp-Collapse-header-collapsed .jp-Collapser-icon {\n transform: rotate(-90deg);\n margin: auto 0;\n}\n\n.jp-Collapser-title {\n line-height: 25px;\n}\n\n.jp-Collapse-contents {\n padding: 0 12px;\n background-color: var(--jp-layout-color1);\n color: var(--jp-ui-font-color1);\n overflow: auto;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/* This file was auto-generated by ensureUiComponents() in @jupyterlab\/buildutils *\/\n\n\/**\n * (DEPRECATED) Support for consuming icons as CSS background images\n *\/\n\n\/* Icons urls *\/\n\n:root {\n --jp-icon-add-above: 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--jp-icon-add-below: 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--jp-icon-add: url(data:image\/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNiIgdmlld0JveD0iMCAwIDI0IDI0Ij4KICA8ZyBjbGFzcz0ianAtaWNvbjMiIGZpbGw9IiM2MTYxNjEiPgogICAgPHBhdGggZD0iTTE5IDEzaC02djZoLTJ2LTZINXYtMmg2VjVoMnY2aDZ2MnoiLz4KICA8L2c+Cjwvc3ZnPgo=);\n --jp-icon-bell: 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--jp-icon-bug: url(data:image\/svg+xml;base64,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);\n --jp-icon-build: 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url(data:image\/svg+xml;base64,PHN2ZyBoZWlnaHQ9IjI0IiB2aWV3Qm94PSIwIDAgMjQgMjQiIHdpZHRoPSIyNCIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj4KICAgIDxnIGNsYXNzPSJqcC1pY29uMyIgZmlsbD0iIzYxNjE2MSI+CiAgICAgICAgPHBhdGggZD0iTTAgMGgyNHYyNEgweiIgZmlsbD0ibm9uZSIvPgogICAgICAgIDxwYXRoIGQ9Ik0yMiAxMVYzaC03djNIOVYzSDJ2OGg3VjhoMnYxMGg0djNoN3YtOGgtN3YzaC0yVjhoMnYzeiIvPgogICAgPC9nPgo8L3N2Zz4K);\n --jp-icon-trusted: url(data:image\/svg+xml;base64,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);\n --jp-icon-undo: url(data:image\/svg+xml;base64,PHN2ZyB2aWV3Qm94PSIwIDAgMjQgMjQiIHdpZHRoPSIxNiIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj4KICA8ZyBjbGFzcz0ianAtaWNvbjMiIGZpbGw9IiM2MTYxNjEiPgogICAgPHBhdGggZD0iTTEyLjUgOGMtMi42NSAwLTUuMDUuOTktNi45IDIuNkwyIDd2OWg5bC0zLjYyLTMuNjJjMS4zOS0xLjE2IDMuMTYtMS44OCA1LjEyLTEuODggMy41NCAwIDYuNTUgMi4zMSA3LjYgNS41bDIuMzctLjc4QzIxLjA4IDExLjAzIDE3LjE1IDggMTIuNSA4eiIvPgogIDwvZz4KPC9zdmc+Cg==);\n --jp-icon-user: url(data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMTYiIHZpZXdCb3g9IjAgMCAyNCAyNCIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj4KICA8ZyBjbGFzcz0ianAtaWNvbjMiIGZpbGw9IiM2MTYxNjEiPgogICAgPHBhdGggZD0iTTE2IDdhNCA0IDAgMTEtOCAwIDQgNCAwIDAxOCAwek0xMiAxNGE3IDcgMCAwMC03IDdoMTRhNyA3IDAgMDAtNy03eiIvPgogIDwvZz4KPC9zdmc+Cg==);\n --jp-icon-users: url(data:image\/svg+xml;base64,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);\n --jp-icon-vega: url(data:image\/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNiIgdmlld0JveD0iMCAwIDIyIDIyIj4KICA8ZyBjbGFzcz0ianAtaWNvbjEganAtaWNvbi1zZWxlY3RhYmxlIiBmaWxsPSIjMjEyMTIxIj4KICAgIDxwYXRoIGQ9Ik0xMC42IDUuNGwyLjItMy4ySDIuMnY3LjNsNC02LjZ6Ii8+CiAgICA8cGF0aCBkPSJNMTUuOCAyLjJsLTQuNCA2LjZMNyA2LjNsLTQuOCA4djUuNWgxNy42VjIuMmgtNHptLTcgMTUuNEg1LjV2LTQuNGgzLjN2NC40em00LjQgMEg5LjhWOS44aDMuNHY3Ljh6bTQuNCAwaC0zLjRWNi41aDMuNHYxMS4xeiIvPgogIDwvZz4KPC9zdmc+Cg==);\n --jp-icon-word: url(data:image\/svg+xml;base64,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);\n --jp-icon-yaml: url(data:image\/svg+xml;base64,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);\n}\n\n\/* Icon CSS class declarations *\/\n\n.jp-AddAboveIcon {\n background-image: var(--jp-icon-add-above);\n}\n\n.jp-AddBelowIcon {\n background-image: var(--jp-icon-add-below);\n}\n\n.jp-AddIcon {\n background-image: var(--jp-icon-add);\n}\n\n.jp-BellIcon {\n background-image: var(--jp-icon-bell);\n}\n\n.jp-BugDotIcon {\n background-image: var(--jp-icon-bug-dot);\n}\n\n.jp-BugIcon {\n background-image: var(--jp-icon-bug);\n}\n\n.jp-BuildIcon {\n background-image: var(--jp-icon-build);\n}\n\n.jp-CaretDownEmptyIcon {\n background-image: var(--jp-icon-caret-down-empty);\n}\n\n.jp-CaretDownEmptyThinIcon {\n background-image: var(--jp-icon-caret-down-empty-thin);\n}\n\n.jp-CaretDownIcon {\n background-image: var(--jp-icon-caret-down);\n}\n\n.jp-CaretLeftIcon {\n background-image: var(--jp-icon-caret-left);\n}\n\n.jp-CaretRightIcon {\n background-image: var(--jp-icon-caret-right);\n}\n\n.jp-CaretUpEmptyThinIcon {\n background-image: var(--jp-icon-caret-up-empty-thin);\n}\n\n.jp-CaretUpIcon {\n background-image: var(--jp-icon-caret-up);\n}\n\n.jp-CaseSensitiveIcon {\n background-image: var(--jp-icon-case-sensitive);\n}\n\n.jp-CheckIcon {\n background-image: var(--jp-icon-check);\n}\n\n.jp-CircleEmptyIcon {\n background-image: var(--jp-icon-circle-empty);\n}\n\n.jp-CircleIcon {\n background-image: var(--jp-icon-circle);\n}\n\n.jp-ClearIcon {\n background-image: var(--jp-icon-clear);\n}\n\n.jp-CloseIcon {\n background-image: var(--jp-icon-close);\n}\n\n.jp-CodeCheckIcon {\n background-image: var(--jp-icon-code-check);\n}\n\n.jp-CodeIcon {\n background-image: var(--jp-icon-code);\n}\n\n.jp-CollapseAllIcon {\n background-image: var(--jp-icon-collapse-all);\n}\n\n.jp-ConsoleIcon {\n background-image: var(--jp-icon-console);\n}\n\n.jp-CopyIcon {\n background-image: var(--jp-icon-copy);\n}\n\n.jp-CopyrightIcon {\n background-image: var(--jp-icon-copyright);\n}\n\n.jp-CutIcon {\n background-image: var(--jp-icon-cut);\n}\n\n.jp-DeleteIcon {\n background-image: var(--jp-icon-delete);\n}\n\n.jp-DownloadIcon {\n background-image: var(--jp-icon-download);\n}\n\n.jp-DuplicateIcon {\n background-image: var(--jp-icon-duplicate);\n}\n\n.jp-EditIcon {\n background-image: var(--jp-icon-edit);\n}\n\n.jp-EllipsesIcon {\n background-image: var(--jp-icon-ellipses);\n}\n\n.jp-ErrorIcon {\n background-image: var(--jp-icon-error);\n}\n\n.jp-ExpandAllIcon {\n background-image: var(--jp-icon-expand-all);\n}\n\n.jp-ExtensionIcon {\n background-image: var(--jp-icon-extension);\n}\n\n.jp-FastForwardIcon {\n background-image: var(--jp-icon-fast-forward);\n}\n\n.jp-FileIcon {\n background-image: var(--jp-icon-file);\n}\n\n.jp-FileUploadIcon {\n background-image: var(--jp-icon-file-upload);\n}\n\n.jp-FilterDotIcon {\n background-image: var(--jp-icon-filter-dot);\n}\n\n.jp-FilterIcon {\n background-image: var(--jp-icon-filter);\n}\n\n.jp-FilterListIcon {\n background-image: var(--jp-icon-filter-list);\n}\n\n.jp-FolderFavoriteIcon {\n background-image: var(--jp-icon-folder-favorite);\n}\n\n.jp-FolderIcon {\n background-image: var(--jp-icon-folder);\n}\n\n.jp-HomeIcon {\n background-image: var(--jp-icon-home);\n}\n\n.jp-Html5Icon {\n background-image: var(--jp-icon-html5);\n}\n\n.jp-ImageIcon {\n background-image: var(--jp-icon-image);\n}\n\n.jp-InfoIcon {\n background-image: var(--jp-icon-info);\n}\n\n.jp-InspectorIcon {\n background-image: var(--jp-icon-inspector);\n}\n\n.jp-JsonIcon {\n background-image: var(--jp-icon-json);\n}\n\n.jp-JuliaIcon {\n background-image: var(--jp-icon-julia);\n}\n\n.jp-JupyterFaviconIcon {\n background-image: var(--jp-icon-jupyter-favicon);\n}\n\n.jp-JupyterIcon {\n background-image: var(--jp-icon-jupyter);\n}\n\n.jp-JupyterlabWordmarkIcon {\n background-image: var(--jp-icon-jupyterlab-wordmark);\n}\n\n.jp-KernelIcon {\n background-image: var(--jp-icon-kernel);\n}\n\n.jp-KeyboardIcon {\n background-image: var(--jp-icon-keyboard);\n}\n\n.jp-LaunchIcon {\n background-image: var(--jp-icon-launch);\n}\n\n.jp-LauncherIcon {\n background-image: var(--jp-icon-launcher);\n}\n\n.jp-LineFormIcon {\n background-image: var(--jp-icon-line-form);\n}\n\n.jp-LinkIcon {\n background-image: var(--jp-icon-link);\n}\n\n.jp-ListIcon {\n background-image: var(--jp-icon-list);\n}\n\n.jp-MarkdownIcon {\n background-image: var(--jp-icon-markdown);\n}\n\n.jp-MoveDownIcon {\n background-image: var(--jp-icon-move-down);\n}\n\n.jp-MoveUpIcon {\n background-image: var(--jp-icon-move-up);\n}\n\n.jp-NewFolderIcon {\n background-image: var(--jp-icon-new-folder);\n}\n\n.jp-NotTrustedIcon {\n background-image: var(--jp-icon-not-trusted);\n}\n\n.jp-NotebookIcon {\n background-image: var(--jp-icon-notebook);\n}\n\n.jp-NumberingIcon {\n background-image: var(--jp-icon-numbering);\n}\n\n.jp-OfflineBoltIcon {\n background-image: var(--jp-icon-offline-bolt);\n}\n\n.jp-PaletteIcon {\n background-image: var(--jp-icon-palette);\n}\n\n.jp-PasteIcon {\n background-image: var(--jp-icon-paste);\n}\n\n.jp-PdfIcon {\n background-image: var(--jp-icon-pdf);\n}\n\n.jp-PythonIcon {\n background-image: var(--jp-icon-python);\n}\n\n.jp-RKernelIcon {\n background-image: var(--jp-icon-r-kernel);\n}\n\n.jp-ReactIcon {\n background-image: var(--jp-icon-react);\n}\n\n.jp-RedoIcon {\n background-image: var(--jp-icon-redo);\n}\n\n.jp-RefreshIcon {\n background-image: var(--jp-icon-refresh);\n}\n\n.jp-RegexIcon {\n background-image: var(--jp-icon-regex);\n}\n\n.jp-RunIcon {\n background-image: var(--jp-icon-run);\n}\n\n.jp-RunningIcon {\n background-image: var(--jp-icon-running);\n}\n\n.jp-SaveIcon {\n background-image: var(--jp-icon-save);\n}\n\n.jp-SearchIcon {\n background-image: var(--jp-icon-search);\n}\n\n.jp-SettingsIcon {\n background-image: var(--jp-icon-settings);\n}\n\n.jp-ShareIcon {\n background-image: var(--jp-icon-share);\n}\n\n.jp-SpreadsheetIcon {\n background-image: var(--jp-icon-spreadsheet);\n}\n\n.jp-StopIcon {\n background-image: var(--jp-icon-stop);\n}\n\n.jp-TabIcon {\n background-image: var(--jp-icon-tab);\n}\n\n.jp-TableRowsIcon {\n background-image: var(--jp-icon-table-rows);\n}\n\n.jp-TagIcon {\n background-image: var(--jp-icon-tag);\n}\n\n.jp-TerminalIcon {\n background-image: var(--jp-icon-terminal);\n}\n\n.jp-TextEditorIcon {\n background-image: var(--jp-icon-text-editor);\n}\n\n.jp-TocIcon {\n background-image: var(--jp-icon-toc);\n}\n\n.jp-TreeViewIcon {\n background-image: var(--jp-icon-tree-view);\n}\n\n.jp-TrustedIcon {\n background-image: var(--jp-icon-trusted);\n}\n\n.jp-UndoIcon {\n background-image: var(--jp-icon-undo);\n}\n\n.jp-UserIcon {\n background-image: var(--jp-icon-user);\n}\n\n.jp-UsersIcon {\n background-image: var(--jp-icon-users);\n}\n\n.jp-VegaIcon {\n background-image: var(--jp-icon-vega);\n}\n\n.jp-WordIcon {\n background-image: var(--jp-icon-word);\n}\n\n.jp-YamlIcon {\n background-image: var(--jp-icon-yaml);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/**\n * (DEPRECATED) Support for consuming icons as CSS background images\n *\/\n\n.jp-Icon,\n.jp-MaterialIcon {\n background-position: center;\n background-repeat: no-repeat;\n background-size: 16px;\n min-width: 16px;\n min-height: 16px;\n}\n\n.jp-Icon-cover {\n background-position: center;\n background-repeat: no-repeat;\n background-size: cover;\n}\n\n\/**\n * (DEPRECATED) Support for specific CSS icon sizes\n *\/\n\n.jp-Icon-16 {\n background-size: 16px;\n min-width: 16px;\n min-height: 16px;\n}\n\n.jp-Icon-18 {\n background-size: 18px;\n min-width: 18px;\n min-height: 18px;\n}\n\n.jp-Icon-20 {\n background-size: 20px;\n min-width: 20px;\n min-height: 20px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.lm-TabBar .lm-TabBar-addButton {\n align-items: center;\n display: flex;\n padding: 4px;\n padding-bottom: 5px;\n margin-right: 1px;\n background-color: var(--jp-layout-color2);\n}\n\n.lm-TabBar .lm-TabBar-addButton:hover {\n background-color: var(--jp-layout-color1);\n}\n\n.lm-DockPanel-tabBar .lm-TabBar-tab {\n width: var(--jp-private-horizontal-tab-width);\n}\n\n.lm-DockPanel-tabBar .lm-TabBar-content {\n flex: unset;\n}\n\n.lm-DockPanel-tabBar[data-orientation='horizontal'] {\n flex: 1 1 auto;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/**\n * Support for icons as inline SVG HTMLElements\n *\/\n\n\/* recolor the primary elements of an icon *\/\n.jp-icon0[fill] {\n fill: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon1[fill] {\n fill: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon2[fill] {\n fill: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon3[fill] {\n fill: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon4[fill] {\n fill: var(--jp-inverse-layout-color4);\n}\n\n.jp-icon0[stroke] {\n stroke: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon1[stroke] {\n stroke: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon2[stroke] {\n stroke: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon3[stroke] {\n stroke: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon4[stroke] {\n stroke: var(--jp-inverse-layout-color4);\n}\n\n\/* recolor the accent elements of an icon *\/\n.jp-icon-accent0[fill] {\n fill: var(--jp-layout-color0);\n}\n\n.jp-icon-accent1[fill] {\n fill: var(--jp-layout-color1);\n}\n\n.jp-icon-accent2[fill] {\n fill: var(--jp-layout-color2);\n}\n\n.jp-icon-accent3[fill] {\n fill: var(--jp-layout-color3);\n}\n\n.jp-icon-accent4[fill] {\n fill: var(--jp-layout-color4);\n}\n\n.jp-icon-accent0[stroke] {\n stroke: var(--jp-layout-color0);\n}\n\n.jp-icon-accent1[stroke] {\n stroke: var(--jp-layout-color1);\n}\n\n.jp-icon-accent2[stroke] {\n stroke: var(--jp-layout-color2);\n}\n\n.jp-icon-accent3[stroke] {\n stroke: var(--jp-layout-color3);\n}\n\n.jp-icon-accent4[stroke] {\n stroke: var(--jp-layout-color4);\n}\n\n\/* set the color of an icon to transparent *\/\n.jp-icon-none[fill] {\n fill: none;\n}\n\n.jp-icon-none[stroke] {\n stroke: none;\n}\n\n\/* brand icon colors. Same for light and dark *\/\n.jp-icon-brand0[fill] {\n fill: var(--jp-brand-color0);\n}\n\n.jp-icon-brand1[fill] {\n fill: var(--jp-brand-color1);\n}\n\n.jp-icon-brand2[fill] {\n fill: var(--jp-brand-color2);\n}\n\n.jp-icon-brand3[fill] {\n fill: var(--jp-brand-color3);\n}\n\n.jp-icon-brand4[fill] {\n fill: var(--jp-brand-color4);\n}\n\n.jp-icon-brand0[stroke] {\n stroke: var(--jp-brand-color0);\n}\n\n.jp-icon-brand1[stroke] {\n stroke: var(--jp-brand-color1);\n}\n\n.jp-icon-brand2[stroke] {\n stroke: var(--jp-brand-color2);\n}\n\n.jp-icon-brand3[stroke] {\n stroke: var(--jp-brand-color3);\n}\n\n.jp-icon-brand4[stroke] {\n stroke: var(--jp-brand-color4);\n}\n\n\/* warn icon colors. Same for light and dark *\/\n.jp-icon-warn0[fill] {\n fill: var(--jp-warn-color0);\n}\n\n.jp-icon-warn1[fill] {\n fill: var(--jp-warn-color1);\n}\n\n.jp-icon-warn2[fill] {\n fill: var(--jp-warn-color2);\n}\n\n.jp-icon-warn3[fill] {\n fill: var(--jp-warn-color3);\n}\n\n.jp-icon-warn0[stroke] {\n stroke: var(--jp-warn-color0);\n}\n\n.jp-icon-warn1[stroke] {\n stroke: var(--jp-warn-color1);\n}\n\n.jp-icon-warn2[stroke] {\n stroke: var(--jp-warn-color2);\n}\n\n.jp-icon-warn3[stroke] {\n stroke: var(--jp-warn-color3);\n}\n\n\/* icon colors that contrast well with each other and most backgrounds *\/\n.jp-icon-contrast0[fill] {\n fill: var(--jp-icon-contrast-color0);\n}\n\n.jp-icon-contrast1[fill] {\n fill: var(--jp-icon-contrast-color1);\n}\n\n.jp-icon-contrast2[fill] {\n fill: var(--jp-icon-contrast-color2);\n}\n\n.jp-icon-contrast3[fill] {\n fill: var(--jp-icon-contrast-color3);\n}\n\n.jp-icon-contrast0[stroke] {\n stroke: var(--jp-icon-contrast-color0);\n}\n\n.jp-icon-contrast1[stroke] {\n stroke: var(--jp-icon-contrast-color1);\n}\n\n.jp-icon-contrast2[stroke] {\n stroke: var(--jp-icon-contrast-color2);\n}\n\n.jp-icon-contrast3[stroke] {\n stroke: var(--jp-icon-contrast-color3);\n}\n\n.jp-icon-dot[fill] {\n fill: var(--jp-warn-color0);\n}\n\n.jp-jupyter-icon-color[fill] {\n fill: var(--jp-jupyter-icon-color, var(--jp-warn-color0));\n}\n\n.jp-notebook-icon-color[fill] {\n fill: var(--jp-notebook-icon-color, var(--jp-warn-color0));\n}\n\n.jp-json-icon-color[fill] {\n fill: var(--jp-json-icon-color, var(--jp-warn-color1));\n}\n\n.jp-console-icon-color[fill] {\n fill: var(--jp-console-icon-color, white);\n}\n\n.jp-console-icon-background-color[fill] {\n fill: var(--jp-console-icon-background-color, var(--jp-brand-color1));\n}\n\n.jp-terminal-icon-color[fill] {\n fill: var(--jp-terminal-icon-color, var(--jp-layout-color2));\n}\n\n.jp-terminal-icon-background-color[fill] {\n fill: var(\n --jp-terminal-icon-background-color,\n var(--jp-inverse-layout-color2)\n );\n}\n\n.jp-text-editor-icon-color[fill] {\n fill: var(--jp-text-editor-icon-color, var(--jp-inverse-layout-color3));\n}\n\n.jp-inspector-icon-color[fill] {\n fill: var(--jp-inspector-icon-color, var(--jp-inverse-layout-color3));\n}\n\n\/* CSS for icons in selected filebrowser listing items *\/\n.jp-DirListing-item.jp-mod-selected .jp-icon-selectable[fill] {\n fill: #fff;\n}\n\n.jp-DirListing-item.jp-mod-selected .jp-icon-selectable-inverse[fill] {\n fill: var(--jp-brand-color1);\n}\n\n\/* stylelint-disable selector-max-class, selector-max-compound-selectors *\/\n\n\/**\n* TODO: come up with non css-hack solution for showing the busy icon on top\n* of the close icon\n* CSS for complex behavior of close icon of tabs in the main area tabbar\n*\/\n.lm-DockPanel-tabBar\n .lm-TabBar-tab.lm-mod-closable.jp-mod-dirty\n > .lm-TabBar-tabCloseIcon\n > :not(:hover)\n > .jp-icon3[fill] {\n fill: none;\n}\n\n.lm-DockPanel-tabBar\n .lm-TabBar-tab.lm-mod-closable.jp-mod-dirty\n > .lm-TabBar-tabCloseIcon\n > :not(:hover)\n > .jp-icon-busy[fill] {\n fill: var(--jp-inverse-layout-color3);\n}\n\n\/* stylelint-enable selector-max-class, selector-max-compound-selectors *\/\n\n\/* CSS for icons in status bar *\/\n#jp-main-statusbar .jp-mod-selected .jp-icon-selectable[fill] {\n fill: #fff;\n}\n\n#jp-main-statusbar .jp-mod-selected .jp-icon-selectable-inverse[fill] {\n fill: var(--jp-brand-color1);\n}\n\n\/* special handling for splash icon CSS. While the theme CSS reloads during\n splash, the splash icon can loose theming. To prevent that, we set a\n default for its color variable *\/\n:root {\n --jp-warn-color0: var(--md-orange-700);\n}\n\n\/* not sure what to do with this one, used in filebrowser listing *\/\n.jp-DragIcon {\n margin-right: 4px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/**\n * Support for alt colors for icons as inline SVG HTMLElements\n *\/\n\n\/* alt recolor the primary elements of an icon *\/\n.jp-icon-alt .jp-icon0[fill] {\n fill: var(--jp-layout-color0);\n}\n\n.jp-icon-alt .jp-icon1[fill] {\n fill: var(--jp-layout-color1);\n}\n\n.jp-icon-alt .jp-icon2[fill] {\n fill: var(--jp-layout-color2);\n}\n\n.jp-icon-alt .jp-icon3[fill] {\n fill: var(--jp-layout-color3);\n}\n\n.jp-icon-alt .jp-icon4[fill] {\n fill: var(--jp-layout-color4);\n}\n\n.jp-icon-alt .jp-icon0[stroke] {\n stroke: var(--jp-layout-color0);\n}\n\n.jp-icon-alt .jp-icon1[stroke] {\n stroke: var(--jp-layout-color1);\n}\n\n.jp-icon-alt .jp-icon2[stroke] {\n stroke: var(--jp-layout-color2);\n}\n\n.jp-icon-alt .jp-icon3[stroke] {\n stroke: var(--jp-layout-color3);\n}\n\n.jp-icon-alt .jp-icon4[stroke] {\n stroke: var(--jp-layout-color4);\n}\n\n\/* alt recolor the accent elements of an icon *\/\n.jp-icon-alt .jp-icon-accent0[fill] {\n fill: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon-alt .jp-icon-accent1[fill] {\n fill: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon-alt .jp-icon-accent2[fill] {\n fill: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon-alt .jp-icon-accent3[fill] {\n fill: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon-alt .jp-icon-accent4[fill] {\n fill: var(--jp-inverse-layout-color4);\n}\n\n.jp-icon-alt .jp-icon-accent0[stroke] {\n stroke: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon-alt .jp-icon-accent1[stroke] {\n stroke: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon-alt .jp-icon-accent2[stroke] {\n stroke: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon-alt .jp-icon-accent3[stroke] {\n stroke: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon-alt .jp-icon-accent4[stroke] {\n stroke: var(--jp-inverse-layout-color4);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-icon-hoverShow:not(:hover) .jp-icon-hoverShow-content {\n display: none !important;\n}\n\n\/**\n * Support for hover colors for icons as inline SVG HTMLElements\n *\/\n\n\/**\n * regular colors\n *\/\n\n\/* recolor the primary elements of an icon *\/\n.jp-icon-hover :hover .jp-icon0-hover[fill] {\n fill: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon-hover :hover .jp-icon1-hover[fill] {\n fill: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon-hover :hover .jp-icon2-hover[fill] {\n fill: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon-hover :hover .jp-icon3-hover[fill] {\n fill: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon-hover :hover .jp-icon4-hover[fill] {\n fill: var(--jp-inverse-layout-color4);\n}\n\n.jp-icon-hover :hover .jp-icon0-hover[stroke] {\n stroke: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon-hover :hover .jp-icon1-hover[stroke] {\n stroke: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon-hover :hover .jp-icon2-hover[stroke] {\n stroke: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon-hover :hover .jp-icon3-hover[stroke] {\n stroke: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon-hover :hover .jp-icon4-hover[stroke] {\n stroke: var(--jp-inverse-layout-color4);\n}\n\n\/* recolor the accent elements of an icon *\/\n.jp-icon-hover :hover .jp-icon-accent0-hover[fill] {\n fill: var(--jp-layout-color0);\n}\n\n.jp-icon-hover :hover .jp-icon-accent1-hover[fill] {\n fill: var(--jp-layout-color1);\n}\n\n.jp-icon-hover :hover .jp-icon-accent2-hover[fill] {\n fill: var(--jp-layout-color2);\n}\n\n.jp-icon-hover :hover .jp-icon-accent3-hover[fill] {\n fill: var(--jp-layout-color3);\n}\n\n.jp-icon-hover :hover .jp-icon-accent4-hover[fill] {\n fill: var(--jp-layout-color4);\n}\n\n.jp-icon-hover :hover .jp-icon-accent0-hover[stroke] {\n stroke: var(--jp-layout-color0);\n}\n\n.jp-icon-hover :hover .jp-icon-accent1-hover[stroke] {\n stroke: var(--jp-layout-color1);\n}\n\n.jp-icon-hover :hover .jp-icon-accent2-hover[stroke] {\n stroke: var(--jp-layout-color2);\n}\n\n.jp-icon-hover :hover .jp-icon-accent3-hover[stroke] {\n stroke: var(--jp-layout-color3);\n}\n\n.jp-icon-hover :hover .jp-icon-accent4-hover[stroke] {\n stroke: var(--jp-layout-color4);\n}\n\n\/* set the color of an icon to transparent *\/\n.jp-icon-hover :hover .jp-icon-none-hover[fill] {\n fill: none;\n}\n\n.jp-icon-hover :hover .jp-icon-none-hover[stroke] {\n stroke: none;\n}\n\n\/**\n * inverse colors\n *\/\n\n\/* inverse recolor the primary elements of an icon *\/\n.jp-icon-hover.jp-icon-alt :hover .jp-icon0-hover[fill] {\n fill: var(--jp-layout-color0);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon1-hover[fill] {\n fill: var(--jp-layout-color1);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon2-hover[fill] {\n fill: var(--jp-layout-color2);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon3-hover[fill] {\n fill: var(--jp-layout-color3);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon4-hover[fill] {\n fill: var(--jp-layout-color4);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon0-hover[stroke] {\n stroke: var(--jp-layout-color0);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon1-hover[stroke] {\n stroke: var(--jp-layout-color1);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon2-hover[stroke] {\n stroke: var(--jp-layout-color2);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon3-hover[stroke] {\n stroke: var(--jp-layout-color3);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon4-hover[stroke] {\n stroke: var(--jp-layout-color4);\n}\n\n\/* inverse recolor the accent elements of an icon *\/\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent0-hover[fill] {\n fill: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent1-hover[fill] {\n fill: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent2-hover[fill] {\n fill: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent3-hover[fill] {\n fill: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent4-hover[fill] {\n fill: var(--jp-inverse-layout-color4);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent0-hover[stroke] {\n stroke: var(--jp-inverse-layout-color0);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent1-hover[stroke] {\n stroke: var(--jp-inverse-layout-color1);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent2-hover[stroke] {\n stroke: var(--jp-inverse-layout-color2);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent3-hover[stroke] {\n stroke: var(--jp-inverse-layout-color3);\n}\n\n.jp-icon-hover.jp-icon-alt :hover .jp-icon-accent4-hover[stroke] {\n stroke: var(--jp-inverse-layout-color4);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-IFrame {\n width: 100%;\n height: 100%;\n}\n\n.jp-IFrame > iframe {\n border: none;\n}\n\n\/*\nWhen drag events occur, `lm-mod-override-cursor` is added to the body.\nBecause iframes steal all cursor events, the following two rules are necessary\nto suppress pointer events while resize drags are occurring. There may be a\nbetter solution to this problem.\n*\/\nbody.lm-mod-override-cursor .jp-IFrame {\n position: relative;\n}\n\nbody.lm-mod-override-cursor .jp-IFrame::before {\n content: '';\n position: absolute;\n top: 0;\n left: 0;\n right: 0;\n bottom: 0;\n background: transparent;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2016, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-HoverBox {\n position: fixed;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-FormGroup-content fieldset {\n border: none;\n padding: 0;\n min-width: 0;\n width: 100%;\n}\n\n\/* stylelint-disable selector-max-type *\/\n\n.jp-FormGroup-content fieldset .jp-inputFieldWrapper input,\n.jp-FormGroup-content fieldset .jp-inputFieldWrapper select,\n.jp-FormGroup-content fieldset .jp-inputFieldWrapper textarea {\n font-size: var(--jp-content-font-size2);\n border-color: var(--jp-input-border-color);\n border-style: solid;\n border-radius: var(--jp-border-radius);\n border-width: 1px;\n padding: 6px 8px;\n background: none;\n color: var(--jp-ui-font-color0);\n height: inherit;\n}\n\n.jp-FormGroup-content fieldset input[type='checkbox'] {\n position: relative;\n top: 2px;\n margin-left: 0;\n}\n\n.jp-FormGroup-content button.jp-mod-styled {\n cursor: pointer;\n}\n\n.jp-FormGroup-content .checkbox label {\n cursor: pointer;\n font-size: var(--jp-content-font-size1);\n}\n\n.jp-FormGroup-content .jp-root > fieldset > legend {\n display: none;\n}\n\n.jp-FormGroup-content .jp-root > fieldset > p {\n display: none;\n}\n\n\/** copy of `input.jp-mod-styled:focus` style *\/\n.jp-FormGroup-content fieldset input:focus,\n.jp-FormGroup-content fieldset select:focus {\n -moz-outline-radius: unset;\n outline: var(--jp-border-width) solid var(--md-blue-500);\n outline-offset: -1px;\n box-shadow: inset 0 0 4px var(--md-blue-300);\n}\n\n.jp-FormGroup-content fieldset input:hover:not(:focus),\n.jp-FormGroup-content fieldset select:hover:not(:focus) {\n background-color: var(--jp-border-color2);\n}\n\n\/* stylelint-enable selector-max-type *\/\n\n.jp-FormGroup-content .checkbox .field-description {\n \/* Disable default description field for checkbox:\n because other widgets do not have description fields,\n we add descriptions to each widget on the field level.\n *\/\n display: none;\n}\n\n.jp-FormGroup-content #root__description {\n display: none;\n}\n\n.jp-FormGroup-content .jp-modifiedIndicator {\n width: 5px;\n background-color: var(--jp-brand-color2);\n margin-top: 0;\n margin-left: calc(var(--jp-private-settingeditor-modifier-indent) * -1);\n flex-shrink: 0;\n}\n\n.jp-FormGroup-content .jp-modifiedIndicator.jp-errorIndicator {\n background-color: var(--jp-error-color0);\n margin-right: 0.5em;\n}\n\n\/* RJSF ARRAY style *\/\n\n.jp-arrayFieldWrapper legend {\n font-size: var(--jp-content-font-size2);\n color: var(--jp-ui-font-color0);\n flex-basis: 100%;\n padding: 4px 0;\n font-weight: var(--jp-content-heading-font-weight);\n border-bottom: 1px solid var(--jp-border-color2);\n}\n\n.jp-arrayFieldWrapper .field-description {\n padding: 4px 0;\n white-space: pre-wrap;\n}\n\n.jp-arrayFieldWrapper .array-item {\n width: 100%;\n border: 1px solid var(--jp-border-color2);\n border-radius: 4px;\n margin: 4px;\n}\n\n.jp-ArrayOperations {\n display: flex;\n margin-left: 8px;\n}\n\n.jp-ArrayOperationsButton {\n margin: 2px;\n}\n\n.jp-ArrayOperationsButton .jp-icon3[fill] {\n fill: var(--jp-ui-font-color0);\n}\n\nbutton.jp-ArrayOperationsButton.jp-mod-styled:disabled {\n cursor: not-allowed;\n opacity: 0.5;\n}\n\n\/* RJSF form validation error *\/\n\n.jp-FormGroup-content .validationErrors {\n color: var(--jp-error-color0);\n}\n\n\/* Hide panel level error as duplicated the field level error *\/\n.jp-FormGroup-content .panel.errors {\n display: none;\n}\n\n\/* RJSF normal content (settings-editor) *\/\n\n.jp-FormGroup-contentNormal {\n display: flex;\n align-items: center;\n flex-wrap: wrap;\n}\n\n.jp-FormGroup-contentNormal .jp-FormGroup-contentItem {\n margin-left: 7px;\n color: var(--jp-ui-font-color0);\n}\n\n.jp-FormGroup-contentNormal .jp-FormGroup-description {\n flex-basis: 100%;\n padding: 4px 7px;\n}\n\n.jp-FormGroup-contentNormal .jp-FormGroup-default {\n flex-basis: 100%;\n padding: 4px 7px;\n}\n\n.jp-FormGroup-contentNormal .jp-FormGroup-fieldLabel {\n font-size: var(--jp-content-font-size1);\n font-weight: normal;\n min-width: 120px;\n}\n\n.jp-FormGroup-contentNormal fieldset:not(:first-child) {\n margin-left: 7px;\n}\n\n.jp-FormGroup-contentNormal .field-array-of-string .array-item {\n \/* Display `jp-ArrayOperations` buttons side-by-side with content except\n for small screens where flex-wrap will place them one below the other.\n *\/\n display: flex;\n align-items: center;\n flex-wrap: wrap;\n}\n\n.jp-FormGroup-contentNormal .jp-objectFieldWrapper .form-group {\n padding: 2px 8px 2px var(--jp-private-settingeditor-modifier-indent);\n margin-top: 2px;\n}\n\n\/* RJSF compact content (metadata-form) *\/\n\n.jp-FormGroup-content.jp-FormGroup-contentCompact {\n width: 100%;\n}\n\n.jp-FormGroup-contentCompact .form-group {\n display: flex;\n padding: 0.5em 0.2em 0.5em 0;\n}\n\n.jp-FormGroup-contentCompact\n .jp-FormGroup-compactTitle\n .jp-FormGroup-description {\n font-size: var(--jp-ui-font-size1);\n color: var(--jp-ui-font-color2);\n}\n\n.jp-FormGroup-contentCompact .jp-FormGroup-fieldLabel {\n padding-bottom: 0.3em;\n}\n\n.jp-FormGroup-contentCompact .jp-inputFieldWrapper .form-control {\n width: 100%;\n box-sizing: border-box;\n}\n\n.jp-FormGroup-contentCompact .jp-arrayFieldWrapper .jp-FormGroup-compactTitle {\n padding-bottom: 7px;\n}\n\n.jp-FormGroup-contentCompact\n .jp-objectFieldWrapper\n .jp-objectFieldWrapper\n .form-group {\n padding: 2px 8px 2px var(--jp-private-settingeditor-modifier-indent);\n margin-top: 2px;\n}\n\n.jp-FormGroup-contentCompact ul.error-detail {\n margin-block-start: 0.5em;\n margin-block-end: 0.5em;\n padding-inline-start: 1em;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n.jp-SidePanel {\n display: flex;\n flex-direction: column;\n min-width: var(--jp-sidebar-min-width);\n overflow-y: auto;\n color: var(--jp-ui-font-color1);\n background: var(--jp-layout-color1);\n font-size: var(--jp-ui-font-size1);\n}\n\n.jp-SidePanel-header {\n flex: 0 0 auto;\n display: flex;\n border-bottom: var(--jp-border-width) solid var(--jp-border-color2);\n font-size: var(--jp-ui-font-size0);\n font-weight: 600;\n letter-spacing: 1px;\n margin: 0;\n padding: 2px;\n text-transform: uppercase;\n}\n\n.jp-SidePanel-toolbar {\n flex: 0 0 auto;\n}\n\n.jp-SidePanel-content {\n flex: 1 1 auto;\n}\n\n.jp-SidePanel-toolbar,\n.jp-AccordionPanel-toolbar {\n height: var(--jp-private-toolbar-height);\n}\n\n.jp-SidePanel-toolbar.jp-Toolbar-micro {\n display: none;\n}\n\n.lm-AccordionPanel .jp-AccordionPanel-title {\n box-sizing: border-box;\n line-height: 25px;\n margin: 0;\n display: flex;\n align-items: center;\n background: var(--jp-layout-color1);\n color: var(--jp-ui-font-color1);\n border-bottom: var(--jp-border-width) solid var(--jp-toolbar-border-color);\n box-shadow: var(--jp-toolbar-box-shadow);\n font-size: var(--jp-ui-font-size0);\n}\n\n.jp-AccordionPanel-title {\n cursor: pointer;\n user-select: none;\n -moz-user-select: none;\n -webkit-user-select: none;\n text-transform: uppercase;\n}\n\n.lm-AccordionPanel[data-orientation='horizontal'] > .jp-AccordionPanel-title {\n \/* Title is rotated for horizontal accordion panel using CSS *\/\n display: block;\n transform-origin: top left;\n transform: rotate(-90deg) translate(-100%);\n}\n\n.jp-AccordionPanel-title .lm-AccordionPanel-titleLabel {\n user-select: none;\n text-overflow: ellipsis;\n white-space: nowrap;\n overflow: hidden;\n}\n\n.jp-AccordionPanel-title .lm-AccordionPanel-titleCollapser {\n transform: rotate(-90deg);\n margin: auto 0;\n height: 16px;\n}\n\n.jp-AccordionPanel-title.lm-mod-expanded .lm-AccordionPanel-titleCollapser {\n transform: rotate(0deg);\n}\n\n.lm-AccordionPanel .jp-AccordionPanel-toolbar {\n background: none;\n box-shadow: none;\n border: none;\n margin-left: auto;\n}\n\n.lm-AccordionPanel .lm-SplitPanel-handle:hover {\n background: var(--jp-layout-color3);\n}\n\n.jp-text-truncated {\n overflow: hidden;\n text-overflow: ellipsis;\n white-space: nowrap;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2017, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-Spinner {\n position: absolute;\n display: flex;\n justify-content: center;\n align-items: center;\n z-index: 10;\n left: 0;\n top: 0;\n width: 100%;\n height: 100%;\n background: var(--jp-layout-color0);\n outline: none;\n}\n\n.jp-SpinnerContent {\n font-size: 10px;\n margin: 50px auto;\n text-indent: -9999em;\n width: 3em;\n height: 3em;\n border-radius: 50%;\n background: var(--jp-brand-color3);\n background: linear-gradient(\n to right,\n #f37626 10%,\n rgba(255, 255, 255, 0) 42%\n );\n position: relative;\n animation: load3 1s infinite linear, fadeIn 1s;\n}\n\n.jp-SpinnerContent::before {\n width: 50%;\n height: 50%;\n background: #f37626;\n border-radius: 100% 0 0;\n position: absolute;\n top: 0;\n left: 0;\n content: '';\n}\n\n.jp-SpinnerContent::after {\n background: var(--jp-layout-color0);\n width: 75%;\n height: 75%;\n border-radius: 50%;\n content: '';\n margin: auto;\n position: absolute;\n top: 0;\n left: 0;\n bottom: 0;\n right: 0;\n}\n\n@keyframes fadeIn {\n 0% {\n opacity: 0;\n }\n\n 100% {\n opacity: 1;\n }\n}\n\n@keyframes load3 {\n 0% {\n transform: rotate(0deg);\n }\n\n 100% {\n transform: rotate(360deg);\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2017, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\nbutton.jp-mod-styled {\n font-size: var(--jp-ui-font-size1);\n color: var(--jp-ui-font-color0);\n border: none;\n box-sizing: border-box;\n text-align: center;\n line-height: 32px;\n height: 32px;\n padding: 0 12px;\n letter-spacing: 0.8px;\n outline: none;\n appearance: none;\n -webkit-appearance: none;\n -moz-appearance: none;\n}\n\ninput.jp-mod-styled {\n background: var(--jp-input-background);\n height: 28px;\n box-sizing: border-box;\n border: var(--jp-border-width) solid var(--jp-border-color1);\n padding-left: 7px;\n padding-right: 7px;\n font-size: var(--jp-ui-font-size2);\n color: var(--jp-ui-font-color0);\n outline: none;\n appearance: none;\n -webkit-appearance: none;\n -moz-appearance: none;\n}\n\ninput[type='checkbox'].jp-mod-styled {\n appearance: checkbox;\n -webkit-appearance: checkbox;\n -moz-appearance: checkbox;\n height: auto;\n}\n\ninput.jp-mod-styled:focus {\n border: var(--jp-border-width) solid var(--md-blue-500);\n box-shadow: inset 0 0 4px var(--md-blue-300);\n}\n\n.jp-select-wrapper {\n display: flex;\n position: relative;\n flex-direction: column;\n padding: 1px;\n background-color: var(--jp-layout-color1);\n box-sizing: border-box;\n margin-bottom: 12px;\n}\n\n.jp-select-wrapper:not(.multiple) {\n height: 28px;\n}\n\n.jp-select-wrapper.jp-mod-focused select.jp-mod-styled {\n border: var(--jp-border-width) solid var(--jp-input-active-border-color);\n box-shadow: var(--jp-input-box-shadow);\n background-color: var(--jp-input-active-background);\n}\n\nselect.jp-mod-styled:hover {\n cursor: pointer;\n color: var(--jp-ui-font-color0);\n background-color: var(--jp-input-hover-background);\n box-shadow: inset 0 0 1px rgba(0, 0, 0, 0.5);\n}\n\nselect.jp-mod-styled {\n flex: 1 1 auto;\n width: 100%;\n font-size: var(--jp-ui-font-size2);\n background: var(--jp-input-background);\n color: var(--jp-ui-font-color0);\n padding: 0 25px 0 8px;\n border: var(--jp-border-width) solid var(--jp-input-border-color);\n border-radius: 0;\n outline: none;\n appearance: none;\n -webkit-appearance: none;\n -moz-appearance: none;\n}\n\nselect.jp-mod-styled:not([multiple]) {\n height: 32px;\n}\n\nselect.jp-mod-styled[multiple] {\n max-height: 200px;\n overflow-y: auto;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-switch {\n display: flex;\n align-items: center;\n padding-left: 4px;\n padding-right: 4px;\n font-size: var(--jp-ui-font-size1);\n background-color: transparent;\n color: var(--jp-ui-font-color1);\n border: none;\n height: 20px;\n}\n\n.jp-switch:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-switch-label {\n margin-right: 5px;\n font-family: var(--jp-ui-font-family);\n}\n\n.jp-switch-track {\n cursor: pointer;\n background-color: var(--jp-switch-color, var(--jp-border-color1));\n -webkit-transition: 0.4s;\n transition: 0.4s;\n border-radius: 34px;\n height: 16px;\n width: 35px;\n position: relative;\n}\n\n.jp-switch-track::before {\n content: '';\n position: absolute;\n height: 10px;\n width: 10px;\n margin: 3px;\n left: 0;\n background-color: var(--jp-ui-inverse-font-color1);\n -webkit-transition: 0.4s;\n transition: 0.4s;\n border-radius: 50%;\n}\n\n.jp-switch[aria-checked='true'] .jp-switch-track {\n background-color: var(--jp-switch-true-position-color, var(--jp-warn-color0));\n}\n\n.jp-switch[aria-checked='true'] .jp-switch-track::before {\n \/* track width (35) - margins (3 + 3) - thumb width (10) *\/\n left: 19px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2016, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-private-toolbar-height: calc(\n 28px + var(--jp-border-width)\n ); \/* leave 28px for content *\/\n}\n\n.jp-Toolbar {\n color: var(--jp-ui-font-color1);\n flex: 0 0 auto;\n display: flex;\n flex-direction: row;\n border-bottom: var(--jp-border-width) solid var(--jp-toolbar-border-color);\n box-shadow: var(--jp-toolbar-box-shadow);\n background: var(--jp-toolbar-background);\n min-height: var(--jp-toolbar-micro-height);\n padding: 2px;\n z-index: 8;\n overflow-x: hidden;\n}\n\n\/* Toolbar items *\/\n\n.jp-Toolbar > .jp-Toolbar-item.jp-Toolbar-spacer {\n flex-grow: 1;\n flex-shrink: 1;\n}\n\n.jp-Toolbar-item.jp-Toolbar-kernelStatus {\n display: inline-block;\n width: 32px;\n background-repeat: no-repeat;\n background-position: center;\n background-size: 16px;\n}\n\n.jp-Toolbar > .jp-Toolbar-item {\n flex: 0 0 auto;\n display: flex;\n padding-left: 1px;\n padding-right: 1px;\n font-size: var(--jp-ui-font-size1);\n line-height: var(--jp-private-toolbar-height);\n height: 100%;\n}\n\n\/* Toolbar buttons *\/\n\n\/* This is the div we use to wrap the react component into a Widget *\/\ndiv.jp-ToolbarButton {\n color: transparent;\n border: none;\n box-sizing: border-box;\n outline: none;\n appearance: none;\n -webkit-appearance: none;\n -moz-appearance: none;\n padding: 0;\n margin: 0;\n}\n\nbutton.jp-ToolbarButtonComponent {\n background: var(--jp-layout-color1);\n border: none;\n box-sizing: border-box;\n outline: none;\n appearance: none;\n -webkit-appearance: none;\n -moz-appearance: none;\n padding: 0 6px;\n margin: 0;\n height: 24px;\n border-radius: var(--jp-border-radius);\n display: flex;\n align-items: center;\n text-align: center;\n font-size: 14px;\n min-width: unset;\n min-height: unset;\n}\n\nbutton.jp-ToolbarButtonComponent:disabled {\n opacity: 0.4;\n}\n\nbutton.jp-ToolbarButtonComponent > span {\n padding: 0;\n flex: 0 0 auto;\n}\n\nbutton.jp-ToolbarButtonComponent .jp-ToolbarButtonComponent-label {\n font-size: var(--jp-ui-font-size1);\n line-height: 100%;\n padding-left: 2px;\n color: var(--jp-ui-font-color1);\n font-family: var(--jp-ui-font-family);\n}\n\n#jp-main-dock-panel[data-mode='single-document']\n .jp-MainAreaWidget\n > .jp-Toolbar.jp-Toolbar-micro {\n padding: 0;\n min-height: 0;\n}\n\n#jp-main-dock-panel[data-mode='single-document']\n .jp-MainAreaWidget\n > .jp-Toolbar {\n border: none;\n box-shadow: none;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n.jp-WindowedPanel-outer {\n position: relative;\n overflow-y: auto;\n}\n\n.jp-WindowedPanel-inner {\n position: relative;\n}\n\n.jp-WindowedPanel-window {\n position: absolute;\n left: 0;\n right: 0;\n overflow: visible;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/* Sibling imports *\/\n\nbody {\n color: var(--jp-ui-font-color1);\n font-size: var(--jp-ui-font-size1);\n}\n\n\/* Disable native link decoration styles everywhere outside of dialog boxes *\/\na {\n text-decoration: unset;\n color: unset;\n}\n\na:hover {\n text-decoration: unset;\n color: unset;\n}\n\n\/* Accessibility for links inside dialog box text *\/\n.jp-Dialog-content a {\n text-decoration: revert;\n color: var(--jp-content-link-color);\n}\n\n.jp-Dialog-content a:hover {\n text-decoration: revert;\n}\n\n\/* Styles for ui-components *\/\n.jp-Button {\n color: var(--jp-ui-font-color2);\n border-radius: var(--jp-border-radius);\n padding: 0 12px;\n font-size: var(--jp-ui-font-size1);\n\n \/* Copy from blueprint 3 *\/\n display: inline-flex;\n flex-direction: row;\n border: none;\n cursor: pointer;\n align-items: center;\n justify-content: center;\n text-align: left;\n vertical-align: middle;\n min-height: 30px;\n min-width: 30px;\n}\n\n.jp-Button:disabled {\n cursor: not-allowed;\n}\n\n.jp-Button:empty {\n padding: 0 !important;\n}\n\n.jp-Button.jp-mod-small {\n min-height: 24px;\n min-width: 24px;\n font-size: 12px;\n padding: 0 7px;\n}\n\n\/* Use our own theme for hover styles *\/\n.jp-Button.jp-mod-minimal:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-Button.jp-mod-minimal {\n background: none;\n}\n\n.jp-InputGroup {\n display: block;\n position: relative;\n}\n\n.jp-InputGroup input {\n box-sizing: border-box;\n border: none;\n border-radius: 0;\n background-color: transparent;\n color: var(--jp-ui-font-color0);\n box-shadow: inset 0 0 0 var(--jp-border-width) var(--jp-input-border-color);\n padding-bottom: 0;\n padding-top: 0;\n padding-left: 10px;\n padding-right: 28px;\n position: relative;\n width: 100%;\n -webkit-appearance: none;\n -moz-appearance: none;\n appearance: none;\n font-size: 14px;\n font-weight: 400;\n height: 30px;\n line-height: 30px;\n outline: none;\n vertical-align: middle;\n}\n\n.jp-InputGroup input:focus {\n box-shadow: inset 0 0 0 var(--jp-border-width)\n var(--jp-input-active-box-shadow-color),\n inset 0 0 0 3px var(--jp-input-active-box-shadow-color);\n}\n\n.jp-InputGroup input:disabled {\n cursor: not-allowed;\n resize: block;\n background-color: var(--jp-layout-color2);\n color: var(--jp-ui-font-color2);\n}\n\n.jp-InputGroup input:disabled ~ span {\n cursor: not-allowed;\n color: var(--jp-ui-font-color2);\n}\n\n.jp-InputGroup input::placeholder,\ninput::placeholder {\n color: var(--jp-ui-font-color2);\n}\n\n.jp-InputGroupAction {\n position: absolute;\n bottom: 1px;\n right: 0;\n padding: 6px;\n}\n\n.jp-HTMLSelect.jp-DefaultStyle select {\n background-color: initial;\n border: none;\n border-radius: 0;\n box-shadow: none;\n color: var(--jp-ui-font-color0);\n display: block;\n font-size: var(--jp-ui-font-size1);\n font-family: var(--jp-ui-font-family);\n height: 24px;\n line-height: 14px;\n padding: 0 25px 0 10px;\n text-align: left;\n -moz-appearance: none;\n -webkit-appearance: none;\n}\n\n.jp-HTMLSelect.jp-DefaultStyle select:disabled {\n background-color: var(--jp-layout-color2);\n color: var(--jp-ui-font-color2);\n cursor: not-allowed;\n resize: block;\n}\n\n.jp-HTMLSelect.jp-DefaultStyle select:disabled ~ span {\n cursor: not-allowed;\n}\n\n\/* Use our own theme for hover and option styles *\/\n\/* stylelint-disable-next-line selector-max-type *\/\n.jp-HTMLSelect.jp-DefaultStyle select:hover,\n.jp-HTMLSelect.jp-DefaultStyle select > option {\n background-color: var(--jp-layout-color2);\n color: var(--jp-ui-font-color0);\n}\n\nselect {\n box-sizing: border-box;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Styles\n|----------------------------------------------------------------------------*\/\n\n.jp-StatusBar-Widget {\n display: flex;\n align-items: center;\n background: var(--jp-layout-color2);\n min-height: var(--jp-statusbar-height);\n justify-content: space-between;\n padding: 0 10px;\n}\n\n.jp-StatusBar-Left {\n display: flex;\n align-items: center;\n flex-direction: row;\n}\n\n.jp-StatusBar-Middle {\n display: flex;\n align-items: center;\n}\n\n.jp-StatusBar-Right {\n display: flex;\n align-items: center;\n flex-direction: row-reverse;\n}\n\n.jp-StatusBar-Item {\n max-height: var(--jp-statusbar-height);\n margin: 0 2px;\n height: var(--jp-statusbar-height);\n white-space: nowrap;\n text-overflow: ellipsis;\n color: var(--jp-ui-font-color1);\n padding: 0 6px;\n}\n\n.jp-mod-highlighted:hover {\n background-color: var(--jp-layout-color3);\n}\n\n.jp-mod-clicked {\n background-color: var(--jp-brand-color1);\n}\n\n.jp-mod-clicked:hover {\n background-color: var(--jp-brand-color0);\n}\n\n.jp-mod-clicked .jp-StatusBar-TextItem {\n color: var(--jp-ui-inverse-font-color1);\n}\n\n.jp-StatusBar-HoverItem {\n box-shadow: '0px 4px 4px rgba(0, 0, 0, 0.25)';\n}\n\n.jp-StatusBar-TextItem {\n font-size: var(--jp-ui-font-size1);\n font-family: var(--jp-ui-font-family);\n line-height: 24px;\n color: var(--jp-ui-font-color1);\n}\n\n.jp-StatusBar-GroupItem {\n display: flex;\n align-items: center;\n flex-direction: row;\n}\n\n.jp-Statusbar-ProgressCircle svg {\n display: block;\n margin: 0 auto;\n width: 16px;\n height: 24px;\n align-self: normal;\n}\n\n.jp-Statusbar-ProgressCircle path {\n fill: var(--jp-inverse-layout-color3);\n}\n\n.jp-Statusbar-ProgressBar-progress-bar {\n height: 10px;\n width: 100px;\n border: solid 0.25px var(--jp-brand-color2);\n border-radius: 3px;\n overflow: hidden;\n align-self: center;\n}\n\n.jp-Statusbar-ProgressBar-progress-bar > div {\n background-color: var(--jp-brand-color2);\n background-image: linear-gradient(\n -45deg,\n rgba(255, 255, 255, 0.2) 25%,\n transparent 25%,\n transparent 50%,\n rgba(255, 255, 255, 0.2) 50%,\n rgba(255, 255, 255, 0.2) 75%,\n transparent 75%,\n transparent\n );\n background-size: 40px 40px;\n float: left;\n width: 0%;\n height: 100%;\n font-size: 12px;\n line-height: 14px;\n color: #fff;\n text-align: center;\n animation: jp-Statusbar-ExecutionTime-progress-bar 2s linear infinite;\n}\n\n.jp-Statusbar-ProgressBar-progress-bar p {\n color: var(--jp-ui-font-color1);\n font-family: var(--jp-ui-font-family);\n font-size: var(--jp-ui-font-size1);\n line-height: 10px;\n width: 100px;\n}\n\n@keyframes jp-Statusbar-ExecutionTime-progress-bar {\n 0% {\n background-position: 0 0;\n }\n\n 100% {\n background-position: 40px 40px;\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Variables\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-private-commandpalette-search-height: 28px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Overall styles\n|----------------------------------------------------------------------------*\/\n\n.lm-CommandPalette {\n padding-bottom: 0;\n color: var(--jp-ui-font-color1);\n background: var(--jp-layout-color1);\n\n \/* This is needed so that all font sizing of children done in ems is\n * relative to this base size *\/\n font-size: var(--jp-ui-font-size1);\n}\n\n\/*-----------------------------------------------------------------------------\n| Modal variant\n|----------------------------------------------------------------------------*\/\n\n.jp-ModalCommandPalette {\n position: absolute;\n z-index: 10000;\n top: 38px;\n left: 30%;\n margin: 0;\n padding: 4px;\n width: 40%;\n box-shadow: var(--jp-elevation-z4);\n border-radius: 4px;\n background: var(--jp-layout-color0);\n}\n\n.jp-ModalCommandPalette .lm-CommandPalette {\n max-height: 40vh;\n}\n\n.jp-ModalCommandPalette .lm-CommandPalette .lm-close-icon::after {\n display: none;\n}\n\n.jp-ModalCommandPalette .lm-CommandPalette .lm-CommandPalette-header {\n display: none;\n}\n\n.jp-ModalCommandPalette .lm-CommandPalette .lm-CommandPalette-item {\n margin-left: 4px;\n margin-right: 4px;\n}\n\n.jp-ModalCommandPalette\n .lm-CommandPalette\n .lm-CommandPalette-item.lm-mod-disabled {\n display: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Search\n|----------------------------------------------------------------------------*\/\n\n.lm-CommandPalette-search {\n padding: 4px;\n background-color: var(--jp-layout-color1);\n z-index: 2;\n}\n\n.lm-CommandPalette-wrapper {\n overflow: overlay;\n padding: 0 9px;\n background-color: var(--jp-input-active-background);\n height: 30px;\n box-shadow: inset 0 0 0 var(--jp-border-width) var(--jp-input-border-color);\n}\n\n.lm-CommandPalette.lm-mod-focused .lm-CommandPalette-wrapper {\n box-shadow: inset 0 0 0 1px var(--jp-input-active-box-shadow-color),\n inset 0 0 0 3px var(--jp-input-active-box-shadow-color);\n}\n\n.jp-SearchIconGroup {\n color: white;\n background-color: var(--jp-brand-color1);\n position: absolute;\n top: 4px;\n right: 4px;\n padding: 5px 5px 1px;\n}\n\n.jp-SearchIconGroup svg {\n height: 20px;\n width: 20px;\n}\n\n.jp-SearchIconGroup .jp-icon3[fill] {\n fill: var(--jp-layout-color0);\n}\n\n.lm-CommandPalette-input {\n background: transparent;\n width: calc(100% - 18px);\n float: left;\n border: none;\n outline: none;\n font-size: var(--jp-ui-font-size1);\n color: var(--jp-ui-font-color0);\n line-height: var(--jp-private-commandpalette-search-height);\n}\n\n.lm-CommandPalette-input::-webkit-input-placeholder,\n.lm-CommandPalette-input::-moz-placeholder,\n.lm-CommandPalette-input:-ms-input-placeholder {\n color: var(--jp-ui-font-color2);\n font-size: var(--jp-ui-font-size1);\n}\n\n\/*-----------------------------------------------------------------------------\n| Results\n|----------------------------------------------------------------------------*\/\n\n.lm-CommandPalette-header:first-child {\n margin-top: 0;\n}\n\n.lm-CommandPalette-header {\n border-bottom: solid var(--jp-border-width) var(--jp-border-color2);\n color: var(--jp-ui-font-color1);\n cursor: pointer;\n display: flex;\n font-size: var(--jp-ui-font-size0);\n font-weight: 600;\n letter-spacing: 1px;\n margin-top: 8px;\n padding: 8px 0 8px 12px;\n text-transform: uppercase;\n}\n\n.lm-CommandPalette-header.lm-mod-active {\n background: var(--jp-layout-color2);\n}\n\n.lm-CommandPalette-header > mark {\n background-color: transparent;\n font-weight: bold;\n color: var(--jp-ui-font-color1);\n}\n\n.lm-CommandPalette-item {\n padding: 4px 12px 4px 4px;\n color: var(--jp-ui-font-color1);\n font-size: var(--jp-ui-font-size1);\n font-weight: 400;\n display: flex;\n}\n\n.lm-CommandPalette-item.lm-mod-disabled {\n color: var(--jp-ui-font-color2);\n}\n\n.lm-CommandPalette-item.lm-mod-active {\n color: var(--jp-ui-inverse-font-color1);\n background: var(--jp-brand-color1);\n}\n\n.lm-CommandPalette-item.lm-mod-active .lm-CommandPalette-itemLabel > mark {\n color: var(--jp-ui-inverse-font-color0);\n}\n\n.lm-CommandPalette-item.lm-mod-active .jp-icon-selectable[fill] {\n fill: var(--jp-layout-color0);\n}\n\n.lm-CommandPalette-item.lm-mod-active:hover:not(.lm-mod-disabled) {\n color: var(--jp-ui-inverse-font-color1);\n background: var(--jp-brand-color1);\n}\n\n.lm-CommandPalette-item:hover:not(.lm-mod-active):not(.lm-mod-disabled) {\n background: var(--jp-layout-color2);\n}\n\n.lm-CommandPalette-itemContent {\n overflow: hidden;\n}\n\n.lm-CommandPalette-itemLabel > mark {\n color: var(--jp-ui-font-color0);\n background-color: transparent;\n font-weight: bold;\n}\n\n.lm-CommandPalette-item.lm-mod-disabled mark {\n color: var(--jp-ui-font-color2);\n}\n\n.lm-CommandPalette-item .lm-CommandPalette-itemIcon {\n margin: 0 4px 0 0;\n position: relative;\n width: 16px;\n top: 2px;\n flex: 0 0 auto;\n}\n\n.lm-CommandPalette-item.lm-mod-disabled .lm-CommandPalette-itemIcon {\n opacity: 0.6;\n}\n\n.lm-CommandPalette-item .lm-CommandPalette-itemShortcut {\n flex: 0 0 auto;\n}\n\n.lm-CommandPalette-itemCaption {\n display: none;\n}\n\n.lm-CommandPalette-content {\n background-color: var(--jp-layout-color1);\n}\n\n.lm-CommandPalette-content:empty::after {\n content: 'No results';\n margin: auto;\n margin-top: 20px;\n width: 100px;\n display: block;\n font-size: var(--jp-ui-font-size2);\n font-family: var(--jp-ui-font-family);\n font-weight: lighter;\n}\n\n.lm-CommandPalette-emptyMessage {\n text-align: center;\n margin-top: 24px;\n line-height: 1.32;\n padding: 0 8px;\n color: var(--jp-content-font-color3);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2017, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-Dialog {\n position: absolute;\n z-index: 10000;\n display: flex;\n flex-direction: column;\n align-items: center;\n justify-content: center;\n top: 0;\n left: 0;\n margin: 0;\n padding: 0;\n width: 100%;\n height: 100%;\n background: var(--jp-dialog-background);\n}\n\n.jp-Dialog-content {\n display: flex;\n flex-direction: column;\n margin-left: auto;\n margin-right: auto;\n background: var(--jp-layout-color1);\n padding: 24px 24px 12px;\n min-width: 300px;\n min-height: 150px;\n max-width: 1000px;\n max-height: 500px;\n box-sizing: border-box;\n box-shadow: var(--jp-elevation-z20);\n word-wrap: break-word;\n border-radius: var(--jp-border-radius);\n\n \/* This is needed so that all font sizing of children done in ems is\n * relative to this base size *\/\n font-size: var(--jp-ui-font-size1);\n color: var(--jp-ui-font-color1);\n resize: both;\n}\n\n.jp-Dialog-content.jp-Dialog-content-small {\n max-width: 500px;\n}\n\n.jp-Dialog-button {\n overflow: visible;\n}\n\nbutton.jp-Dialog-button:focus {\n outline: 1px solid var(--jp-brand-color1);\n outline-offset: 4px;\n -moz-outline-radius: 0;\n}\n\nbutton.jp-Dialog-button:focus::-moz-focus-inner {\n border: 0;\n}\n\nbutton.jp-Dialog-button.jp-mod-styled.jp-mod-accept:focus,\nbutton.jp-Dialog-button.jp-mod-styled.jp-mod-warn:focus,\nbutton.jp-Dialog-button.jp-mod-styled.jp-mod-reject:focus {\n outline-offset: 4px;\n -moz-outline-radius: 0;\n}\n\nbutton.jp-Dialog-button.jp-mod-styled.jp-mod-accept:focus {\n outline: 1px solid var(--jp-accept-color-normal, var(--jp-brand-color1));\n}\n\nbutton.jp-Dialog-button.jp-mod-styled.jp-mod-warn:focus {\n outline: 1px solid var(--jp-warn-color-normal, var(--jp-error-color1));\n}\n\nbutton.jp-Dialog-button.jp-mod-styled.jp-mod-reject:focus {\n outline: 1px solid var(--jp-reject-color-normal, var(--md-grey-600));\n}\n\nbutton.jp-Dialog-close-button {\n padding: 0;\n height: 100%;\n min-width: unset;\n min-height: unset;\n}\n\n.jp-Dialog-header {\n display: flex;\n justify-content: space-between;\n flex: 0 0 auto;\n padding-bottom: 12px;\n font-size: var(--jp-ui-font-size3);\n font-weight: 400;\n color: var(--jp-ui-font-color1);\n}\n\n.jp-Dialog-body {\n display: flex;\n flex-direction: column;\n flex: 1 1 auto;\n font-size: var(--jp-ui-font-size1);\n background: var(--jp-layout-color1);\n color: var(--jp-ui-font-color1);\n overflow: auto;\n}\n\n.jp-Dialog-footer {\n display: flex;\n flex-direction: row;\n justify-content: flex-end;\n align-items: center;\n flex: 0 0 auto;\n margin-left: -12px;\n margin-right: -12px;\n padding: 12px;\n}\n\n.jp-Dialog-checkbox {\n padding-right: 5px;\n}\n\n.jp-Dialog-checkbox > input:focus-visible {\n outline: 1px solid var(--jp-input-active-border-color);\n outline-offset: 1px;\n}\n\n.jp-Dialog-spacer {\n flex: 1 1 auto;\n}\n\n.jp-Dialog-title {\n overflow: hidden;\n white-space: nowrap;\n text-overflow: ellipsis;\n}\n\n.jp-Dialog-body > .jp-select-wrapper {\n width: 100%;\n}\n\n.jp-Dialog-body > button {\n padding: 0 16px;\n}\n\n.jp-Dialog-body > label {\n line-height: 1.4;\n color: var(--jp-ui-font-color0);\n}\n\n.jp-Dialog-button.jp-mod-styled:not(:last-child) {\n margin-right: 12px;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n.jp-Input-Boolean-Dialog {\n flex-direction: row-reverse;\n align-items: end;\n width: 100%;\n}\n\n.jp-Input-Boolean-Dialog > label {\n flex: 1 1 auto;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2016, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-MainAreaWidget > :focus {\n outline: none;\n}\n\n.jp-MainAreaWidget .jp-MainAreaWidget-error {\n padding: 6px;\n}\n\n.jp-MainAreaWidget .jp-MainAreaWidget-error > pre {\n width: auto;\n padding: 10px;\n background: var(--jp-error-color3);\n border: var(--jp-border-width) solid var(--jp-error-color1);\n border-radius: var(--jp-border-radius);\n color: var(--jp-ui-font-color1);\n font-size: var(--jp-ui-font-size1);\n white-space: pre-wrap;\n word-wrap: break-word;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/**\n * google-material-color v1.2.6\n * https:\/\/github.com\/danlevan\/google-material-color\n *\/\n:root {\n --md-red-50: #ffebee;\n --md-red-100: #ffcdd2;\n --md-red-200: #ef9a9a;\n --md-red-300: #e57373;\n --md-red-400: #ef5350;\n --md-red-500: #f44336;\n --md-red-600: #e53935;\n --md-red-700: #d32f2f;\n --md-red-800: #c62828;\n --md-red-900: #b71c1c;\n --md-red-A100: #ff8a80;\n --md-red-A200: #ff5252;\n --md-red-A400: #ff1744;\n --md-red-A700: #d50000;\n --md-pink-50: #fce4ec;\n --md-pink-100: #f8bbd0;\n --md-pink-200: #f48fb1;\n --md-pink-300: #f06292;\n --md-pink-400: #ec407a;\n --md-pink-500: #e91e63;\n --md-pink-600: #d81b60;\n --md-pink-700: #c2185b;\n --md-pink-800: #ad1457;\n --md-pink-900: #880e4f;\n --md-pink-A100: #ff80ab;\n --md-pink-A200: #ff4081;\n --md-pink-A400: #f50057;\n --md-pink-A700: #c51162;\n --md-purple-50: #f3e5f5;\n --md-purple-100: #e1bee7;\n --md-purple-200: #ce93d8;\n --md-purple-300: #ba68c8;\n --md-purple-400: #ab47bc;\n --md-purple-500: #9c27b0;\n --md-purple-600: #8e24aa;\n --md-purple-700: #7b1fa2;\n --md-purple-800: #6a1b9a;\n --md-purple-900: #4a148c;\n --md-purple-A100: #ea80fc;\n --md-purple-A200: #e040fb;\n --md-purple-A400: #d500f9;\n --md-purple-A700: #a0f;\n --md-deep-purple-50: #ede7f6;\n --md-deep-purple-100: #d1c4e9;\n --md-deep-purple-200: #b39ddb;\n --md-deep-purple-300: #9575cd;\n --md-deep-purple-400: #7e57c2;\n --md-deep-purple-500: #673ab7;\n --md-deep-purple-600: #5e35b1;\n --md-deep-purple-700: #512da8;\n --md-deep-purple-800: #4527a0;\n --md-deep-purple-900: #311b92;\n --md-deep-purple-A100: #b388ff;\n --md-deep-purple-A200: #7c4dff;\n --md-deep-purple-A400: #651fff;\n --md-deep-purple-A700: #6200ea;\n --md-indigo-50: #e8eaf6;\n --md-indigo-100: #c5cae9;\n --md-indigo-200: #9fa8da;\n --md-indigo-300: #7986cb;\n --md-indigo-400: #5c6bc0;\n --md-indigo-500: #3f51b5;\n --md-indigo-600: #3949ab;\n --md-indigo-700: #303f9f;\n --md-indigo-800: #283593;\n --md-indigo-900: #1a237e;\n --md-indigo-A100: #8c9eff;\n --md-indigo-A200: #536dfe;\n --md-indigo-A400: #3d5afe;\n --md-indigo-A700: #304ffe;\n --md-blue-50: #e3f2fd;\n --md-blue-100: #bbdefb;\n --md-blue-200: #90caf9;\n --md-blue-300: #64b5f6;\n --md-blue-400: #42a5f5;\n --md-blue-500: #2196f3;\n --md-blue-600: #1e88e5;\n --md-blue-700: #1976d2;\n --md-blue-800: #1565c0;\n --md-blue-900: #0d47a1;\n --md-blue-A100: #82b1ff;\n --md-blue-A200: #448aff;\n --md-blue-A400: #2979ff;\n --md-blue-A700: #2962ff;\n --md-light-blue-50: #e1f5fe;\n --md-light-blue-100: #b3e5fc;\n --md-light-blue-200: #81d4fa;\n --md-light-blue-300: #4fc3f7;\n --md-light-blue-400: #29b6f6;\n --md-light-blue-500: #03a9f4;\n --md-light-blue-600: #039be5;\n --md-light-blue-700: #0288d1;\n --md-light-blue-800: #0277bd;\n --md-light-blue-900: #01579b;\n --md-light-blue-A100: #80d8ff;\n --md-light-blue-A200: #40c4ff;\n --md-light-blue-A400: #00b0ff;\n --md-light-blue-A700: #0091ea;\n --md-cyan-50: #e0f7fa;\n --md-cyan-100: #b2ebf2;\n --md-cyan-200: #80deea;\n --md-cyan-300: #4dd0e1;\n --md-cyan-400: #26c6da;\n --md-cyan-500: #00bcd4;\n --md-cyan-600: #00acc1;\n --md-cyan-700: #0097a7;\n --md-cyan-800: #00838f;\n --md-cyan-900: #006064;\n --md-cyan-A100: #84ffff;\n --md-cyan-A200: #18ffff;\n --md-cyan-A400: #00e5ff;\n --md-cyan-A700: #00b8d4;\n --md-teal-50: #e0f2f1;\n --md-teal-100: #b2dfdb;\n --md-teal-200: #80cbc4;\n --md-teal-300: #4db6ac;\n --md-teal-400: #26a69a;\n --md-teal-500: #009688;\n --md-teal-600: #00897b;\n --md-teal-700: #00796b;\n --md-teal-800: #00695c;\n --md-teal-900: #004d40;\n --md-teal-A100: #a7ffeb;\n --md-teal-A200: #64ffda;\n --md-teal-A400: #1de9b6;\n --md-teal-A700: #00bfa5;\n --md-green-50: #e8f5e9;\n --md-green-100: #c8e6c9;\n --md-green-200: #a5d6a7;\n --md-green-300: #81c784;\n --md-green-400: #66bb6a;\n --md-green-500: #4caf50;\n --md-green-600: #43a047;\n --md-green-700: #388e3c;\n --md-green-800: #2e7d32;\n --md-green-900: #1b5e20;\n --md-green-A100: #b9f6ca;\n --md-green-A200: #69f0ae;\n --md-green-A400: #00e676;\n --md-green-A700: #00c853;\n --md-light-green-50: #f1f8e9;\n --md-light-green-100: #dcedc8;\n --md-light-green-200: #c5e1a5;\n --md-light-green-300: #aed581;\n --md-light-green-400: #9ccc65;\n --md-light-green-500: #8bc34a;\n --md-light-green-600: #7cb342;\n --md-light-green-700: #689f38;\n --md-light-green-800: #558b2f;\n --md-light-green-900: #33691e;\n --md-light-green-A100: #ccff90;\n --md-light-green-A200: #b2ff59;\n --md-light-green-A400: #76ff03;\n --md-light-green-A700: #64dd17;\n --md-lime-50: #f9fbe7;\n --md-lime-100: #f0f4c3;\n --md-lime-200: #e6ee9c;\n --md-lime-300: #dce775;\n --md-lime-400: #d4e157;\n --md-lime-500: #cddc39;\n --md-lime-600: #c0ca33;\n --md-lime-700: #afb42b;\n --md-lime-800: #9e9d24;\n --md-lime-900: #827717;\n --md-lime-A100: #f4ff81;\n --md-lime-A200: #eeff41;\n --md-lime-A400: #c6ff00;\n --md-lime-A700: #aeea00;\n --md-yellow-50: #fffde7;\n --md-yellow-100: #fff9c4;\n --md-yellow-200: #fff59d;\n --md-yellow-300: #fff176;\n --md-yellow-400: #ffee58;\n --md-yellow-500: #ffeb3b;\n --md-yellow-600: #fdd835;\n --md-yellow-700: #fbc02d;\n --md-yellow-800: #f9a825;\n --md-yellow-900: #f57f17;\n --md-yellow-A100: #ffff8d;\n --md-yellow-A200: #ff0;\n --md-yellow-A400: #ffea00;\n --md-yellow-A700: #ffd600;\n --md-amber-50: #fff8e1;\n --md-amber-100: #ffecb3;\n --md-amber-200: #ffe082;\n --md-amber-300: #ffd54f;\n --md-amber-400: #ffca28;\n --md-amber-500: #ffc107;\n --md-amber-600: #ffb300;\n --md-amber-700: #ffa000;\n --md-amber-800: #ff8f00;\n --md-amber-900: #ff6f00;\n --md-amber-A100: #ffe57f;\n --md-amber-A200: #ffd740;\n --md-amber-A400: #ffc400;\n --md-amber-A700: #ffab00;\n --md-orange-50: #fff3e0;\n --md-orange-100: #ffe0b2;\n --md-orange-200: #ffcc80;\n --md-orange-300: #ffb74d;\n --md-orange-400: #ffa726;\n --md-orange-500: #ff9800;\n --md-orange-600: #fb8c00;\n --md-orange-700: #f57c00;\n --md-orange-800: #ef6c00;\n --md-orange-900: #e65100;\n --md-orange-A100: #ffd180;\n --md-orange-A200: #ffab40;\n --md-orange-A400: #ff9100;\n --md-orange-A700: #ff6d00;\n --md-deep-orange-50: #fbe9e7;\n --md-deep-orange-100: #ffccbc;\n --md-deep-orange-200: #ffab91;\n --md-deep-orange-300: #ff8a65;\n --md-deep-orange-400: #ff7043;\n --md-deep-orange-500: #ff5722;\n --md-deep-orange-600: #f4511e;\n --md-deep-orange-700: #e64a19;\n --md-deep-orange-800: #d84315;\n --md-deep-orange-900: #bf360c;\n --md-deep-orange-A100: #ff9e80;\n --md-deep-orange-A200: #ff6e40;\n --md-deep-orange-A400: #ff3d00;\n --md-deep-orange-A700: #dd2c00;\n --md-brown-50: #efebe9;\n --md-brown-100: #d7ccc8;\n --md-brown-200: #bcaaa4;\n --md-brown-300: #a1887f;\n --md-brown-400: #8d6e63;\n --md-brown-500: #795548;\n --md-brown-600: #6d4c41;\n --md-brown-700: #5d4037;\n --md-brown-800: #4e342e;\n --md-brown-900: #3e2723;\n --md-grey-50: #fafafa;\n --md-grey-100: #f5f5f5;\n --md-grey-200: #eee;\n --md-grey-300: #e0e0e0;\n --md-grey-400: #bdbdbd;\n --md-grey-500: #9e9e9e;\n --md-grey-600: #757575;\n --md-grey-700: #616161;\n --md-grey-800: #424242;\n --md-grey-900: #212121;\n --md-blue-grey-50: #eceff1;\n --md-blue-grey-100: #cfd8dc;\n --md-blue-grey-200: #b0bec5;\n --md-blue-grey-300: #90a4ae;\n --md-blue-grey-400: #78909c;\n --md-blue-grey-500: #607d8b;\n --md-blue-grey-600: #546e7a;\n --md-blue-grey-700: #455a64;\n --md-blue-grey-800: #37474f;\n --md-blue-grey-900: #263238;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2017, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| RenderedText\n|----------------------------------------------------------------------------*\/\n\n:root {\n \/* This is the padding value to fill the gaps between lines containing spans with background color. *\/\n --jp-private-code-span-padding: calc(\n (var(--jp-code-line-height) - 1) * var(--jp-code-font-size) \/ 2\n );\n}\n\n.jp-RenderedText {\n text-align: left;\n padding-left: var(--jp-code-padding);\n line-height: var(--jp-code-line-height);\n font-family: var(--jp-code-font-family);\n}\n\n.jp-RenderedText pre,\n.jp-RenderedJavaScript pre,\n.jp-RenderedHTMLCommon pre {\n color: var(--jp-content-font-color1);\n font-size: var(--jp-code-font-size);\n border: none;\n margin: 0;\n padding: 0;\n}\n\n.jp-RenderedText pre a:link {\n text-decoration: none;\n color: var(--jp-content-link-color);\n}\n\n.jp-RenderedText pre a:hover {\n text-decoration: underline;\n color: var(--jp-content-link-color);\n}\n\n.jp-RenderedText pre a:visited {\n text-decoration: none;\n color: var(--jp-content-link-color);\n}\n\n\/* console foregrounds and backgrounds *\/\n.jp-RenderedText pre .ansi-black-fg {\n color: #3e424d;\n}\n\n.jp-RenderedText pre .ansi-red-fg {\n color: #e75c58;\n}\n\n.jp-RenderedText pre .ansi-green-fg {\n color: #00a250;\n}\n\n.jp-RenderedText pre .ansi-yellow-fg {\n color: #ddb62b;\n}\n\n.jp-RenderedText pre .ansi-blue-fg {\n color: #208ffb;\n}\n\n.jp-RenderedText pre .ansi-magenta-fg {\n color: #d160c4;\n}\n\n.jp-RenderedText pre .ansi-cyan-fg {\n color: #60c6c8;\n}\n\n.jp-RenderedText pre .ansi-white-fg {\n color: #c5c1b4;\n}\n\n.jp-RenderedText pre .ansi-black-bg {\n background-color: #3e424d;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-red-bg {\n background-color: #e75c58;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-green-bg {\n background-color: #00a250;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-yellow-bg {\n background-color: #ddb62b;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-blue-bg {\n background-color: #208ffb;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-magenta-bg {\n background-color: #d160c4;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-cyan-bg {\n background-color: #60c6c8;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-white-bg {\n background-color: #c5c1b4;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-black-intense-fg {\n color: #282c36;\n}\n\n.jp-RenderedText pre .ansi-red-intense-fg {\n color: #b22b31;\n}\n\n.jp-RenderedText pre .ansi-green-intense-fg {\n color: #007427;\n}\n\n.jp-RenderedText pre .ansi-yellow-intense-fg {\n color: #b27d12;\n}\n\n.jp-RenderedText pre .ansi-blue-intense-fg {\n color: #0065ca;\n}\n\n.jp-RenderedText pre .ansi-magenta-intense-fg {\n color: #a03196;\n}\n\n.jp-RenderedText pre .ansi-cyan-intense-fg {\n color: #258f8f;\n}\n\n.jp-RenderedText pre .ansi-white-intense-fg {\n color: #a1a6b2;\n}\n\n.jp-RenderedText pre .ansi-black-intense-bg {\n background-color: #282c36;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-red-intense-bg {\n background-color: #b22b31;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-green-intense-bg {\n background-color: #007427;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-yellow-intense-bg {\n background-color: #b27d12;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-blue-intense-bg {\n background-color: #0065ca;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-magenta-intense-bg {\n background-color: #a03196;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-cyan-intense-bg {\n background-color: #258f8f;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-white-intense-bg {\n background-color: #a1a6b2;\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-default-inverse-fg {\n color: var(--jp-ui-inverse-font-color0);\n}\n\n.jp-RenderedText pre .ansi-default-inverse-bg {\n background-color: var(--jp-inverse-layout-color0);\n padding: var(--jp-private-code-span-padding) 0;\n}\n\n.jp-RenderedText pre .ansi-bold {\n font-weight: bold;\n}\n\n.jp-RenderedText pre .ansi-underline {\n text-decoration: underline;\n}\n\n.jp-RenderedText[data-mime-type='application\/vnd.jupyter.stderr'] {\n background: var(--jp-rendermime-error-background);\n padding-top: var(--jp-code-padding);\n}\n\n\/*-----------------------------------------------------------------------------\n| RenderedLatex\n|----------------------------------------------------------------------------*\/\n\n.jp-RenderedLatex {\n color: var(--jp-content-font-color1);\n font-size: var(--jp-content-font-size1);\n line-height: var(--jp-content-line-height);\n}\n\n\/* Left-justify outputs.*\/\n.jp-OutputArea-output.jp-RenderedLatex {\n padding: var(--jp-code-padding);\n text-align: left;\n}\n\n\/*-----------------------------------------------------------------------------\n| RenderedHTML\n|----------------------------------------------------------------------------*\/\n\n.jp-RenderedHTMLCommon {\n color: var(--jp-content-font-color1);\n font-family: var(--jp-content-font-family);\n font-size: var(--jp-content-font-size1);\n line-height: var(--jp-content-line-height);\n\n \/* Give a bit more R padding on Markdown text to keep line lengths reasonable *\/\n padding-right: 20px;\n}\n\n.jp-RenderedHTMLCommon em {\n font-style: italic;\n}\n\n.jp-RenderedHTMLCommon strong {\n font-weight: bold;\n}\n\n.jp-RenderedHTMLCommon u {\n text-decoration: underline;\n}\n\n.jp-RenderedHTMLCommon a:link {\n text-decoration: none;\n color: var(--jp-content-link-color);\n}\n\n.jp-RenderedHTMLCommon a:hover {\n text-decoration: underline;\n color: var(--jp-content-link-color);\n}\n\n.jp-RenderedHTMLCommon a:visited {\n text-decoration: none;\n color: var(--jp-content-link-color);\n}\n\n\/* Headings *\/\n\n.jp-RenderedHTMLCommon h1,\n.jp-RenderedHTMLCommon h2,\n.jp-RenderedHTMLCommon h3,\n.jp-RenderedHTMLCommon h4,\n.jp-RenderedHTMLCommon h5,\n.jp-RenderedHTMLCommon h6 {\n line-height: var(--jp-content-heading-line-height);\n font-weight: var(--jp-content-heading-font-weight);\n font-style: normal;\n margin: var(--jp-content-heading-margin-top) 0\n var(--jp-content-heading-margin-bottom) 0;\n}\n\n.jp-RenderedHTMLCommon h1:first-child,\n.jp-RenderedHTMLCommon h2:first-child,\n.jp-RenderedHTMLCommon h3:first-child,\n.jp-RenderedHTMLCommon h4:first-child,\n.jp-RenderedHTMLCommon h5:first-child,\n.jp-RenderedHTMLCommon h6:first-child {\n margin-top: calc(0.5 * var(--jp-content-heading-margin-top));\n}\n\n.jp-RenderedHTMLCommon h1:last-child,\n.jp-RenderedHTMLCommon h2:last-child,\n.jp-RenderedHTMLCommon h3:last-child,\n.jp-RenderedHTMLCommon h4:last-child,\n.jp-RenderedHTMLCommon h5:last-child,\n.jp-RenderedHTMLCommon h6:last-child {\n margin-bottom: calc(0.5 * var(--jp-content-heading-margin-bottom));\n}\n\n.jp-RenderedHTMLCommon h1 {\n font-size: var(--jp-content-font-size5);\n}\n\n.jp-RenderedHTMLCommon h2 {\n font-size: var(--jp-content-font-size4);\n}\n\n.jp-RenderedHTMLCommon h3 {\n font-size: var(--jp-content-font-size3);\n}\n\n.jp-RenderedHTMLCommon h4 {\n font-size: var(--jp-content-font-size2);\n}\n\n.jp-RenderedHTMLCommon h5 {\n font-size: var(--jp-content-font-size1);\n}\n\n.jp-RenderedHTMLCommon h6 {\n font-size: var(--jp-content-font-size0);\n}\n\n\/* Lists *\/\n\n\/* stylelint-disable selector-max-type, selector-max-compound-selectors *\/\n\n.jp-RenderedHTMLCommon ul:not(.list-inline),\n.jp-RenderedHTMLCommon ol:not(.list-inline) {\n padding-left: 2em;\n}\n\n.jp-RenderedHTMLCommon ul {\n list-style: disc;\n}\n\n.jp-RenderedHTMLCommon ul ul {\n list-style: square;\n}\n\n.jp-RenderedHTMLCommon ul ul ul {\n list-style: circle;\n}\n\n.jp-RenderedHTMLCommon ol {\n list-style: decimal;\n}\n\n.jp-RenderedHTMLCommon ol ol {\n list-style: upper-alpha;\n}\n\n.jp-RenderedHTMLCommon ol ol ol {\n list-style: lower-alpha;\n}\n\n.jp-RenderedHTMLCommon ol ol ol ol {\n list-style: lower-roman;\n}\n\n.jp-RenderedHTMLCommon ol ol ol ol ol {\n list-style: decimal;\n}\n\n.jp-RenderedHTMLCommon ol,\n.jp-RenderedHTMLCommon ul {\n margin-bottom: 1em;\n}\n\n.jp-RenderedHTMLCommon ul ul,\n.jp-RenderedHTMLCommon ul ol,\n.jp-RenderedHTMLCommon ol ul,\n.jp-RenderedHTMLCommon ol ol {\n margin-bottom: 0;\n}\n\n\/* stylelint-enable selector-max-type, selector-max-compound-selectors *\/\n\n.jp-RenderedHTMLCommon hr {\n color: var(--jp-border-color2);\n background-color: var(--jp-border-color1);\n margin-top: 1em;\n margin-bottom: 1em;\n}\n\n.jp-RenderedHTMLCommon > pre {\n margin: 1.5em 2em;\n}\n\n.jp-RenderedHTMLCommon pre,\n.jp-RenderedHTMLCommon code {\n border: 0;\n background-color: var(--jp-layout-color0);\n color: var(--jp-content-font-color1);\n font-family: var(--jp-code-font-family);\n font-size: inherit;\n line-height: var(--jp-code-line-height);\n padding: 0;\n white-space: pre-wrap;\n}\n\n.jp-RenderedHTMLCommon :not(pre) > code {\n background-color: var(--jp-layout-color2);\n padding: 1px 5px;\n}\n\n\/* Tables *\/\n\n.jp-RenderedHTMLCommon table {\n border-collapse: collapse;\n border-spacing: 0;\n border: none;\n color: var(--jp-ui-font-color1);\n font-size: var(--jp-ui-font-size1);\n table-layout: fixed;\n margin-left: auto;\n margin-bottom: 1em;\n margin-right: auto;\n}\n\n.jp-RenderedHTMLCommon thead {\n border-bottom: var(--jp-border-width) solid var(--jp-border-color1);\n vertical-align: bottom;\n}\n\n.jp-RenderedHTMLCommon td,\n.jp-RenderedHTMLCommon th,\n.jp-RenderedHTMLCommon tr {\n vertical-align: middle;\n padding: 0.5em;\n line-height: normal;\n white-space: normal;\n max-width: none;\n border: none;\n}\n\n.jp-RenderedMarkdown.jp-RenderedHTMLCommon td,\n.jp-RenderedMarkdown.jp-RenderedHTMLCommon th {\n max-width: none;\n}\n\n:not(.jp-RenderedMarkdown).jp-RenderedHTMLCommon td,\n:not(.jp-RenderedMarkdown).jp-RenderedHTMLCommon th,\n:not(.jp-RenderedMarkdown).jp-RenderedHTMLCommon tr {\n text-align: right;\n}\n\n.jp-RenderedHTMLCommon th {\n font-weight: bold;\n}\n\n.jp-RenderedHTMLCommon tbody tr:nth-child(odd) {\n background: var(--jp-layout-color0);\n}\n\n.jp-RenderedHTMLCommon tbody tr:nth-child(even) {\n background: var(--jp-rendermime-table-row-background);\n}\n\n.jp-RenderedHTMLCommon tbody tr:hover {\n background: var(--jp-rendermime-table-row-hover-background);\n}\n\n.jp-RenderedHTMLCommon p {\n text-align: left;\n margin: 0;\n margin-bottom: 1em;\n}\n\n.jp-RenderedHTMLCommon img {\n -moz-force-broken-image-icon: 1;\n}\n\n\/* Restrict to direct children as other images could be nested in other content. *\/\n.jp-RenderedHTMLCommon > img {\n display: block;\n margin-left: 0;\n margin-right: 0;\n margin-bottom: 1em;\n}\n\n\/* Change color behind transparent images if they need it... *\/\n[data-jp-theme-light='false'] .jp-RenderedImage img.jp-needs-light-background {\n background-color: var(--jp-inverse-layout-color1);\n}\n\n[data-jp-theme-light='true'] .jp-RenderedImage img.jp-needs-dark-background {\n background-color: var(--jp-inverse-layout-color1);\n}\n\n.jp-RenderedHTMLCommon img,\n.jp-RenderedImage img,\n.jp-RenderedHTMLCommon svg,\n.jp-RenderedSVG svg {\n max-width: 100%;\n height: auto;\n}\n\n.jp-RenderedHTMLCommon img.jp-mod-unconfined,\n.jp-RenderedImage img.jp-mod-unconfined,\n.jp-RenderedHTMLCommon svg.jp-mod-unconfined,\n.jp-RenderedSVG svg.jp-mod-unconfined {\n max-width: none;\n}\n\n.jp-RenderedHTMLCommon .alert {\n padding: var(--jp-notebook-padding);\n border: var(--jp-border-width) solid transparent;\n border-radius: var(--jp-border-radius);\n margin-bottom: 1em;\n}\n\n.jp-RenderedHTMLCommon .alert-info {\n color: var(--jp-info-color0);\n background-color: var(--jp-info-color3);\n border-color: var(--jp-info-color2);\n}\n\n.jp-RenderedHTMLCommon .alert-info hr {\n border-color: var(--jp-info-color3);\n}\n\n.jp-RenderedHTMLCommon .alert-info > p:last-child,\n.jp-RenderedHTMLCommon .alert-info > ul:last-child {\n margin-bottom: 0;\n}\n\n.jp-RenderedHTMLCommon .alert-warning {\n color: var(--jp-warn-color0);\n background-color: var(--jp-warn-color3);\n border-color: var(--jp-warn-color2);\n}\n\n.jp-RenderedHTMLCommon .alert-warning hr {\n border-color: var(--jp-warn-color3);\n}\n\n.jp-RenderedHTMLCommon .alert-warning > p:last-child,\n.jp-RenderedHTMLCommon .alert-warning > ul:last-child {\n margin-bottom: 0;\n}\n\n.jp-RenderedHTMLCommon .alert-success {\n color: var(--jp-success-color0);\n background-color: var(--jp-success-color3);\n border-color: var(--jp-success-color2);\n}\n\n.jp-RenderedHTMLCommon .alert-success hr {\n border-color: var(--jp-success-color3);\n}\n\n.jp-RenderedHTMLCommon .alert-success > p:last-child,\n.jp-RenderedHTMLCommon .alert-success > ul:last-child {\n margin-bottom: 0;\n}\n\n.jp-RenderedHTMLCommon .alert-danger {\n color: var(--jp-error-color0);\n background-color: var(--jp-error-color3);\n border-color: var(--jp-error-color2);\n}\n\n.jp-RenderedHTMLCommon .alert-danger hr {\n border-color: var(--jp-error-color3);\n}\n\n.jp-RenderedHTMLCommon .alert-danger > p:last-child,\n.jp-RenderedHTMLCommon .alert-danger > ul:last-child {\n margin-bottom: 0;\n}\n\n.jp-RenderedHTMLCommon blockquote {\n margin: 1em 2em;\n padding: 0 1em;\n border-left: 5px solid var(--jp-border-color2);\n}\n\na.jp-InternalAnchorLink {\n visibility: hidden;\n margin-left: 8px;\n color: var(--md-blue-800);\n}\n\nh1:hover .jp-InternalAnchorLink,\nh2:hover .jp-InternalAnchorLink,\nh3:hover .jp-InternalAnchorLink,\nh4:hover .jp-InternalAnchorLink,\nh5:hover .jp-InternalAnchorLink,\nh6:hover .jp-InternalAnchorLink {\n visibility: visible;\n}\n\n.jp-RenderedHTMLCommon kbd {\n background-color: var(--jp-rendermime-table-row-background);\n border: 1px solid var(--jp-border-color0);\n border-bottom-color: var(--jp-border-color2);\n border-radius: 3px;\n box-shadow: inset 0 -1px 0 rgba(0, 0, 0, 0.25);\n display: inline-block;\n font-size: var(--jp-ui-font-size0);\n line-height: 1em;\n padding: 0.2em 0.5em;\n}\n\n\/* Most direct children of .jp-RenderedHTMLCommon have a margin-bottom of 1.0.\n * At the bottom of cells this is a bit too much as there is also spacing\n * between cells. Going all the way to 0 gets too tight between markdown and\n * code cells.\n *\/\n.jp-RenderedHTMLCommon > *:last-child {\n margin-bottom: 0.5em;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Copyright (c) 2014-2017, PhosphorJS Contributors\n|\n| Distributed under the terms of the BSD 3-Clause License.\n|\n| The full license is in the file LICENSE, distributed with this software.\n|----------------------------------------------------------------------------*\/\n\n.lm-cursor-backdrop {\n position: fixed;\n width: 200px;\n height: 200px;\n margin-top: -100px;\n margin-left: -100px;\n will-change: transform;\n z-index: 100;\n}\n\n.lm-mod-drag-image {\n will-change: transform;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n.jp-lineFormSearch {\n padding: 4px 12px;\n background-color: var(--jp-layout-color2);\n box-shadow: var(--jp-toolbar-box-shadow);\n z-index: 2;\n font-size: var(--jp-ui-font-size1);\n}\n\n.jp-lineFormCaption {\n font-size: var(--jp-ui-font-size0);\n line-height: var(--jp-ui-font-size1);\n margin-top: 4px;\n color: var(--jp-ui-font-color0);\n}\n\n.jp-baseLineForm {\n border: none;\n border-radius: 0;\n position: absolute;\n background-size: 16px;\n background-repeat: no-repeat;\n background-position: center;\n outline: none;\n}\n\n.jp-lineFormButtonContainer {\n top: 4px;\n right: 8px;\n height: 24px;\n padding: 0 12px;\n width: 12px;\n}\n\n.jp-lineFormButtonIcon {\n top: 0;\n right: 0;\n background-color: var(--jp-brand-color1);\n height: 100%;\n width: 100%;\n box-sizing: border-box;\n padding: 4px 6px;\n}\n\n.jp-lineFormButton {\n top: 0;\n right: 0;\n background-color: transparent;\n height: 100%;\n width: 100%;\n box-sizing: border-box;\n}\n\n.jp-lineFormWrapper {\n overflow: hidden;\n padding: 0 8px;\n border: 1px solid var(--jp-border-color0);\n background-color: var(--jp-input-active-background);\n height: 22px;\n}\n\n.jp-lineFormWrapperFocusWithin {\n border: var(--jp-border-width) solid var(--md-blue-500);\n box-shadow: inset 0 0 4px var(--md-blue-300);\n}\n\n.jp-lineFormInput {\n background: transparent;\n width: 200px;\n height: 100%;\n border: none;\n outline: none;\n color: var(--jp-ui-font-color0);\n line-height: 28px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) 2014-2016, Jupyter Development Team.\n|\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-JSONEditor {\n display: flex;\n flex-direction: column;\n width: 100%;\n}\n\n.jp-JSONEditor-host {\n flex: 1 1 auto;\n border: var(--jp-border-width) solid var(--jp-input-border-color);\n border-radius: 0;\n background: var(--jp-layout-color0);\n min-height: 50px;\n padding: 1px;\n}\n\n.jp-JSONEditor.jp-mod-error .jp-JSONEditor-host {\n border-color: red;\n outline-color: red;\n}\n\n.jp-JSONEditor-header {\n display: flex;\n flex: 1 0 auto;\n padding: 0 0 0 12px;\n}\n\n.jp-JSONEditor-header label {\n flex: 0 0 auto;\n}\n\n.jp-JSONEditor-commitButton {\n height: 16px;\n width: 16px;\n background-size: 18px;\n background-repeat: no-repeat;\n background-position: center;\n}\n\n.jp-JSONEditor-host.jp-mod-focused {\n background-color: var(--jp-input-active-background);\n border: 1px solid var(--jp-input-active-border-color);\n box-shadow: var(--jp-input-box-shadow);\n}\n\n.jp-Editor.jp-mod-dropTarget {\n border: var(--jp-border-width) solid var(--jp-input-active-border-color);\n box-shadow: var(--jp-input-box-shadow);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n.jp-DocumentSearch-input {\n border: none;\n outline: none;\n color: var(--jp-ui-font-color0);\n font-size: var(--jp-ui-font-size1);\n background-color: var(--jp-layout-color0);\n font-family: var(--jp-ui-font-family);\n padding: 2px 1px;\n resize: none;\n}\n\n.jp-DocumentSearch-overlay {\n position: absolute;\n background-color: var(--jp-toolbar-background);\n border-bottom: var(--jp-border-width) solid var(--jp-toolbar-border-color);\n border-left: var(--jp-border-width) solid var(--jp-toolbar-border-color);\n top: 0;\n right: 0;\n z-index: 7;\n min-width: 405px;\n padding: 2px;\n font-size: var(--jp-ui-font-size1);\n\n --jp-private-document-search-button-height: 20px;\n}\n\n.jp-DocumentSearch-overlay button {\n background-color: var(--jp-toolbar-background);\n outline: 0;\n}\n\n.jp-DocumentSearch-overlay button:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-DocumentSearch-overlay button:active {\n background-color: var(--jp-layout-color3);\n}\n\n.jp-DocumentSearch-overlay-row {\n display: flex;\n align-items: center;\n margin-bottom: 2px;\n}\n\n.jp-DocumentSearch-button-content {\n display: inline-block;\n cursor: pointer;\n box-sizing: border-box;\n width: 100%;\n height: 100%;\n}\n\n.jp-DocumentSearch-button-content svg {\n width: 100%;\n height: 100%;\n}\n\n.jp-DocumentSearch-input-wrapper {\n border: var(--jp-border-width) solid var(--jp-border-color0);\n display: flex;\n background-color: var(--jp-layout-color0);\n margin: 2px;\n}\n\n.jp-DocumentSearch-input-wrapper:focus-within {\n border-color: var(--jp-cell-editor-active-border-color);\n}\n\n.jp-DocumentSearch-toggle-wrapper,\n.jp-DocumentSearch-button-wrapper {\n all: initial;\n overflow: hidden;\n display: inline-block;\n border: none;\n box-sizing: border-box;\n}\n\n.jp-DocumentSearch-toggle-wrapper {\n width: 14px;\n height: 14px;\n}\n\n.jp-DocumentSearch-button-wrapper {\n width: var(--jp-private-document-search-button-height);\n height: var(--jp-private-document-search-button-height);\n}\n\n.jp-DocumentSearch-toggle-wrapper:focus,\n.jp-DocumentSearch-button-wrapper:focus {\n outline: var(--jp-border-width) solid\n var(--jp-cell-editor-active-border-color);\n outline-offset: -1px;\n}\n\n.jp-DocumentSearch-toggle-wrapper,\n.jp-DocumentSearch-button-wrapper,\n.jp-DocumentSearch-button-content:focus {\n outline: none;\n}\n\n.jp-DocumentSearch-toggle-placeholder {\n width: 5px;\n}\n\n.jp-DocumentSearch-input-button::before {\n display: block;\n padding-top: 100%;\n}\n\n.jp-DocumentSearch-input-button-off {\n opacity: var(--jp-search-toggle-off-opacity);\n}\n\n.jp-DocumentSearch-input-button-off:hover {\n opacity: var(--jp-search-toggle-hover-opacity);\n}\n\n.jp-DocumentSearch-input-button-on {\n opacity: var(--jp-search-toggle-on-opacity);\n}\n\n.jp-DocumentSearch-index-counter {\n padding-left: 10px;\n padding-right: 10px;\n user-select: none;\n min-width: 35px;\n display: inline-block;\n}\n\n.jp-DocumentSearch-up-down-wrapper {\n display: inline-block;\n padding-right: 2px;\n margin-left: auto;\n white-space: nowrap;\n}\n\n.jp-DocumentSearch-spacer {\n margin-left: auto;\n}\n\n.jp-DocumentSearch-up-down-wrapper button {\n outline: 0;\n border: none;\n width: var(--jp-private-document-search-button-height);\n height: var(--jp-private-document-search-button-height);\n vertical-align: middle;\n margin: 1px 5px 2px;\n}\n\n.jp-DocumentSearch-up-down-button:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-DocumentSearch-up-down-button:active {\n background-color: var(--jp-layout-color3);\n}\n\n.jp-DocumentSearch-filter-button {\n border-radius: var(--jp-border-radius);\n}\n\n.jp-DocumentSearch-filter-button:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-DocumentSearch-filter-button-enabled {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-DocumentSearch-filter-button-enabled:hover {\n background-color: var(--jp-layout-color3);\n}\n\n.jp-DocumentSearch-search-options {\n padding: 0 8px;\n margin-left: 3px;\n width: 100%;\n display: grid;\n justify-content: start;\n grid-template-columns: 1fr 1fr;\n align-items: center;\n justify-items: stretch;\n}\n\n.jp-DocumentSearch-search-filter-disabled {\n color: var(--jp-ui-font-color2);\n}\n\n.jp-DocumentSearch-search-filter {\n display: flex;\n align-items: center;\n user-select: none;\n}\n\n.jp-DocumentSearch-regex-error {\n color: var(--jp-error-color0);\n}\n\n.jp-DocumentSearch-replace-button-wrapper {\n overflow: hidden;\n display: inline-block;\n box-sizing: border-box;\n border: var(--jp-border-width) solid var(--jp-border-color0);\n margin: auto 2px;\n padding: 1px 4px;\n height: calc(var(--jp-private-document-search-button-height) + 2px);\n}\n\n.jp-DocumentSearch-replace-button-wrapper:focus {\n border: var(--jp-border-width) solid var(--jp-cell-editor-active-border-color);\n}\n\n.jp-DocumentSearch-replace-button {\n display: inline-block;\n text-align: center;\n cursor: pointer;\n box-sizing: border-box;\n color: var(--jp-ui-font-color1);\n\n \/* height - 2 * (padding of wrapper) *\/\n line-height: calc(var(--jp-private-document-search-button-height) - 2px);\n width: 100%;\n height: 100%;\n}\n\n.jp-DocumentSearch-replace-button:focus {\n outline: none;\n}\n\n.jp-DocumentSearch-replace-wrapper-class {\n margin-left: 14px;\n display: flex;\n}\n\n.jp-DocumentSearch-replace-toggle {\n border: none;\n background-color: var(--jp-toolbar-background);\n border-radius: var(--jp-border-radius);\n}\n\n.jp-DocumentSearch-replace-toggle:hover {\n background-color: var(--jp-layout-color2);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.cm-editor {\n line-height: var(--jp-code-line-height);\n font-size: var(--jp-code-font-size);\n font-family: var(--jp-code-font-family);\n border: 0;\n border-radius: 0;\n height: auto;\n\n \/* Changed to auto to autogrow *\/\n}\n\n.cm-editor pre {\n padding: 0 var(--jp-code-padding);\n}\n\n.jp-CodeMirrorEditor[data-type='inline'] .cm-dialog {\n background-color: var(--jp-layout-color0);\n color: var(--jp-content-font-color1);\n}\n\n.jp-CodeMirrorEditor {\n cursor: text;\n}\n\n\/* When zoomed out 67% and 33% on a screen of 1440 width x 900 height *\/\n@media screen and (min-width: 2138px) and (max-width: 4319px) {\n .jp-CodeMirrorEditor[data-type='inline'] .cm-cursor {\n border-left: var(--jp-code-cursor-width1) solid\n var(--jp-editor-cursor-color);\n }\n}\n\n\/* When zoomed out less than 33% *\/\n@media screen and (min-width: 4320px) {\n .jp-CodeMirrorEditor[data-type='inline'] .cm-cursor {\n border-left: var(--jp-code-cursor-width2) solid\n var(--jp-editor-cursor-color);\n }\n}\n\n.cm-editor.jp-mod-readOnly .cm-cursor {\n display: none;\n}\n\n.jp-CollaboratorCursor {\n border-left: 5px solid transparent;\n border-right: 5px solid transparent;\n border-top: none;\n border-bottom: 3px solid;\n background-clip: content-box;\n margin-left: -5px;\n margin-right: -5px;\n}\n\n.cm-searching,\n.cm-searching span {\n \/* `.cm-searching span`: we need to override syntax highlighting *\/\n background-color: var(--jp-search-unselected-match-background-color);\n color: var(--jp-search-unselected-match-color);\n}\n\n.cm-searching::selection,\n.cm-searching span::selection {\n background-color: var(--jp-search-unselected-match-background-color);\n color: var(--jp-search-unselected-match-color);\n}\n\n.jp-current-match > .cm-searching,\n.jp-current-match > .cm-searching span,\n.cm-searching > .jp-current-match,\n.cm-searching > .jp-current-match span {\n background-color: var(--jp-search-selected-match-background-color);\n color: var(--jp-search-selected-match-color);\n}\n\n.jp-current-match > .cm-searching::selection,\n.cm-searching > .jp-current-match::selection,\n.jp-current-match > .cm-searching span::selection {\n background-color: var(--jp-search-selected-match-background-color);\n color: var(--jp-search-selected-match-color);\n}\n\n.cm-trailingspace {\n background-image: url(data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAFCAYAAAB4ka1VAAAAsElEQVQIHQGlAFr\/AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA7+r3zKmT0\/+pk9P\/7+r3zAAAAAAAAAAABAAAAAAAAAAA6OPzM+\/q9wAAAAAA6OPzMwAAAAAAAAAAAgAAAAAAAAAAGR8NiRQaCgAZIA0AGR8NiQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQyoYJ\/SY80UAAAAASUVORK5CYII=);\n background-position: center left;\n background-repeat: repeat-x;\n}\n\n.jp-CollaboratorCursor-hover {\n position: absolute;\n z-index: 1;\n transform: translateX(-50%);\n color: white;\n border-radius: 3px;\n padding-left: 4px;\n padding-right: 4px;\n padding-top: 1px;\n padding-bottom: 1px;\n text-align: center;\n font-size: var(--jp-ui-font-size1);\n white-space: nowrap;\n}\n\n.jp-CodeMirror-ruler {\n border-left: 1px dashed var(--jp-border-color2);\n}\n\n\/* Styles for shared cursors (remote cursor locations and selected ranges) *\/\n.jp-CodeMirrorEditor .cm-ySelectionCaret {\n position: relative;\n border-left: 1px solid black;\n margin-left: -1px;\n margin-right: -1px;\n box-sizing: border-box;\n}\n\n.jp-CodeMirrorEditor .cm-ySelectionCaret > .cm-ySelectionInfo {\n white-space: nowrap;\n position: absolute;\n top: -1.15em;\n padding-bottom: 0.05em;\n left: -1px;\n font-size: 0.95em;\n font-family: var(--jp-ui-font-family);\n font-weight: bold;\n line-height: normal;\n user-select: none;\n color: white;\n padding-left: 2px;\n padding-right: 2px;\n z-index: 101;\n transition: opacity 0.3s ease-in-out;\n}\n\n.jp-CodeMirrorEditor .cm-ySelectionInfo {\n transition-delay: 0.7s;\n opacity: 0;\n}\n\n.jp-CodeMirrorEditor .cm-ySelectionCaret:hover > .cm-ySelectionInfo {\n opacity: 1;\n transition-delay: 0s;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-MimeDocument {\n outline: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Variables\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-private-filebrowser-button-height: 28px;\n --jp-private-filebrowser-button-width: 48px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-FileBrowser .jp-SidePanel-content {\n display: flex;\n flex-direction: column;\n}\n\n.jp-FileBrowser-toolbar.jp-Toolbar {\n flex-wrap: wrap;\n row-gap: 12px;\n border-bottom: none;\n height: auto;\n margin: 8px 12px 0;\n box-shadow: none;\n padding: 0;\n justify-content: flex-start;\n}\n\n.jp-FileBrowser-Panel {\n flex: 1 1 auto;\n display: flex;\n flex-direction: column;\n}\n\n.jp-BreadCrumbs {\n flex: 0 0 auto;\n margin: 8px 12px;\n}\n\n.jp-BreadCrumbs-item {\n margin: 0 2px;\n padding: 0 2px;\n border-radius: var(--jp-border-radius);\n cursor: pointer;\n}\n\n.jp-BreadCrumbs-item:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-BreadCrumbs-item:first-child {\n margin-left: 0;\n}\n\n.jp-BreadCrumbs-item.jp-mod-dropTarget {\n background-color: var(--jp-brand-color2);\n opacity: 0.7;\n}\n\n\/*-----------------------------------------------------------------------------\n| Buttons\n|----------------------------------------------------------------------------*\/\n\n.jp-FileBrowser-toolbar > .jp-Toolbar-item {\n flex: 0 0 auto;\n padding-left: 0;\n padding-right: 2px;\n align-items: center;\n height: unset;\n}\n\n.jp-FileBrowser-toolbar > .jp-Toolbar-item .jp-ToolbarButtonComponent {\n width: 40px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Other styles\n|----------------------------------------------------------------------------*\/\n\n.jp-FileDialog.jp-mod-conflict input {\n color: var(--jp-error-color1);\n}\n\n.jp-FileDialog .jp-new-name-title {\n margin-top: 12px;\n}\n\n.jp-LastModified-hidden {\n display: none;\n}\n\n.jp-FileSize-hidden {\n display: none;\n}\n\n.jp-FileBrowser .lm-AccordionPanel > h3:first-child {\n display: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| DirListing\n|----------------------------------------------------------------------------*\/\n\n.jp-DirListing {\n flex: 1 1 auto;\n display: flex;\n flex-direction: column;\n outline: 0;\n}\n\n.jp-DirListing-header {\n flex: 0 0 auto;\n display: flex;\n flex-direction: row;\n align-items: center;\n overflow: hidden;\n border-top: var(--jp-border-width) solid var(--jp-border-color2);\n border-bottom: var(--jp-border-width) solid var(--jp-border-color1);\n box-shadow: var(--jp-toolbar-box-shadow);\n z-index: 2;\n}\n\n.jp-DirListing-headerItem {\n padding: 4px 12px 2px;\n font-weight: 500;\n}\n\n.jp-DirListing-headerItem:hover {\n background: var(--jp-layout-color2);\n}\n\n.jp-DirListing-headerItem.jp-id-name {\n flex: 1 0 84px;\n}\n\n.jp-DirListing-headerItem.jp-id-modified {\n flex: 0 0 112px;\n border-left: var(--jp-border-width) solid var(--jp-border-color2);\n text-align: right;\n}\n\n.jp-DirListing-headerItem.jp-id-filesize {\n flex: 0 0 75px;\n border-left: var(--jp-border-width) solid var(--jp-border-color2);\n text-align: right;\n}\n\n.jp-id-narrow {\n display: none;\n flex: 0 0 5px;\n padding: 4px;\n border-left: var(--jp-border-width) solid var(--jp-border-color2);\n text-align: right;\n color: var(--jp-border-color2);\n}\n\n.jp-DirListing-narrow .jp-id-narrow {\n display: block;\n}\n\n.jp-DirListing-narrow .jp-id-modified,\n.jp-DirListing-narrow .jp-DirListing-itemModified {\n display: none;\n}\n\n.jp-DirListing-headerItem.jp-mod-selected {\n font-weight: 600;\n}\n\n\/* increase specificity to override bundled default *\/\n.jp-DirListing-content {\n flex: 1 1 auto;\n margin: 0;\n padding: 0;\n list-style-type: none;\n overflow: auto;\n background-color: var(--jp-layout-color1);\n}\n\n.jp-DirListing-content mark {\n color: var(--jp-ui-font-color0);\n background-color: transparent;\n font-weight: bold;\n}\n\n.jp-DirListing-content .jp-DirListing-item.jp-mod-selected mark {\n color: var(--jp-ui-inverse-font-color0);\n}\n\n\/* Style the directory listing content when a user drops a file to upload *\/\n.jp-DirListing.jp-mod-native-drop .jp-DirListing-content {\n outline: 5px dashed rgba(128, 128, 128, 0.5);\n outline-offset: -10px;\n cursor: copy;\n}\n\n.jp-DirListing-item {\n display: flex;\n flex-direction: row;\n align-items: center;\n padding: 4px 12px;\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n.jp-DirListing-checkboxWrapper {\n \/* Increases hit area of checkbox. *\/\n padding: 4px;\n}\n\n.jp-DirListing-header\n .jp-DirListing-checkboxWrapper\n + .jp-DirListing-headerItem {\n padding-left: 4px;\n}\n\n.jp-DirListing-content .jp-DirListing-checkboxWrapper {\n position: relative;\n left: -4px;\n margin: -4px 0 -4px -8px;\n}\n\n.jp-DirListing-checkboxWrapper.jp-mod-visible {\n visibility: visible;\n}\n\n\/* For devices that support hovering, hide checkboxes until hovered, selected...\n*\/\n@media (hover: hover) {\n .jp-DirListing-checkboxWrapper {\n visibility: hidden;\n }\n\n .jp-DirListing-item:hover .jp-DirListing-checkboxWrapper,\n .jp-DirListing-item.jp-mod-selected .jp-DirListing-checkboxWrapper {\n visibility: visible;\n }\n}\n\n.jp-DirListing-item[data-is-dot] {\n opacity: 75%;\n}\n\n.jp-DirListing-item.jp-mod-selected {\n color: var(--jp-ui-inverse-font-color1);\n background: var(--jp-brand-color1);\n}\n\n.jp-DirListing-item.jp-mod-dropTarget {\n background: var(--jp-brand-color3);\n}\n\n.jp-DirListing-item:hover:not(.jp-mod-selected) {\n background: var(--jp-layout-color2);\n}\n\n.jp-DirListing-itemIcon {\n flex: 0 0 20px;\n margin-right: 4px;\n}\n\n.jp-DirListing-itemText {\n flex: 1 0 64px;\n white-space: nowrap;\n overflow: hidden;\n text-overflow: ellipsis;\n user-select: none;\n}\n\n.jp-DirListing-itemText:focus {\n outline-width: 2px;\n outline-color: var(--jp-inverse-layout-color1);\n outline-style: solid;\n outline-offset: 1px;\n}\n\n.jp-DirListing-item.jp-mod-selected .jp-DirListing-itemText:focus {\n outline-color: var(--jp-layout-color1);\n}\n\n.jp-DirListing-itemModified {\n flex: 0 0 125px;\n text-align: right;\n}\n\n.jp-DirListing-itemFileSize {\n flex: 0 0 90px;\n text-align: right;\n}\n\n.jp-DirListing-editor {\n flex: 1 0 64px;\n outline: none;\n border: none;\n color: var(--jp-ui-font-color1);\n background-color: var(--jp-layout-color1);\n}\n\n.jp-DirListing-item.jp-mod-running .jp-DirListing-itemIcon::before {\n color: var(--jp-success-color1);\n content: '\\25CF';\n font-size: 8px;\n position: absolute;\n left: -8px;\n}\n\n.jp-DirListing-item.jp-mod-running.jp-mod-selected\n .jp-DirListing-itemIcon::before {\n color: var(--jp-ui-inverse-font-color1);\n}\n\n.jp-DirListing-item.lm-mod-drag-image,\n.jp-DirListing-item.jp-mod-selected.lm-mod-drag-image {\n font-size: var(--jp-ui-font-size1);\n padding-left: 4px;\n margin-left: 4px;\n width: 160px;\n background-color: var(--jp-ui-inverse-font-color2);\n box-shadow: var(--jp-elevation-z2);\n border-radius: 0;\n color: var(--jp-ui-font-color1);\n transform: translateX(-40%) translateY(-58%);\n}\n\n.jp-Document {\n min-width: 120px;\n min-height: 120px;\n outline: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Main OutputArea\n| OutputArea has a list of Outputs\n|----------------------------------------------------------------------------*\/\n\n.jp-OutputArea {\n overflow-y: auto;\n}\n\n.jp-OutputArea-child {\n display: table;\n table-layout: fixed;\n width: 100%;\n overflow: hidden;\n}\n\n.jp-OutputPrompt {\n width: var(--jp-cell-prompt-width);\n color: var(--jp-cell-outprompt-font-color);\n font-family: var(--jp-cell-prompt-font-family);\n padding: var(--jp-code-padding);\n letter-spacing: var(--jp-cell-prompt-letter-spacing);\n line-height: var(--jp-code-line-height);\n font-size: var(--jp-code-font-size);\n border: var(--jp-border-width) solid transparent;\n opacity: var(--jp-cell-prompt-opacity);\n\n \/* Right align prompt text, don't wrap to handle large prompt numbers *\/\n text-align: right;\n white-space: nowrap;\n overflow: hidden;\n text-overflow: ellipsis;\n\n \/* Disable text selection *\/\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n.jp-OutputArea-prompt {\n display: table-cell;\n vertical-align: top;\n}\n\n.jp-OutputArea-output {\n display: table-cell;\n width: 100%;\n height: auto;\n overflow: auto;\n user-select: text;\n -moz-user-select: text;\n -webkit-user-select: text;\n -ms-user-select: text;\n}\n\n.jp-OutputArea .jp-RenderedText {\n padding-left: 1ch;\n}\n\n\/**\n * Prompt overlay.\n *\/\n\n.jp-OutputArea-promptOverlay {\n position: absolute;\n top: 0;\n width: var(--jp-cell-prompt-width);\n height: 100%;\n opacity: 0.5;\n}\n\n.jp-OutputArea-promptOverlay:hover {\n background: var(--jp-layout-color2);\n box-shadow: inset 0 0 1px var(--jp-inverse-layout-color0);\n cursor: zoom-out;\n}\n\n.jp-mod-outputsScrolled .jp-OutputArea-promptOverlay:hover {\n cursor: zoom-in;\n}\n\n\/**\n * Isolated output.\n *\/\n.jp-OutputArea-output.jp-mod-isolated {\n width: 100%;\n display: block;\n}\n\n\/*\nWhen drag events occur, `lm-mod-override-cursor` is added to the body.\nBecause iframes steal all cursor events, the following two rules are necessary\nto suppress pointer events while resize drags are occurring. There may be a\nbetter solution to this problem.\n*\/\nbody.lm-mod-override-cursor .jp-OutputArea-output.jp-mod-isolated {\n position: relative;\n}\n\nbody.lm-mod-override-cursor .jp-OutputArea-output.jp-mod-isolated::before {\n content: '';\n position: absolute;\n top: 0;\n left: 0;\n right: 0;\n bottom: 0;\n background: transparent;\n}\n\n\/* pre *\/\n\n.jp-OutputArea-output pre {\n border: none;\n margin: 0;\n padding: 0;\n overflow-x: auto;\n overflow-y: auto;\n word-break: break-all;\n word-wrap: break-word;\n white-space: pre-wrap;\n}\n\n\/* tables *\/\n\n.jp-OutputArea-output.jp-RenderedHTMLCommon table {\n margin-left: 0;\n margin-right: 0;\n}\n\n\/* description lists *\/\n\n.jp-OutputArea-output dl,\n.jp-OutputArea-output dt,\n.jp-OutputArea-output dd {\n display: block;\n}\n\n.jp-OutputArea-output dl {\n width: 100%;\n overflow: hidden;\n padding: 0;\n margin: 0;\n}\n\n.jp-OutputArea-output dt {\n font-weight: bold;\n float: left;\n width: 20%;\n padding: 0;\n margin: 0;\n}\n\n.jp-OutputArea-output dd {\n float: left;\n width: 80%;\n padding: 0;\n margin: 0;\n}\n\n.jp-TrimmedOutputs pre {\n background: var(--jp-layout-color3);\n font-size: calc(var(--jp-code-font-size) * 1.4);\n text-align: center;\n text-transform: uppercase;\n}\n\n\/* Hide the gutter in case of\n * - nested output areas (e.g. in the case of output widgets)\n * - mirrored output areas\n *\/\n.jp-OutputArea .jp-OutputArea .jp-OutputArea-prompt {\n display: none;\n}\n\n\/* Hide empty lines in the output area, for instance due to cleared widgets *\/\n.jp-OutputArea-prompt:empty {\n padding: 0;\n border: 0;\n}\n\n\/*-----------------------------------------------------------------------------\n| executeResult is added to any Output-result for the display of the object\n| returned by a cell\n|----------------------------------------------------------------------------*\/\n\n.jp-OutputArea-output.jp-OutputArea-executeResult {\n margin-left: 0;\n width: 100%;\n}\n\n\/* Text output with the Out[] prompt needs a top padding to match the\n * alignment of the Out[] prompt itself.\n *\/\n.jp-OutputArea-executeResult .jp-RenderedText.jp-OutputArea-output {\n padding-top: var(--jp-code-padding);\n border-top: var(--jp-border-width) solid transparent;\n}\n\n\/*-----------------------------------------------------------------------------\n| The Stdin output\n|----------------------------------------------------------------------------*\/\n\n.jp-Stdin-prompt {\n color: var(--jp-content-font-color0);\n padding-right: var(--jp-code-padding);\n vertical-align: baseline;\n flex: 0 0 auto;\n}\n\n.jp-Stdin-input {\n font-family: var(--jp-code-font-family);\n font-size: inherit;\n color: inherit;\n background-color: inherit;\n width: 42%;\n min-width: 200px;\n\n \/* make sure input baseline aligns with prompt *\/\n vertical-align: baseline;\n\n \/* padding + margin = 0.5em between prompt and cursor *\/\n padding: 0 0.25em;\n margin: 0 0.25em;\n flex: 0 0 70%;\n}\n\n.jp-Stdin-input::placeholder {\n opacity: 0;\n}\n\n.jp-Stdin-input:focus {\n box-shadow: none;\n}\n\n.jp-Stdin-input:focus::placeholder {\n opacity: 1;\n}\n\n\/*-----------------------------------------------------------------------------\n| Output Area View\n|----------------------------------------------------------------------------*\/\n\n.jp-LinkedOutputView .jp-OutputArea {\n height: 100%;\n display: block;\n}\n\n.jp-LinkedOutputView .jp-OutputArea-output:only-child {\n height: 100%;\n}\n\n\/*-----------------------------------------------------------------------------\n| Printing\n|----------------------------------------------------------------------------*\/\n\n@media print {\n .jp-OutputArea-child {\n break-inside: avoid-page;\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Mobile\n|----------------------------------------------------------------------------*\/\n@media only screen and (max-width: 760px) {\n .jp-OutputPrompt {\n display: table-row;\n text-align: left;\n }\n\n .jp-OutputArea-child .jp-OutputArea-output {\n display: table-row;\n margin-left: var(--jp-notebook-padding);\n }\n}\n\n\/* Trimmed outputs warning *\/\n.jp-TrimmedOutputs > a {\n margin: 10px;\n text-decoration: none;\n cursor: pointer;\n}\n\n.jp-TrimmedOutputs > a:hover {\n text-decoration: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Table of Contents\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-private-toc-active-width: 4px;\n}\n\n.jp-TableOfContents {\n display: flex;\n flex-direction: column;\n background: var(--jp-layout-color1);\n color: var(--jp-ui-font-color1);\n font-size: var(--jp-ui-font-size1);\n height: 100%;\n}\n\n.jp-TableOfContents-placeholder {\n text-align: center;\n}\n\n.jp-TableOfContents-placeholderContent {\n color: var(--jp-content-font-color2);\n padding: 8px;\n}\n\n.jp-TableOfContents-placeholderContent > h3 {\n margin-bottom: var(--jp-content-heading-margin-bottom);\n}\n\n.jp-TableOfContents .jp-SidePanel-content {\n overflow-y: auto;\n}\n\n.jp-TableOfContents-tree {\n margin: 4px;\n}\n\n.jp-TableOfContents ol {\n list-style-type: none;\n}\n\n\/* stylelint-disable-next-line selector-max-type *\/\n.jp-TableOfContents li > ol {\n \/* Align left border with triangle icon center *\/\n padding-left: 11px;\n}\n\n.jp-TableOfContents-content {\n \/* left margin for the active heading indicator *\/\n margin: 0 0 0 var(--jp-private-toc-active-width);\n padding: 0;\n background-color: var(--jp-layout-color1);\n}\n\n.jp-tocItem {\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n.jp-tocItem-heading {\n display: flex;\n cursor: pointer;\n}\n\n.jp-tocItem-heading:hover {\n background-color: var(--jp-layout-color2);\n}\n\n.jp-tocItem-content {\n display: block;\n padding: 4px 0;\n white-space: nowrap;\n text-overflow: ellipsis;\n overflow-x: hidden;\n}\n\n.jp-tocItem-collapser {\n height: 20px;\n margin: 2px 2px 0;\n padding: 0;\n background: none;\n border: none;\n cursor: pointer;\n}\n\n.jp-tocItem-collapser:hover {\n background-color: var(--jp-layout-color3);\n}\n\n\/* Active heading indicator *\/\n\n.jp-tocItem-heading::before {\n content: ' ';\n background: transparent;\n width: var(--jp-private-toc-active-width);\n height: 24px;\n position: absolute;\n left: 0;\n border-radius: var(--jp-border-radius);\n}\n\n.jp-tocItem-heading.jp-tocItem-active::before {\n background-color: var(--jp-brand-color1);\n}\n\n.jp-tocItem-heading:hover.jp-tocItem-active::before {\n background: var(--jp-brand-color0);\n opacity: 1;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n.jp-Collapser {\n flex: 0 0 var(--jp-cell-collapser-width);\n padding: 0;\n margin: 0;\n border: none;\n outline: none;\n background: transparent;\n border-radius: var(--jp-border-radius);\n opacity: 1;\n}\n\n.jp-Collapser-child {\n display: block;\n width: 100%;\n box-sizing: border-box;\n\n \/* height: 100% doesn't work because the height of its parent is computed from content *\/\n position: absolute;\n top: 0;\n bottom: 0;\n}\n\n\/*-----------------------------------------------------------------------------\n| Printing\n|----------------------------------------------------------------------------*\/\n\n\/*\nHiding collapsers in print mode.\n\nNote: input and output wrappers have \"display: block\" propery in print mode.\n*\/\n\n@media print {\n .jp-Collapser {\n display: none;\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Header\/Footer\n|----------------------------------------------------------------------------*\/\n\n\/* Hidden by zero height by default *\/\n.jp-CellHeader,\n.jp-CellFooter {\n height: 0;\n width: 100%;\n padding: 0;\n margin: 0;\n border: none;\n outline: none;\n background: transparent;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Input\n|----------------------------------------------------------------------------*\/\n\n\/* All input areas *\/\n.jp-InputArea {\n display: table;\n table-layout: fixed;\n width: 100%;\n overflow: hidden;\n}\n\n.jp-InputArea-editor {\n display: table-cell;\n overflow: hidden;\n vertical-align: top;\n\n \/* This is the non-active, default styling *\/\n border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);\n border-radius: 0;\n background: var(--jp-cell-editor-background);\n}\n\n.jp-InputPrompt {\n display: table-cell;\n vertical-align: top;\n width: var(--jp-cell-prompt-width);\n color: var(--jp-cell-inprompt-font-color);\n font-family: var(--jp-cell-prompt-font-family);\n padding: var(--jp-code-padding);\n letter-spacing: var(--jp-cell-prompt-letter-spacing);\n opacity: var(--jp-cell-prompt-opacity);\n line-height: var(--jp-code-line-height);\n font-size: var(--jp-code-font-size);\n border: var(--jp-border-width) solid transparent;\n\n \/* Right align prompt text, don't wrap to handle large prompt numbers *\/\n text-align: right;\n white-space: nowrap;\n overflow: hidden;\n text-overflow: ellipsis;\n\n \/* Disable text selection *\/\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Mobile\n|----------------------------------------------------------------------------*\/\n@media only screen and (max-width: 760px) {\n .jp-InputArea-editor {\n display: table-row;\n margin-left: var(--jp-notebook-padding);\n }\n\n .jp-InputPrompt {\n display: table-row;\n text-align: left;\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Placeholder\n|----------------------------------------------------------------------------*\/\n\n.jp-Placeholder {\n display: table;\n table-layout: fixed;\n width: 100%;\n}\n\n.jp-Placeholder-prompt {\n display: table-cell;\n box-sizing: border-box;\n}\n\n.jp-Placeholder-content {\n display: table-cell;\n padding: 4px 6px;\n border: 1px solid transparent;\n border-radius: 0;\n background: none;\n box-sizing: border-box;\n cursor: pointer;\n}\n\n.jp-Placeholder-contentContainer {\n display: flex;\n}\n\n.jp-Placeholder-content:hover,\n.jp-InputPlaceholder > .jp-Placeholder-content:hover {\n border-color: var(--jp-layout-color3);\n}\n\n.jp-Placeholder-content .jp-MoreHorizIcon {\n width: 32px;\n height: 16px;\n border: 1px solid transparent;\n border-radius: var(--jp-border-radius);\n}\n\n.jp-Placeholder-content .jp-MoreHorizIcon:hover {\n border: 1px solid var(--jp-border-color1);\n box-shadow: 0 0 2px 0 rgba(0, 0, 0, 0.25);\n background-color: var(--jp-layout-color0);\n}\n\n.jp-PlaceholderText {\n white-space: nowrap;\n overflow-x: hidden;\n color: var(--jp-inverse-layout-color3);\n font-family: var(--jp-code-font-family);\n}\n\n.jp-InputPlaceholder > .jp-Placeholder-content {\n border-color: var(--jp-cell-editor-border-color);\n background: var(--jp-cell-editor-background);\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Private CSS variables\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-private-cell-scrolling-output-offset: 5px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Cell\n|----------------------------------------------------------------------------*\/\n\n.jp-Cell {\n padding: var(--jp-cell-padding);\n margin: 0;\n border: none;\n outline: none;\n background: transparent;\n}\n\n\/*-----------------------------------------------------------------------------\n| Common input\/output\n|----------------------------------------------------------------------------*\/\n\n.jp-Cell-inputWrapper,\n.jp-Cell-outputWrapper {\n display: flex;\n flex-direction: row;\n padding: 0;\n margin: 0;\n\n \/* Added to reveal the box-shadow on the input and output collapsers. *\/\n overflow: visible;\n}\n\n\/* Only input\/output areas inside cells *\/\n.jp-Cell-inputArea,\n.jp-Cell-outputArea {\n flex: 1 1 auto;\n}\n\n\/*-----------------------------------------------------------------------------\n| Collapser\n|----------------------------------------------------------------------------*\/\n\n\/* Make the output collapser disappear when there is not output, but do so\n * in a manner that leaves it in the layout and preserves its width.\n *\/\n.jp-Cell.jp-mod-noOutputs .jp-Cell-outputCollapser {\n border: none !important;\n background: transparent !important;\n}\n\n.jp-Cell:not(.jp-mod-noOutputs) .jp-Cell-outputCollapser {\n min-height: var(--jp-cell-collapser-min-height);\n}\n\n\/*-----------------------------------------------------------------------------\n| Output\n|----------------------------------------------------------------------------*\/\n\n\/* Put a space between input and output when there IS output *\/\n.jp-Cell:not(.jp-mod-noOutputs) .jp-Cell-outputWrapper {\n margin-top: 5px;\n}\n\n.jp-CodeCell.jp-mod-outputsScrolled .jp-Cell-outputArea {\n overflow-y: auto;\n max-height: 24em;\n margin-left: var(--jp-private-cell-scrolling-output-offset);\n resize: vertical;\n}\n\n.jp-CodeCell.jp-mod-outputsScrolled .jp-Cell-outputArea[style*='height'] {\n max-height: unset;\n}\n\n.jp-CodeCell.jp-mod-outputsScrolled .jp-Cell-outputArea::after {\n content: ' ';\n box-shadow: inset 0 0 6px 2px rgb(0 0 0 \/ 30%);\n width: 100%;\n height: 100%;\n position: sticky;\n bottom: 0;\n top: 0;\n margin-top: -50%;\n float: left;\n display: block;\n pointer-events: none;\n}\n\n.jp-CodeCell.jp-mod-outputsScrolled .jp-OutputArea-child {\n padding-top: 6px;\n}\n\n.jp-CodeCell.jp-mod-outputsScrolled .jp-OutputArea-prompt {\n width: calc(\n var(--jp-cell-prompt-width) - var(--jp-private-cell-scrolling-output-offset)\n );\n}\n\n.jp-CodeCell.jp-mod-outputsScrolled .jp-OutputArea-promptOverlay {\n left: calc(-1 * var(--jp-private-cell-scrolling-output-offset));\n}\n\n\/*-----------------------------------------------------------------------------\n| CodeCell\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| MarkdownCell\n|----------------------------------------------------------------------------*\/\n\n.jp-MarkdownOutput {\n display: table-cell;\n width: 100%;\n margin-top: 0;\n margin-bottom: 0;\n padding-left: var(--jp-code-padding);\n}\n\n.jp-MarkdownOutput.jp-RenderedHTMLCommon {\n overflow: auto;\n}\n\n\/* collapseHeadingButton (show always if hiddenCellsButton is _not_ shown) *\/\n.jp-collapseHeadingButton {\n display: flex;\n min-height: var(--jp-cell-collapser-min-height);\n font-size: var(--jp-code-font-size);\n position: absolute;\n background-color: transparent;\n background-size: 25px;\n background-repeat: no-repeat;\n background-position-x: center;\n background-position-y: top;\n background-image: var(--jp-icon-caret-down);\n right: 0;\n top: 0;\n bottom: 0;\n}\n\n.jp-collapseHeadingButton.jp-mod-collapsed {\n background-image: var(--jp-icon-caret-right);\n}\n\n\/*\n set the container font size to match that of content\n so that the nested collapse buttons have the right size\n*\/\n.jp-MarkdownCell .jp-InputPrompt {\n font-size: var(--jp-content-font-size1);\n}\n\n\/*\n Align collapseHeadingButton with cell top header\n The font sizes are identical to the ones in packages\/rendermime\/style\/base.css\n*\/\n.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='1'] {\n font-size: var(--jp-content-font-size5);\n background-position-y: calc(0.3 * var(--jp-content-font-size5));\n}\n\n.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='2'] {\n font-size: var(--jp-content-font-size4);\n background-position-y: calc(0.3 * var(--jp-content-font-size4));\n}\n\n.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='3'] {\n font-size: var(--jp-content-font-size3);\n background-position-y: calc(0.3 * var(--jp-content-font-size3));\n}\n\n.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='4'] {\n font-size: var(--jp-content-font-size2);\n background-position-y: calc(0.3 * var(--jp-content-font-size2));\n}\n\n.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='5'] {\n font-size: var(--jp-content-font-size1);\n background-position-y: top;\n}\n\n.jp-mod-rendered .jp-collapseHeadingButton[data-heading-level='6'] {\n font-size: var(--jp-content-font-size0);\n background-position-y: top;\n}\n\n\/* collapseHeadingButton (show only on (hover,active) if hiddenCellsButton is shown) *\/\n.jp-Notebook.jp-mod-showHiddenCellsButton .jp-collapseHeadingButton {\n display: none;\n}\n\n.jp-Notebook.jp-mod-showHiddenCellsButton\n :is(.jp-MarkdownCell:hover, .jp-mod-active)\n .jp-collapseHeadingButton {\n display: flex;\n}\n\n\/* showHiddenCellsButton (only show if jp-mod-showHiddenCellsButton is set, which\nis a consequence of the showHiddenCellsButton option in Notebook Settings)*\/\n.jp-Notebook.jp-mod-showHiddenCellsButton .jp-showHiddenCellsButton {\n margin-left: calc(var(--jp-cell-prompt-width) + 2 * var(--jp-code-padding));\n margin-top: var(--jp-code-padding);\n border: 1px solid var(--jp-border-color2);\n background-color: var(--jp-border-color3) !important;\n color: var(--jp-content-font-color0) !important;\n display: flex;\n}\n\n.jp-Notebook.jp-mod-showHiddenCellsButton .jp-showHiddenCellsButton:hover {\n background-color: var(--jp-border-color2) !important;\n}\n\n.jp-showHiddenCellsButton {\n display: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Printing\n|----------------------------------------------------------------------------*\/\n\n\/*\nUsing block instead of flex to allow the use of the break-inside CSS property for\ncell outputs.\n*\/\n\n@media print {\n .jp-Cell-inputWrapper,\n .jp-Cell-outputWrapper {\n display: block;\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Variables\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-notebook-toolbar-padding: 2px 5px 2px 2px;\n}\n\n\/*-----------------------------------------------------------------------------\n\n\/*-----------------------------------------------------------------------------\n| Styles\n|----------------------------------------------------------------------------*\/\n\n.jp-NotebookPanel-toolbar {\n padding: var(--jp-notebook-toolbar-padding);\n\n \/* disable paint containment from lumino 2.0 default strict CSS containment *\/\n contain: style size !important;\n}\n\n.jp-Toolbar-item.jp-Notebook-toolbarCellType .jp-select-wrapper.jp-mod-focused {\n border: none;\n box-shadow: none;\n}\n\n.jp-Notebook-toolbarCellTypeDropdown select {\n height: 24px;\n font-size: var(--jp-ui-font-size1);\n line-height: 14px;\n border-radius: 0;\n display: block;\n}\n\n.jp-Notebook-toolbarCellTypeDropdown span {\n top: 5px !important;\n}\n\n.jp-Toolbar-responsive-popup {\n position: absolute;\n height: fit-content;\n display: flex;\n flex-direction: row;\n flex-wrap: wrap;\n justify-content: flex-end;\n border-bottom: var(--jp-border-width) solid var(--jp-toolbar-border-color);\n box-shadow: var(--jp-toolbar-box-shadow);\n background: var(--jp-toolbar-background);\n min-height: var(--jp-toolbar-micro-height);\n padding: var(--jp-notebook-toolbar-padding);\n z-index: 1;\n right: 0;\n top: 0;\n}\n\n.jp-Toolbar > .jp-Toolbar-responsive-opener {\n margin-left: auto;\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Variables\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n\n\/*-----------------------------------------------------------------------------\n| Styles\n|----------------------------------------------------------------------------*\/\n\n.jp-Notebook-ExecutionIndicator {\n position: relative;\n display: inline-block;\n height: 100%;\n z-index: 9997;\n}\n\n.jp-Notebook-ExecutionIndicator-tooltip {\n visibility: hidden;\n height: auto;\n width: max-content;\n width: -moz-max-content;\n background-color: var(--jp-layout-color2);\n color: var(--jp-ui-font-color1);\n text-align: justify;\n border-radius: 6px;\n padding: 0 5px;\n position: fixed;\n display: table;\n}\n\n.jp-Notebook-ExecutionIndicator-tooltip.up {\n transform: translateX(-50%) translateY(-100%) translateY(-32px);\n}\n\n.jp-Notebook-ExecutionIndicator-tooltip.down {\n transform: translateX(calc(-100% + 16px)) translateY(5px);\n}\n\n.jp-Notebook-ExecutionIndicator-tooltip.hidden {\n display: none;\n}\n\n.jp-Notebook-ExecutionIndicator:hover .jp-Notebook-ExecutionIndicator-tooltip {\n visibility: visible;\n}\n\n.jp-Notebook-ExecutionIndicator span {\n font-size: var(--jp-ui-font-size1);\n font-family: var(--jp-ui-font-family);\n color: var(--jp-ui-font-color1);\n line-height: 24px;\n display: block;\n}\n\n.jp-Notebook-ExecutionIndicator-progress-bar {\n display: flex;\n justify-content: center;\n height: 100%;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n\/*\n * Execution indicator\n *\/\n.jp-tocItem-content::after {\n content: '';\n\n \/* Must be identical to form a circle *\/\n width: 12px;\n height: 12px;\n background: none;\n border: none;\n position: absolute;\n right: 0;\n}\n\n.jp-tocItem-content[data-running='0']::after {\n border-radius: 50%;\n border: var(--jp-border-width) solid var(--jp-inverse-layout-color3);\n background: none;\n}\n\n.jp-tocItem-content[data-running='1']::after {\n border-radius: 50%;\n border: var(--jp-border-width) solid var(--jp-inverse-layout-color3);\n background-color: var(--jp-inverse-layout-color3);\n}\n\n.jp-tocItem-content[data-running='0'],\n.jp-tocItem-content[data-running='1'] {\n margin-right: 12px;\n}\n\n\/*\n * Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n *\/\n\n.jp-Notebook-footer {\n height: 27px;\n margin-left: calc(\n var(--jp-cell-prompt-width) + var(--jp-cell-collapser-width) +\n var(--jp-cell-padding)\n );\n width: calc(\n 100% -\n (\n var(--jp-cell-prompt-width) + var(--jp-cell-collapser-width) +\n var(--jp-cell-padding) + var(--jp-cell-padding)\n )\n );\n border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);\n color: var(--jp-ui-font-color3);\n margin-top: 6px;\n background: none;\n cursor: pointer;\n}\n\n.jp-Notebook-footer:focus {\n border-color: var(--jp-cell-editor-active-border-color);\n}\n\n\/* For devices that support hovering, hide footer until hover *\/\n@media (hover: hover) {\n .jp-Notebook-footer {\n opacity: 0;\n }\n\n .jp-Notebook-footer:focus,\n .jp-Notebook-footer:hover {\n opacity: 1;\n }\n}\n\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| Imports\n|----------------------------------------------------------------------------*\/\n\n\/*-----------------------------------------------------------------------------\n| CSS variables\n|----------------------------------------------------------------------------*\/\n\n:root {\n --jp-side-by-side-output-size: 1fr;\n --jp-side-by-side-resized-cell: var(--jp-side-by-side-output-size);\n --jp-private-notebook-dragImage-width: 304px;\n --jp-private-notebook-dragImage-height: 36px;\n --jp-private-notebook-selected-color: var(--md-blue-400);\n --jp-private-notebook-active-color: var(--md-green-400);\n}\n\n\/*-----------------------------------------------------------------------------\n| Notebook\n|----------------------------------------------------------------------------*\/\n\n\/* stylelint-disable selector-max-class *\/\n\n.jp-NotebookPanel {\n display: block;\n height: 100%;\n}\n\n.jp-NotebookPanel.jp-Document {\n min-width: 240px;\n min-height: 120px;\n}\n\n.jp-Notebook {\n padding: var(--jp-notebook-padding);\n outline: none;\n overflow: auto;\n background: var(--jp-layout-color0);\n}\n\n.jp-Notebook.jp-mod-scrollPastEnd::after {\n display: block;\n content: '';\n min-height: var(--jp-notebook-scroll-padding);\n}\n\n.jp-MainAreaWidget-ContainStrict .jp-Notebook * {\n contain: strict;\n}\n\n.jp-Notebook .jp-Cell {\n overflow: visible;\n}\n\n.jp-Notebook .jp-Cell .jp-InputPrompt {\n cursor: move;\n}\n\n\/*-----------------------------------------------------------------------------\n| Notebook state related styling\n|\n| The notebook and cells each have states, here are the possibilities:\n|\n| - Notebook\n| - Command\n| - Edit\n| - Cell\n| - None\n| - Active (only one can be active)\n| - Selected (the cells actions are applied to)\n| - Multiselected (when multiple selected, the cursor)\n| - No outputs\n|----------------------------------------------------------------------------*\/\n\n\/* Command or edit modes *\/\n\n.jp-Notebook .jp-Cell:not(.jp-mod-active) .jp-InputPrompt {\n opacity: var(--jp-cell-prompt-not-active-opacity);\n color: var(--jp-cell-prompt-not-active-font-color);\n}\n\n.jp-Notebook .jp-Cell:not(.jp-mod-active) .jp-OutputPrompt {\n opacity: var(--jp-cell-prompt-not-active-opacity);\n color: var(--jp-cell-prompt-not-active-font-color);\n}\n\n\/* cell is active *\/\n.jp-Notebook .jp-Cell.jp-mod-active .jp-Collapser {\n background: var(--jp-brand-color1);\n}\n\n\/* cell is dirty *\/\n.jp-Notebook .jp-Cell.jp-mod-dirty .jp-InputPrompt {\n color: var(--jp-warn-color1);\n}\n\n.jp-Notebook .jp-Cell.jp-mod-dirty .jp-InputPrompt::before {\n color: var(--jp-warn-color1);\n content: '\u2022';\n}\n\n.jp-Notebook .jp-Cell.jp-mod-active.jp-mod-dirty .jp-Collapser {\n background: var(--jp-warn-color1);\n}\n\n\/* collapser is hovered *\/\n.jp-Notebook .jp-Cell .jp-Collapser:hover {\n box-shadow: var(--jp-elevation-z2);\n background: var(--jp-brand-color1);\n opacity: var(--jp-cell-collapser-not-active-hover-opacity);\n}\n\n\/* cell is active and collapser is hovered *\/\n.jp-Notebook .jp-Cell.jp-mod-active .jp-Collapser:hover {\n background: var(--jp-brand-color0);\n opacity: 1;\n}\n\n\/* Command mode *\/\n\n.jp-Notebook.jp-mod-commandMode .jp-Cell.jp-mod-selected {\n background: var(--jp-notebook-multiselected-color);\n}\n\n.jp-Notebook.jp-mod-commandMode\n .jp-Cell.jp-mod-active.jp-mod-selected:not(.jp-mod-multiSelected) {\n background: transparent;\n}\n\n\/* Edit mode *\/\n\n.jp-Notebook.jp-mod-editMode .jp-Cell.jp-mod-active .jp-InputArea-editor {\n border: var(--jp-border-width) solid var(--jp-cell-editor-active-border-color);\n box-shadow: var(--jp-input-box-shadow);\n background-color: var(--jp-cell-editor-active-background);\n}\n\n\/*-----------------------------------------------------------------------------\n| Notebook drag and drop\n|----------------------------------------------------------------------------*\/\n\n.jp-Notebook-cell.jp-mod-dropSource {\n opacity: 0.5;\n}\n\n.jp-Notebook-cell.jp-mod-dropTarget,\n.jp-Notebook.jp-mod-commandMode\n .jp-Notebook-cell.jp-mod-active.jp-mod-selected.jp-mod-dropTarget {\n border-top-color: var(--jp-private-notebook-selected-color);\n border-top-style: solid;\n border-top-width: 2px;\n}\n\n.jp-dragImage {\n display: block;\n flex-direction: row;\n width: var(--jp-private-notebook-dragImage-width);\n height: var(--jp-private-notebook-dragImage-height);\n border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);\n background: var(--jp-cell-editor-background);\n overflow: visible;\n}\n\n.jp-dragImage-singlePrompt {\n box-shadow: 2px 2px 4px 0 rgba(0, 0, 0, 0.12);\n}\n\n.jp-dragImage .jp-dragImage-content {\n flex: 1 1 auto;\n z-index: 2;\n font-size: var(--jp-code-font-size);\n font-family: var(--jp-code-font-family);\n line-height: var(--jp-code-line-height);\n padding: var(--jp-code-padding);\n border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);\n background: var(--jp-cell-editor-background-color);\n color: var(--jp-content-font-color3);\n text-align: left;\n margin: 4px 4px 4px 0;\n}\n\n.jp-dragImage .jp-dragImage-prompt {\n flex: 0 0 auto;\n min-width: 36px;\n color: var(--jp-cell-inprompt-font-color);\n padding: var(--jp-code-padding);\n padding-left: 12px;\n font-family: var(--jp-cell-prompt-font-family);\n letter-spacing: var(--jp-cell-prompt-letter-spacing);\n line-height: 1.9;\n font-size: var(--jp-code-font-size);\n border: var(--jp-border-width) solid transparent;\n}\n\n.jp-dragImage-multipleBack {\n z-index: -1;\n position: absolute;\n height: 32px;\n width: 300px;\n top: 8px;\n left: 8px;\n background: var(--jp-layout-color2);\n border: var(--jp-border-width) solid var(--jp-input-border-color);\n box-shadow: 2px 2px 4px 0 rgba(0, 0, 0, 0.12);\n}\n\n\/*-----------------------------------------------------------------------------\n| Cell toolbar\n|----------------------------------------------------------------------------*\/\n\n.jp-NotebookTools {\n display: block;\n min-width: var(--jp-sidebar-min-width);\n color: var(--jp-ui-font-color1);\n background: var(--jp-layout-color1);\n\n \/* This is needed so that all font sizing of children done in ems is\n * relative to this base size *\/\n font-size: var(--jp-ui-font-size1);\n overflow: auto;\n}\n\n.jp-ActiveCellTool {\n padding: 12px 0;\n display: flex;\n}\n\n.jp-ActiveCellTool-Content {\n flex: 1 1 auto;\n}\n\n.jp-ActiveCellTool .jp-ActiveCellTool-CellContent {\n background: var(--jp-cell-editor-background);\n border: var(--jp-border-width) solid var(--jp-cell-editor-border-color);\n border-radius: 0;\n min-height: 29px;\n}\n\n.jp-ActiveCellTool .jp-InputPrompt {\n min-width: calc(var(--jp-cell-prompt-width) * 0.75);\n}\n\n.jp-ActiveCellTool-CellContent > pre {\n padding: 5px 4px;\n margin: 0;\n white-space: normal;\n}\n\n.jp-MetadataEditorTool {\n flex-direction: column;\n padding: 12px 0;\n}\n\n.jp-RankedPanel > :not(:first-child) {\n margin-top: 12px;\n}\n\n.jp-KeySelector select.jp-mod-styled {\n font-size: var(--jp-ui-font-size1);\n color: var(--jp-ui-font-color0);\n border: var(--jp-border-width) solid var(--jp-border-color1);\n}\n\n.jp-KeySelector label,\n.jp-MetadataEditorTool label,\n.jp-NumberSetter label {\n line-height: 1.4;\n}\n\n.jp-NotebookTools .jp-select-wrapper {\n margin-top: 4px;\n margin-bottom: 0;\n}\n\n.jp-NumberSetter input {\n width: 100%;\n margin-top: 4px;\n}\n\n.jp-NotebookTools .jp-Collapse {\n margin-top: 16px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Presentation Mode (.jp-mod-presentationMode)\n|----------------------------------------------------------------------------*\/\n\n.jp-mod-presentationMode .jp-Notebook {\n --jp-content-font-size1: var(--jp-content-presentation-font-size1);\n --jp-code-font-size: var(--jp-code-presentation-font-size);\n}\n\n.jp-mod-presentationMode .jp-Notebook .jp-Cell .jp-InputPrompt,\n.jp-mod-presentationMode .jp-Notebook .jp-Cell .jp-OutputPrompt {\n flex: 0 0 110px;\n}\n\n\/*-----------------------------------------------------------------------------\n| Side-by-side Mode (.jp-mod-sideBySide)\n|----------------------------------------------------------------------------*\/\n.jp-mod-sideBySide.jp-Notebook .jp-Notebook-cell {\n margin-top: 3em;\n margin-bottom: 3em;\n margin-left: 5%;\n margin-right: 5%;\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell {\n display: grid;\n grid-template-columns: minmax(0, 1fr) min-content minmax(\n 0,\n var(--jp-side-by-side-output-size)\n );\n grid-template-rows: auto minmax(0, 1fr) auto;\n grid-template-areas:\n 'header header header'\n 'input handle output'\n 'footer footer footer';\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell.jp-mod-resizedCell {\n grid-template-columns: minmax(0, 1fr) min-content minmax(\n 0,\n var(--jp-side-by-side-resized-cell)\n );\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-CellHeader {\n grid-area: header;\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-Cell-inputWrapper {\n grid-area: input;\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-Cell-outputWrapper {\n \/* overwrite the default margin (no vertical separation needed in side by side move *\/\n margin-top: 0;\n grid-area: output;\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-CellFooter {\n grid-area: footer;\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-CellResizeHandle {\n grid-area: handle;\n user-select: none;\n display: block;\n height: 100%;\n cursor: ew-resize;\n padding: 0 var(--jp-cell-padding);\n}\n\n.jp-mod-sideBySide.jp-Notebook .jp-CodeCell .jp-CellResizeHandle::after {\n content: '';\n display: block;\n background: var(--jp-border-color2);\n height: 100%;\n width: 5px;\n}\n\n.jp-mod-sideBySide.jp-Notebook\n .jp-CodeCell.jp-mod-resizedCell\n .jp-CellResizeHandle::after {\n background: var(--jp-border-color0);\n}\n\n.jp-CellResizeHandle {\n display: none;\n}\n\n\/*-----------------------------------------------------------------------------\n| Placeholder\n|----------------------------------------------------------------------------*\/\n\n.jp-Cell-Placeholder {\n padding-left: 55px;\n}\n\n.jp-Cell-Placeholder-wrapper {\n background: #fff;\n border: 1px solid;\n border-color: #e5e6e9 #dfe0e4 #d0d1d5;\n border-radius: 4px;\n -webkit-border-radius: 4px;\n margin: 10px 15px;\n}\n\n.jp-Cell-Placeholder-wrapper-inner {\n padding: 15px;\n position: relative;\n}\n\n.jp-Cell-Placeholder-wrapper-body {\n background-repeat: repeat;\n background-size: 50% auto;\n}\n\n.jp-Cell-Placeholder-wrapper-body div {\n background: #f6f7f8;\n background-image: -webkit-linear-gradient(\n left,\n #f6f7f8 0%,\n #edeef1 20%,\n #f6f7f8 40%,\n #f6f7f8 100%\n );\n background-repeat: no-repeat;\n background-size: 800px 104px;\n height: 104px;\n position: absolute;\n right: 15px;\n left: 15px;\n top: 15px;\n}\n\ndiv.jp-Cell-Placeholder-h1 {\n top: 20px;\n height: 20px;\n left: 15px;\n width: 150px;\n}\n\ndiv.jp-Cell-Placeholder-h2 {\n left: 15px;\n top: 50px;\n height: 10px;\n width: 100px;\n}\n\ndiv.jp-Cell-Placeholder-content-1,\ndiv.jp-Cell-Placeholder-content-2,\ndiv.jp-Cell-Placeholder-content-3 {\n left: 15px;\n right: 15px;\n height: 10px;\n}\n\ndiv.jp-Cell-Placeholder-content-1 {\n top: 100px;\n}\n\ndiv.jp-Cell-Placeholder-content-2 {\n top: 120px;\n}\n\ndiv.jp-Cell-Placeholder-content-3 {\n top: 140px;\n}\n\n<\/style>\n<style type=\"text\/css\">\n\/*-----------------------------------------------------------------------------\n| Copyright (c) Jupyter Development Team.\n| Distributed under the terms of the Modified BSD License.\n|----------------------------------------------------------------------------*\/\n\n\/*\nThe following CSS variables define the main, public API for styling JupyterLab.\nThese variables should be used by all plugins wherever possible. In other\nwords, plugins should not define custom colors, sizes, etc unless absolutely\nnecessary. This enables users to change the visual theme of JupyterLab\nby changing these variables.\n\nMany variables appear in an ordered sequence (0,1,2,3). These sequences\nare designed to work well together, so for example, `--jp-border-color1` should\nbe used with `--jp-layout-color1`. The numbers have the following meanings:\n\n* 0: super-primary, reserved for special emphasis\n* 1: primary, most important under normal situations\n* 2: secondary, next most important under normal situations\n* 3: tertiary, next most important under normal situations\n\nThroughout JupyterLab, we are mostly following principles from Google's\nMaterial Design when selecting colors. We are not, however, following\nall of MD as it is not optimized for dense, information rich UIs.\n*\/\n\n:root {\n \/* Elevation\n *\n * We style box-shadows using Material Design's idea of elevation. These particular numbers are taken from here:\n *\n * https:\/\/github.com\/material-components\/material-components-web\n * https:\/\/material-components-web.appspot.com\/elevation.html\n *\/\n\n --jp-shadow-base-lightness: 0;\n --jp-shadow-umbra-color: rgba(\n var(--jp-shadow-base-lightness),\n var(--jp-shadow-base-lightness),\n var(--jp-shadow-base-lightness),\n 0.2\n );\n --jp-shadow-penumbra-color: rgba(\n var(--jp-shadow-base-lightness),\n var(--jp-shadow-base-lightness),\n var(--jp-shadow-base-lightness),\n 0.14\n );\n --jp-shadow-ambient-color: rgba(\n var(--jp-shadow-base-lightness),\n var(--jp-shadow-base-lightness),\n var(--jp-shadow-base-lightness),\n 0.12\n );\n --jp-elevation-z0: none;\n --jp-elevation-z1: 0 2px 1px -1px var(--jp-shadow-umbra-color),\n 0 1px 1px 0 var(--jp-shadow-penumbra-color),\n 0 1px 3px 0 var(--jp-shadow-ambient-color);\n --jp-elevation-z2: 0 3px 1px -2px var(--jp-shadow-umbra-color),\n 0 2px 2px 0 var(--jp-shadow-penumbra-color),\n 0 1px 5px 0 var(--jp-shadow-ambient-color);\n --jp-elevation-z4: 0 2px 4px -1px var(--jp-shadow-umbra-color),\n 0 4px 5px 0 var(--jp-shadow-penumbra-color),\n 0 1px 10px 0 var(--jp-shadow-ambient-color);\n --jp-elevation-z6: 0 3px 5px -1px var(--jp-shadow-umbra-color),\n 0 6px 10px 0 var(--jp-shadow-penumbra-color),\n 0 1px 18px 0 var(--jp-shadow-ambient-color);\n --jp-elevation-z8: 0 5px 5px -3px var(--jp-shadow-umbra-color),\n 0 8px 10px 1px var(--jp-shadow-penumbra-color),\n 0 3px 14px 2px var(--jp-shadow-ambient-color);\n --jp-elevation-z12: 0 7px 8px -4px var(--jp-shadow-umbra-color),\n 0 12px 17px 2px var(--jp-shadow-penumbra-color),\n 0 5px 22px 4px var(--jp-shadow-ambient-color);\n --jp-elevation-z16: 0 8px 10px -5px var(--jp-shadow-umbra-color),\n 0 16px 24px 2px var(--jp-shadow-penumbra-color),\n 0 6px 30px 5px var(--jp-shadow-ambient-color);\n --jp-elevation-z20: 0 10px 13px -6px var(--jp-shadow-umbra-color),\n 0 20px 31px 3px var(--jp-shadow-penumbra-color),\n 0 8px 38px 7px var(--jp-shadow-ambient-color);\n --jp-elevation-z24: 0 11px 15px -7px var(--jp-shadow-umbra-color),\n 0 24px 38px 3px var(--jp-shadow-penumbra-color),\n 0 9px 46px 8px var(--jp-shadow-ambient-color);\n\n \/* Borders\n *\n * The following variables, specify the visual styling of borders in JupyterLab.\n *\/\n\n --jp-border-width: 1px;\n --jp-border-color0: var(--md-grey-400);\n --jp-border-color1: var(--md-grey-400);\n --jp-border-color2: var(--md-grey-300);\n --jp-border-color3: var(--md-grey-200);\n --jp-inverse-border-color: var(--md-grey-600);\n --jp-border-radius: 2px;\n\n \/* UI Fonts\n *\n * The UI font CSS variables are used for the typography all of the JupyterLab\n * user interface elements that are not directly user generated content.\n *\n * The font sizing here is done assuming that the body font size of --jp-ui-font-size1\n * is applied to a parent element. When children elements, such as headings, are sized\n * in em all things will be computed relative to that body size.\n *\/\n\n --jp-ui-font-scale-factor: 1.2;\n --jp-ui-font-size0: 0.83333em;\n --jp-ui-font-size1: 13px; \/* Base font size *\/\n --jp-ui-font-size2: 1.2em;\n --jp-ui-font-size3: 1.44em;\n --jp-ui-font-family: system-ui, -apple-system, blinkmacsystemfont, 'Segoe UI',\n helvetica, arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji',\n 'Segoe UI Symbol';\n\n \/*\n * Use these font colors against the corresponding main layout colors.\n * In a light theme, these go from dark to light.\n *\/\n\n \/* Defaults use Material Design specification *\/\n --jp-ui-font-color0: rgba(0, 0, 0, 1);\n --jp-ui-font-color1: rgba(0, 0, 0, 0.87);\n --jp-ui-font-color2: rgba(0, 0, 0, 0.54);\n --jp-ui-font-color3: rgba(0, 0, 0, 0.38);\n\n \/*\n * Use these against the brand\/accent\/warn\/error colors.\n * These will typically go from light to darker, in both a dark and light theme.\n *\/\n\n --jp-ui-inverse-font-color0: rgba(255, 255, 255, 1);\n --jp-ui-inverse-font-color1: rgba(255, 255, 255, 1);\n --jp-ui-inverse-font-color2: rgba(255, 255, 255, 0.7);\n --jp-ui-inverse-font-color3: rgba(255, 255, 255, 0.5);\n\n \/* Content Fonts\n *\n * Content font variables are used for typography of user generated content.\n *\n * The font sizing here is done assuming that the body font size of --jp-content-font-size1\n * is applied to a parent element. When children elements, such as headings, are sized\n * in em all things will be computed relative to that body size.\n *\/\n\n --jp-content-line-height: 1.6;\n --jp-content-font-scale-factor: 1.2;\n --jp-content-font-size0: 0.83333em;\n --jp-content-font-size1: 14px; \/* Base font size *\/\n --jp-content-font-size2: 1.2em;\n --jp-content-font-size3: 1.44em;\n --jp-content-font-size4: 1.728em;\n --jp-content-font-size5: 2.0736em;\n\n \/* This gives a magnification of about 125% in presentation mode over normal. *\/\n --jp-content-presentation-font-size1: 17px;\n --jp-content-heading-line-height: 1;\n --jp-content-heading-margin-top: 1.2em;\n --jp-content-heading-margin-bottom: 0.8em;\n --jp-content-heading-font-weight: 500;\n\n \/* Defaults use Material Design specification *\/\n --jp-content-font-color0: rgba(0, 0, 0, 1);\n --jp-content-font-color1: rgba(0, 0, 0, 0.87);\n --jp-content-font-color2: rgba(0, 0, 0, 0.54);\n --jp-content-font-color3: rgba(0, 0, 0, 0.38);\n --jp-content-link-color: var(--md-blue-900);\n --jp-content-font-family: system-ui, -apple-system, blinkmacsystemfont,\n 'Segoe UI', helvetica, arial, sans-serif, 'Apple Color Emoji',\n 'Segoe UI Emoji', 'Segoe UI Symbol';\n\n \/*\n * Code Fonts\n *\n * Code font variables are used for typography of code and other monospaces content.\n *\/\n\n --jp-code-font-size: 13px;\n --jp-code-line-height: 1.3077; \/* 17px for 13px base *\/\n --jp-code-padding: 5px; \/* 5px for 13px base, codemirror highlighting needs integer px value *\/\n --jp-code-font-family-default: menlo, consolas, 'DejaVu Sans Mono', monospace;\n --jp-code-font-family: var(--jp-code-font-family-default);\n\n \/* This gives a magnification of about 125% in presentation mode over normal. *\/\n --jp-code-presentation-font-size: 16px;\n\n \/* may need to tweak cursor width if you change font size *\/\n --jp-code-cursor-width0: 1.4px;\n --jp-code-cursor-width1: 2px;\n --jp-code-cursor-width2: 4px;\n\n \/* Layout\n *\n * The following are the main layout colors use in JupyterLab. In a light\n * theme these would go from light to dark.\n *\/\n\n --jp-layout-color0: white;\n --jp-layout-color1: white;\n --jp-layout-color2: var(--md-grey-200);\n --jp-layout-color3: var(--md-grey-400);\n --jp-layout-color4: var(--md-grey-600);\n\n \/* Inverse Layout\n *\n * The following are the inverse layout colors use in JupyterLab. In a light\n * theme these would go from dark to light.\n *\/\n\n --jp-inverse-layout-color0: #111;\n --jp-inverse-layout-color1: var(--md-grey-900);\n --jp-inverse-layout-color2: var(--md-grey-800);\n --jp-inverse-layout-color3: var(--md-grey-700);\n --jp-inverse-layout-color4: var(--md-grey-600);\n\n \/* Brand\/accent *\/\n\n --jp-brand-color0: var(--md-blue-900);\n --jp-brand-color1: var(--md-blue-700);\n --jp-brand-color2: var(--md-blue-300);\n --jp-brand-color3: var(--md-blue-100);\n --jp-brand-color4: var(--md-blue-50);\n --jp-accent-color0: var(--md-green-900);\n --jp-accent-color1: var(--md-green-700);\n --jp-accent-color2: var(--md-green-300);\n --jp-accent-color3: var(--md-green-100);\n\n \/* State colors (warn, error, success, info) *\/\n\n --jp-warn-color0: var(--md-orange-900);\n --jp-warn-color1: var(--md-orange-700);\n --jp-warn-color2: var(--md-orange-300);\n --jp-warn-color3: var(--md-orange-100);\n --jp-error-color0: var(--md-red-900);\n --jp-error-color1: var(--md-red-700);\n --jp-error-color2: var(--md-red-300);\n --jp-error-color3: var(--md-red-100);\n --jp-success-color0: var(--md-green-900);\n --jp-success-color1: var(--md-green-700);\n --jp-success-color2: var(--md-green-300);\n --jp-success-color3: var(--md-green-100);\n --jp-info-color0: var(--md-cyan-900);\n --jp-info-color1: var(--md-cyan-700);\n --jp-info-color2: var(--md-cyan-300);\n --jp-info-color3: var(--md-cyan-100);\n\n \/* Cell specific styles *\/\n\n --jp-cell-padding: 5px;\n --jp-cell-collapser-width: 8px;\n --jp-cell-collapser-min-height: 20px;\n --jp-cell-collapser-not-active-hover-opacity: 0.6;\n --jp-cell-editor-background: var(--md-grey-100);\n --jp-cell-editor-border-color: var(--md-grey-300);\n --jp-cell-editor-box-shadow: inset 0 0 2px var(--md-blue-300);\n --jp-cell-editor-active-background: var(--jp-layout-color0);\n --jp-cell-editor-active-border-color: var(--jp-brand-color1);\n --jp-cell-prompt-width: 64px;\n --jp-cell-prompt-font-family: var(--jp-code-font-family-default);\n --jp-cell-prompt-letter-spacing: 0;\n --jp-cell-prompt-opacity: 1;\n --jp-cell-prompt-not-active-opacity: 0.5;\n --jp-cell-prompt-not-active-font-color: var(--md-grey-700);\n\n \/* A custom blend of MD grey and blue 600\n * See https:\/\/meyerweb.com\/eric\/tools\/color-blend\/#546E7A:1E88E5:5:hex *\/\n --jp-cell-inprompt-font-color: #307fc1;\n\n \/* A custom blend of MD grey and orange 600\n * https:\/\/meyerweb.com\/eric\/tools\/color-blend\/#546E7A:F4511E:5:hex *\/\n --jp-cell-outprompt-font-color: #bf5b3d;\n\n \/* Notebook specific styles *\/\n\n --jp-notebook-padding: 10px;\n --jp-notebook-select-background: var(--jp-layout-color1);\n --jp-notebook-multiselected-color: var(--md-blue-50);\n\n \/* The scroll padding is calculated to fill enough space at the bottom of the\n notebook to show one single-line cell (with appropriate padding) at the top\n when the notebook is scrolled all the way to the bottom. We also subtract one\n pixel so that no scrollbar appears if we have just one single-line cell in the\n notebook. This padding is to enable a 'scroll past end' feature in a notebook.\n *\/\n --jp-notebook-scroll-padding: calc(\n 100% - var(--jp-code-font-size) * var(--jp-code-line-height) -\n var(--jp-code-padding) - var(--jp-cell-padding) - 1px\n );\n\n \/* Rendermime styles *\/\n\n --jp-rendermime-error-background: #fdd;\n --jp-rendermime-table-row-background: var(--md-grey-100);\n --jp-rendermime-table-row-hover-background: var(--md-light-blue-50);\n\n \/* Dialog specific styles *\/\n\n --jp-dialog-background: rgba(0, 0, 0, 0.25);\n\n \/* Console specific styles *\/\n\n --jp-console-padding: 10px;\n\n \/* Toolbar specific styles *\/\n\n --jp-toolbar-border-color: var(--jp-border-color1);\n --jp-toolbar-micro-height: 8px;\n --jp-toolbar-background: var(--jp-layout-color1);\n --jp-toolbar-box-shadow: 0 0 2px 0 rgba(0, 0, 0, 0.24);\n --jp-toolbar-header-margin: 4px 4px 0 4px;\n --jp-toolbar-active-background: var(--md-grey-300);\n\n \/* Statusbar specific styles *\/\n\n --jp-statusbar-height: 24px;\n\n \/* Input field styles *\/\n\n --jp-input-box-shadow: inset 0 0 2px var(--md-blue-300);\n --jp-input-active-background: var(--jp-layout-color1);\n --jp-input-hover-background: var(--jp-layout-color1);\n --jp-input-background: var(--md-grey-100);\n --jp-input-border-color: var(--jp-inverse-border-color);\n --jp-input-active-border-color: var(--jp-brand-color1);\n --jp-input-active-box-shadow-color: rgba(19, 124, 189, 0.3);\n\n \/* General editor styles *\/\n\n --jp-editor-selected-background: #d9d9d9;\n --jp-editor-selected-focused-background: #d7d4f0;\n --jp-editor-cursor-color: var(--jp-ui-font-color0);\n\n \/* Code mirror specific styles *\/\n\n --jp-mirror-editor-keyword-color: #008000;\n --jp-mirror-editor-atom-color: #88f;\n --jp-mirror-editor-number-color: #080;\n --jp-mirror-editor-def-color: #00f;\n --jp-mirror-editor-variable-color: var(--md-grey-900);\n --jp-mirror-editor-variable-2-color: rgb(0, 54, 109);\n --jp-mirror-editor-variable-3-color: #085;\n --jp-mirror-editor-punctuation-color: #05a;\n --jp-mirror-editor-property-color: #05a;\n --jp-mirror-editor-operator-color: #a2f;\n --jp-mirror-editor-comment-color: #408080;\n --jp-mirror-editor-string-color: #ba2121;\n --jp-mirror-editor-string-2-color: #708;\n --jp-mirror-editor-meta-color: #a2f;\n --jp-mirror-editor-qualifier-color: #555;\n --jp-mirror-editor-builtin-color: #008000;\n --jp-mirror-editor-bracket-color: #997;\n --jp-mirror-editor-tag-color: #170;\n --jp-mirror-editor-attribute-color: #00c;\n --jp-mirror-editor-header-color: blue;\n --jp-mirror-editor-quote-color: #090;\n --jp-mirror-editor-link-color: #00c;\n --jp-mirror-editor-error-color: #f00;\n --jp-mirror-editor-hr-color: #999;\n\n \/*\n RTC user specific colors.\n These colors are used for the cursor, username in the editor,\n and the icon of the user.\n *\/\n\n --jp-collaborator-color1: #ffad8e;\n --jp-collaborator-color2: #dac83d;\n --jp-collaborator-color3: #72dd76;\n --jp-collaborator-color4: #00e4d0;\n --jp-collaborator-color5: #45d4ff;\n --jp-collaborator-color6: #e2b1ff;\n --jp-collaborator-color7: #ff9de6;\n\n \/* Vega extension styles *\/\n\n --jp-vega-background: white;\n\n \/* Sidebar-related styles *\/\n\n --jp-sidebar-min-width: 250px;\n\n \/* Search-related styles *\/\n\n --jp-search-toggle-off-opacity: 0.5;\n --jp-search-toggle-hover-opacity: 0.8;\n --jp-search-toggle-on-opacity: 1;\n --jp-search-selected-match-background-color: rgb(245, 200, 0);\n --jp-search-selected-match-color: black;\n --jp-search-unselected-match-background-color: var(\n --jp-inverse-layout-color0\n );\n --jp-search-unselected-match-color: var(--jp-ui-inverse-font-color0);\n\n \/* Icon colors that work well with light or dark backgrounds *\/\n --jp-icon-contrast-color0: var(--md-purple-600);\n --jp-icon-contrast-color1: var(--md-green-600);\n --jp-icon-contrast-color2: var(--md-pink-600);\n --jp-icon-contrast-color3: var(--md-blue-600);\n\n \/* Button colors *\/\n --jp-accept-color-normal: var(--md-blue-700);\n --jp-accept-color-hover: var(--md-blue-800);\n --jp-accept-color-active: var(--md-blue-900);\n --jp-warn-color-normal: var(--md-red-700);\n --jp-warn-color-hover: var(--md-red-800);\n --jp-warn-color-active: var(--md-red-900);\n --jp-reject-color-normal: var(--md-grey-600);\n --jp-reject-color-hover: var(--md-grey-700);\n --jp-reject-color-active: var(--md-grey-800);\n\n \/* File or activity icons and switch semantic variables *\/\n --jp-jupyter-icon-color: #f37626;\n --jp-notebook-icon-color: #f37626;\n --jp-json-icon-color: var(--md-orange-700);\n --jp-console-icon-background-color: var(--md-blue-700);\n --jp-console-icon-color: white;\n --jp-terminal-icon-background-color: var(--md-grey-800);\n --jp-terminal-icon-color: var(--md-grey-200);\n --jp-text-editor-icon-color: var(--md-grey-700);\n --jp-inspector-icon-color: var(--md-grey-700);\n --jp-switch-color: var(--md-grey-400);\n --jp-switch-true-position-color: var(--md-orange-900);\n}\n<\/style>\n<style type=\"text\/css\">\n\/* Force rendering true colors when outputing to pdf *\/\n* {\n -webkit-print-color-adjust: exact;\n}\n\n\/* Misc *\/\na.anchor-link {\n display: none;\n}\n\n\/* Input area styling *\/\n.jp-InputArea {\n overflow: hidden;\n}\n\n.jp-InputArea-editor {\n overflow: hidden;\n}\n\n.cm-editor.cm-s-jupyter .highlight pre {\n\/* weird, but --jp-code-padding defined to be 5px but 4px horizontal padding is hardcoded for pre.cm-line *\/\n padding: var(--jp-code-padding) 4px;\n margin: 0;\n\n font-family: inherit;\n font-size: inherit;\n line-height: inherit;\n color: inherit;\n\n}\n\n.jp-OutputArea-output pre {\n line-height: inherit;\n font-family: inherit;\n}\n\n.jp-RenderedText pre {\n color: var(--jp-content-font-color1);\n font-size: var(--jp-code-font-size);\n}\n\n\/* Hiding the collapser by default *\/\n.jp-Collapser {\n display: none;\n}\n\n@page {\n margin: 0.5in; \/* Margin for each printed piece of paper *\/\n}\n\n@media print {\n .jp-Cell-inputWrapper,\n .jp-Cell-outputWrapper {\n display: block;\n }\n}\n<\/style>\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/latest.js?config=TeX-AMS_CHTML-full,Safe\"> <\/script>\n\n<script type=\"text\/x-mathjax-config\">\n init_mathjax = function() {\n if (window.MathJax) {\n \/\/ MathJax loaded\n MathJax.Hub.Config({\n TeX: {\n equationNumbers: {\n autoNumber: \"AMS\",\n useLabelIds: true\n }\n },\n tex2jax: {\n inlineMath: [ ['$','$'], [\"\\\$\",\"\\\$\"] ],\n displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ],\n processEscapes: true,\n processEnvironments: true\n },\n displayAlign: 'center',\n CommonHTML: {\n linebreaks: {\n automatic: true\n }\n }\n });\n\n MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n }\n }\n init_mathjax();\n <\/script>\n<script type=\"module\">\n document.addEventListener(\"DOMContentLoaded\", async () => {\n const diagrams = document.querySelectorAll(\".jp-Mermaid > pre.mermaid\");\n \/\/ do not load mermaidjs if not needed\n if (!diagrams.length) {\n return;\n }\n const mermaid = (await import(\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mermaid\/10.7.0\/mermaid.esm.min.mjs\")).default;\n const parser = new DOMParser();\n\n mermaid.initialize({\n maxTextSize: 100000,\n maxEdges: 100000,\n startOnLoad: false,\n fontFamily: window\n .getComputedStyle(document.body)\n .getPropertyValue(\"--jp-ui-font-family\"),\n theme: document.querySelector(\"body[data-jp-theme-light='true']\")\n ? \"default\"\n : \"dark\",\n });\n\n let _nextMermaidId = 0;\n\n function makeMermaidImage(svg) {\n const img = document.createElement(\"img\");\n const doc = parser.parseFromString(svg, \"image\/svg+xml\");\n const svgEl = doc.querySelector(\"svg\");\n const { maxWidth } = svgEl?.style || {};\n const firstTitle = doc.querySelector(\"title\");\n const firstDesc = doc.querySelector(\"desc\");\n\n img.setAttribute(\"src\", `data:image\/svg+xml,${encodeURIComponent(svg)}`);\n if (maxWidth) {\n img.width = parseInt(maxWidth);\n }\n if 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}\n\n async function renderOneMarmaid(src) {\n const id = `jp-mermaid-${_nextMermaidId++}`;\n const parent = src.parentNode;\n let raw = src.textContent.trim();\n const el = document.createElement(\"div\");\n el.style.visibility = \"hidden\";\n document.body.appendChild(el);\n let results = null;\n let output = null;\n try {\n let { svg } = await mermaid.render(id, raw, el);\n svg = cleanMermaidSvg(svg);\n results = makeMermaidImage(svg);\n output = document.createElement(\"figure\");\n results.map(output.appendChild, output);\n } catch (err) {\n parent.classList.add(\"jp-mod-warning\");\n results = await makeMermaidError(raw);\n output = results[0];\n } finally {\n el.remove();\n }\n parent.classList.add(\"jp-RenderedMermaid\");\n parent.appendChild(output);\n }\n\n\n \/**\n * Post-process to ensure mermaid diagrams contain only valid SVG and XHTML.\n *\/\n function cleanMermaidSvg(svg) {\n return svg.replace(RE_VOID_ELEMENT, replaceVoidElement);\n }\n\n\n \/**\n * A regular expression for all void elements, which may include attributes and\n * a slash.\n *\n * @see https:\/\/developer.mozilla.org\/en-US\/docs\/Glossary\/Void_element\n *\n * Of these, only `<br>` is generated by Mermaid in place of `\\n`,\n * but _any_ \"malformed\" tag will break the SVG rendering entirely.\n *\/\n const RE_VOID_ELEMENT =\n \/<\\s*(area|base|br|col|embed|hr|img|input|link|meta|param|source|track|wbr)\\s*([^>]*?)\\s*>\/gi;\n\n \/**\n * Ensure a void element is closed with a slash, preserving any attributes.\n *\/\n function replaceVoidElement(match, tag, rest) {\n rest = rest.trim();\n if (!rest.endsWith('\/')) {\n rest = `${rest} \/`;\n }\n return `<${tag} ${rest}>`;\n }\n\n void Promise.all([...diagrams].map(renderOneMarmaid));\n });\n<\/script>\n<style>\n .jp-Mermaid:not(.jp-RenderedMermaid) {\n display: none;\n }\n\n .jp-RenderedMermaid {\n overflow: auto;\n display: flex;\n }\n\n .jp-RenderedMermaid.jp-mod-warning {\n width: auto;\n padding: 0.5em;\n margin-top: 0.5em;\n border: var(--jp-border-width) solid var(--jp-warn-color2);\n border-radius: var(--jp-border-radius);\n color: var(--jp-ui-font-color1);\n font-size: var(--jp-ui-font-size1);\n white-space: pre-wrap;\n word-wrap: break-word;\n }\n\n .jp-RenderedMermaid figure {\n margin: 0;\n overflow: auto;\n max-width: 100%;\n }\n\n .jp-RenderedMermaid img {\n max-width: 100%;\n }\n\n .jp-RenderedMermaid-Details > pre {\n margin-top: 1em;\n }\n\n .jp-RenderedMermaid-Summary {\n color: var(--jp-warn-color2);\n }\n\n .jp-RenderedMermaid:not(.jp-mod-warning) pre {\n display: none;\n }\n\n .jp-RenderedMermaid-Summary > pre {\n display: inline-block;\n white-space: normal;\n }\n<\/style>\n<\/head>\n<body class=\"jp-Notebook\" data-jp-theme-light=\"true\" data-jp-theme-name=\"JupyterLab Light\">\n<main>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<h1 id=\"Logarithms-and-heteroskedasticity\">Logarithms and heteroskedasticity<a class=\"anchor-link\" href=\"#Logarithms-and-heteroskedasticity\">\u00b6<\/a><\/h1><p>Here’s a <a href=\"https:\/\/www.reddit.com\/r\/statistics\/comments\/1czsban\/eq_is_it_correct_to_use_logarithmic\/\">question from the Reddit statistics forum<\/a>.<\/p>\n<blockquote>\n<p>Is it correct to use logarithmic transformation in order to mitigate heteroskedasticity?<\/p>\n<p>For my studies I gathered data on certain preferences across a group of people. I am trying to figure out if I can pinpoint preferences to factors such as gender in this case.<\/p>\n<p>I used mixed ANOVA analysis with good success however one of my hypothesis came up with heteroskedasticity when doing Levene’s test. [I’ve been] breaking my head all day on how to solve this. I’ve now used logarithmic transformation to all 3 test results and run another Levene’s. When using the media value the test now results [in] homoskedasticity, however interaction is no longer significant?<\/p>\n<p>Is this the correct way to deal with this problem or is there something I am missing? Thanks in advance to everyone taking their time to help.<\/p>\n<\/blockquote>\n<p>Although the question is about ANOVA, I’m going to reframe it in terms of regression, for two reasons:<\/p>\n<ul>\n<li><p>Discussion of heteroskedasticity is clearer in the context of regression.<\/p>\n<\/li>\n<li><p>For many problems, a regression model is better than ANOVA anyway.<\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput celltag_remove-print\" data-mime-type=\"text\/markdown\">\n<p><a href=\"https:\/\/colab.research.google.com\/github\/AllenDowney\/DataQnA\/blob\/main\/nb\/log_heterosked.ipynb\">Click here to run this notebook on Colab<\/a>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput celltag_hide-cell\" data-mime-type=\"text\/markdown\">\n<p>I’ll download a utilities module with some of my frequently-used functions, and then import the usual libraries.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs celltag_hide-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [1]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"kn\">from<\/span> <span class=\"nn\">os.path<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">basename<\/span><span class=\"p\">,<\/span> <span class=\"n\">exists<\/span>\n\n<span class=\"k\">def<\/span> <span class=\"nf\">download<\/span><span class=\"p\">(<\/span><span class=\"n\">url<\/span><span class=\"p\">):<\/span>\n <span class=\"n\">filename<\/span> <span class=\"o\">=<\/span> <span class=\"n\">basename<\/span><span class=\"p\">(<\/span><span class=\"n\">url<\/span><span class=\"p\">)<\/span>\n <span class=\"k\">if<\/span> <span class=\"ow\">not<\/span> <span class=\"n\">exists<\/span><span class=\"p\">(<\/span><span class=\"n\">filename<\/span><span class=\"p\">):<\/span>\n <span class=\"kn\">from<\/span> <span class=\"nn\">urllib.request<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">urlretrieve<\/span>\n\n <span class=\"n\">local<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">urlretrieve<\/span><span class=\"p\">(<\/span><span class=\"n\">url<\/span><span class=\"p\">,<\/span> <span class=\"n\">filename<\/span><span class=\"p\">)<\/span>\n <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"Downloaded \"<\/span> <span class=\"o\">+<\/span> <span class=\"nb\">str<\/span><span class=\"p\">(<\/span><span class=\"n\">local<\/span><span class=\"p\">))<\/span>\n <span class=\"k\">return<\/span> <span class=\"n\">filename<\/span>\n\n<span class=\"n\">download<\/span><span class=\"p\">(<\/span><span class=\"s1\">'https:\/\/github.com\/AllenDowney\/DataQnA\/raw\/main\/nb\/utils.py'<\/span><span class=\"p\">)<\/span>\n\n<span class=\"kn\">import<\/span> <span class=\"nn\">numpy<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">np<\/span>\n<span class=\"kn\">import<\/span> <span class=\"nn\">matplotlib.pyplot<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">plt<\/span>\n<span class=\"kn\">import<\/span> <span class=\"nn\">pandas<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">pd<\/span>\n<span class=\"kn\">import<\/span> <span class=\"nn\">seaborn<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">sns<\/span>\n\n<span class=\"kn\">from<\/span> <span class=\"nn\">utils<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">decorate<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs celltag_hide-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [2]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"c1\"># install the empiricaldist library, if necessary<\/span>\n\n<span class=\"k\">try<\/span><span class=\"p\">:<\/span>\n <span class=\"kn\">import<\/span> <span class=\"nn\">empiricaldist<\/span>\n<span class=\"k\">except<\/span> <span class=\"ne\">ImportError<\/span><span class=\"p\">:<\/span>\n <span class=\"o\">!<\/span>pip<span class=\"w\"> <\/span>install<span class=\"w\"> <\/span>empiricaldist\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<h2 id=\"What-is-heteroskedasticity?\">What is heteroskedasticity?<a class=\"anchor-link\" href=\"#What-is-heteroskedasticity?\">\u00b6<\/a><\/h2><p>Linear regression is based on a model of the data-generating process where the independent variable <code>y<\/code> is the sum of<\/p>\n<ul>\n<li><p>A linear function of <code>x<\/code> with an unknown slope and intercept, and<\/p>\n<\/li>\n<li><p>Random values drawn from a Gaussian distribution with mean 0 and unknown standard deviation, <code>sigma<\/code>, that does not depend on <code>x<\/code>.<\/p>\n<\/li>\n<\/ul>\n<p>If, contrary to the second assumption, <code>sigma<\/code> depends on <code>x<\/code>, the data-generating process is heteroskedastic.\nSome amount of heteroskedasticity is common in real data, but most of the time it’s not a problem, because:<\/p>\n<ul>\n<li><p>Heteroskedasticity doesn’t bias the estimated parameters of the model, only the standard errors,<\/p>\n<\/li>\n<li><p>Even very strong heteroskedasticity doesn’t affect the standard errors by much, and<\/p>\n<\/li>\n<li><p>For practical purposes we don’t need standard errors to be particularly precise.<\/p>\n<\/li>\n<\/ul>\n<p>To demonstrate, let’s generate some data.\nFirst, we’ll draw <code>xs<\/code> from a normal distribution.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [3]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">seed<\/span><span class=\"p\">(<\/span><span class=\"mi\">17<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">n<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">200<\/span>\n<span class=\"n\">xs<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mi\">30<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"n\">n<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">xs<\/span><span class=\"o\">.<\/span><span class=\"n\">sort<\/span><span class=\"p\">()<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>To generate heteroskedastic data, I’ll use <code>interpolate<\/code> to construct a function where <code>sigma<\/code> depends on <code>x<\/code>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [4]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"kn\">from<\/span> <span class=\"nn\">scipy.interpolate<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">interp1d<\/span>\n\n<span class=\"k\">def<\/span> <span class=\"nf\">interpolate<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigma_seq<\/span><span class=\"p\">):<\/span>\n <span class=\"k\">return<\/span> <span class=\"n\">interp1d<\/span><span class=\"p\">([<\/span><span class=\"n\">xs<\/span><span class=\"o\">.<\/span><span class=\"n\">min<\/span><span class=\"p\">(),<\/span> <span class=\"n\">xs<\/span><span class=\"o\">.<\/span><span class=\"n\">max<\/span><span class=\"p\">()],<\/span> <span class=\"n\">sigma_seq<\/span><span class=\"p\">)(<\/span><span class=\"n\">xs<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>To generate strong heteroskedasticity, I’ll vary sigma over a wide range.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [5]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">sigmas<\/span> <span class=\"o\">=<\/span> <span class=\"n\">interpolate<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"p\">[<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"mf\">6.0<\/span><span class=\"p\">])<\/span>\n<span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">mean<\/span><span class=\"p\">(<\/span><span class=\"n\">sigmas<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[5]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>3.126391153924031<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Here’s what <code>sigma<\/code> looks like as a function of <code>x<\/code>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [6]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigmas<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span>\n <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'sigma'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Now we can generate <code>ys<\/code> with variable values of <code>sigma<\/code>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [7]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">ys<\/span> <span class=\"o\">=<\/span> <span class=\"n\">xs<\/span> <span class=\"o\">+<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">normal<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">sigmas<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>If we make a scatter plot of the data, we see a cone shape that indicates heteroskedasticity.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [8]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">ys<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'y'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Now let’s fit a model to the data.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [9]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"kn\">import<\/span> <span class=\"nn\">statsmodels.api<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">sm<\/span>\n\n<span class=\"n\">X<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sm<\/span><span class=\"o\">.<\/span><span class=\"n\">add_constant<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ols_model<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sm<\/span><span class=\"o\">.<\/span><span class=\"n\">OLS<\/span><span class=\"p\">(<\/span><span class=\"n\">ys<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ols_results<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ols_model<\/span><span class=\"o\">.<\/span><span class=\"n\">fit<\/span><span class=\"p\">()<\/span>\n\n<span class=\"n\">intercept<\/span><span class=\"p\">,<\/span> <span class=\"n\">slope<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ols_results<\/span><span class=\"o\">.<\/span><span class=\"n\">params<\/span>\n<span class=\"n\">intercept<\/span><span class=\"p\">,<\/span> <span class=\"n\">slope<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[9]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>(0.7580177696902339, 0.9672433174107101)<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Here’s what the fitted line looks like.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [10]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">fys<\/span> <span class=\"o\">=<\/span> <span class=\"n\">intercept<\/span> <span class=\"o\">+<\/span> <span class=\"n\">slope<\/span> <span class=\"o\">*<\/span> <span class=\"n\">xs<\/span>\n\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">ys<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">fys<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'y'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>If we plot the absolute values of the residuals, we can see the heteroskedasticity more clearly.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [11]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">resid<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ys<\/span> <span class=\"o\">-<\/span> <span class=\"n\">fys<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">abs<\/span><span class=\"p\">(<\/span><span class=\"n\">resid<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'absolute residual'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<h2 id=\"Testing-for-heteroskedasticity\">Testing for heteroskedasticity<a class=\"anchor-link\" href=\"#Testing-for-heteroskedasticity\">\u00b6<\/a><\/h2><p>OP mentions using the Levene test for heteroskedasticity, which is used to test whether <code>sigma<\/code> is different between groups.\nFor continuous values of <code>x<\/code> and <code>y<\/code>, we can use the Breusch-Pagan Lagrange Multiplier test:<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [12]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"kn\">from<\/span> <span class=\"nn\">statsmodels.stats.diagnostic<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">het_breuschpagan<\/span>\n\n<span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">p_value<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">het_breuschpagan<\/span><span class=\"p\">(<\/span><span class=\"n\">resid<\/span><span class=\"p\">,<\/span> <span class=\"n\">ols_model<\/span><span class=\"o\">.<\/span><span class=\"n\">exog<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">p_value<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[12]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>0.0006411829020109725<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Or White’s Lagrange Multiplier test:<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [13]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"kn\">from<\/span> <span class=\"nn\">statsmodels.stats.diagnostic<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">het_white<\/span>\n\n<span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">p_value<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">het_white<\/span><span class=\"p\">(<\/span><span class=\"n\">resid<\/span><span class=\"p\">,<\/span> <span class=\"n\">ols_model<\/span><span class=\"o\">.<\/span><span class=\"n\">exog<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">p_value<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[13]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>0.0019263142806157931<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Both tests produce small p-values, which means that if we generate a dataset by a homoskedastic process, there is almost no chance it would have as much heteroskedasticity as the dataset we generated.<\/p>\n<p>If you have never heard of either of these tests, don’t panic — neither had I under I looked them up for this example.\nAnd don’t worry about remembering them, because you should never use them again.\nLike testing for normality, testing for heteroskedasticity is never useful.<\/p>\n<p>Why? Because in almost any real dataset, you will find some heteroskedasticity.\nSo if you test for it, there are only two possible results:<\/p>\n<ul>\n<li><p>If the heteroskedasticity is small and you don’t have much data, you will fail to reject the null hypothesis.<\/p>\n<\/li>\n<li><p>If the heteroskedasticity is large or you have a lot of data, you will reject the null hypothesis.<\/p>\n<\/li>\n<\/ul>\n<p>Either way, you learn nothing — and in particular, you don’t learn the answer to the question you actually care about, which is whether the heteroskedasticity is so large that the effect on the standard errors is large enough that you should care.<\/p>\n<p>And the answer to that question is almost always no.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<h2 id=\"Should-we-care?\">Should we care?<a class=\"anchor-link\" href=\"#Should-we-care?\">\u00b6<\/a><\/h2><p>The dataset we generated has very large heteroskedasticity.\nLet’s see how much effect that has on the results.\nHere are the standard errors from simple linear regression:<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [14]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">ols_results<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[14]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>array([6.06159018, 0.20152957])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Now, there are several ways to generate standard errors that are robust in the presence of heteroskedasticity.\nOne is the Huber-White estimator, which we can compute like this:<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [15]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">robust_se<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ols_results<\/span><span class=\"o\">.<\/span><span class=\"n\">get_robustcov_results<\/span><span class=\"p\">(<\/span><span class=\"n\">cov_type<\/span><span class=\"o\">=<\/span><span class=\"s1\">'HC3'<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">robust_se<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[15]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>array([6.73913518, 0.2268012 ])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Another is to use Huber regression.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [16]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">huber_model<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sm<\/span><span class=\"o\">.<\/span><span class=\"n\">RLM<\/span><span class=\"p\">(<\/span><span class=\"n\">ys<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"o\">=<\/span><span class=\"n\">sm<\/span><span class=\"o\">.<\/span><span class=\"n\">robust<\/span><span class=\"o\">.<\/span><span class=\"n\">norms<\/span><span class=\"o\">.<\/span><span class=\"n\">HuberT<\/span><span class=\"p\">())<\/span>\n<span class=\"n\">huber_results<\/span> <span class=\"o\">=<\/span> <span class=\"n\">huber_model<\/span><span class=\"o\">.<\/span><span class=\"n\">fit<\/span><span class=\"p\">()<\/span>\n<span class=\"n\">huber_results<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[16]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>array([5.92709031, 0.19705786])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Another is to use quantile regression.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [17]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">quantile_model<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sm<\/span><span class=\"o\">.<\/span><span class=\"n\">QuantReg<\/span><span class=\"p\">(<\/span><span class=\"n\">ys<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">quantile_results<\/span> <span class=\"o\">=<\/span> <span class=\"n\">quantile_model<\/span><span class=\"o\">.<\/span><span class=\"n\">fit<\/span><span class=\"p\">(<\/span><span class=\"n\">q<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">quantile_results<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[17]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>array([7.6449323 , 0.25417092])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>And one more option is a wild bootstrap, which resamples the residuals by multiplying them by a random sequence of <code>1<\/code> and <code>-1<\/code>.\nThis way of resampling preserves heteroskedasticity, because it only changes the sign of the residuals, not the magnitude, and it maintains the relationship between those magnitudes and <code>x<\/code>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [18]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"kn\">from<\/span> <span class=\"nn\">scipy.stats<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">linregress<\/span>\n\n<span class=\"k\">def<\/span> <span class=\"nf\">wild_bootstrap<\/span><span class=\"p\">():<\/span>\n <span class=\"n\">resampled<\/span> <span class=\"o\">=<\/span> <span class=\"n\">fys<\/span> <span class=\"o\">+<\/span> <span class=\"n\">ols_results<\/span><span class=\"o\">.<\/span><span class=\"n\">resid<\/span> <span class=\"o\">*<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">choice<\/span><span class=\"p\">([<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"n\">n<\/span><span class=\"p\">)<\/span>\n <span class=\"n\">res<\/span> <span class=\"o\">=<\/span> <span class=\"n\">linregress<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">resampled<\/span><span class=\"p\">)<\/span>\n <span class=\"k\">return<\/span> <span class=\"n\">res<\/span><span class=\"o\">.<\/span><span class=\"n\">intercept<\/span><span class=\"p\">,<\/span> <span class=\"n\">res<\/span><span class=\"o\">.<\/span><span class=\"n\">slope<\/span> \n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>We can use <code>wild_bootstrap<\/code> to generate a sample from the sampling distributions of the intercept and slope.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [19]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">sample<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">wild_bootstrap<\/span><span class=\"p\">()<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1001<\/span><span class=\"p\">)]<\/span> \n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>The standard deviation of the sampling distributions is the standard error.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [20]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">bootstrap_bse<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">std<\/span><span class=\"p\">(<\/span><span class=\"n\">sample<\/span><span class=\"p\">,<\/span> <span class=\"n\">axis<\/span><span class=\"o\">=<\/span><span class=\"mi\">0<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">bootstrap_bse<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[20]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>array([6.63622313, 0.22341784])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Now let’s put all of the result in a table.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [21]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">columns<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"s1\">'SE(intercept)'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'SE(slope)'<\/span><span class=\"p\">]<\/span>\n<span class=\"n\">index<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"s1\">'OLS'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'Huber-White'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'Huber'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'quantile'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'bootstrap'<\/span><span class=\"p\">]<\/span>\n<span class=\"n\">data<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">ols_results<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span><span class=\"p\">,<\/span> <span class=\"n\">robust_se<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span><span class=\"p\">,<\/span> <span class=\"n\">huber_results<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span><span class=\"p\">,<\/span> \n <span class=\"n\">quantile_results<\/span><span class=\"o\">.<\/span><span class=\"n\">bse<\/span><span class=\"p\">,<\/span> <span class=\"n\">bootstrap_bse<\/span><span class=\"p\">]<\/span>\n<span class=\"n\">df<\/span> <span class=\"o\">=<\/span> <span class=\"n\">pd<\/span><span class=\"o\">.<\/span><span class=\"n\">DataFrame<\/span><span class=\"p\">(<\/span><span class=\"n\">data<\/span><span class=\"p\">,<\/span> <span class=\"n\">columns<\/span><span class=\"o\">=<\/span><span class=\"n\">columns<\/span><span class=\"p\">,<\/span> <span class=\"n\">index<\/span><span class=\"o\">=<\/span><span class=\"n\">index<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">df<\/span><span class=\"o\">.<\/span><span class=\"n\">sort_values<\/span><span class=\"p\">(<\/span><span class=\"n\">by<\/span><span class=\"o\">=<\/span><span class=\"s1\">'SE(slope)'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[21]:<\/div>\n<div class=\"jp-RenderedHTMLCommon jp-RenderedHTML jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/html\" tabindex=\"0\">\n<div>\n<style scoped=\"\">\n .dataframe tbody tr th:only-of-type {\n vertical-align: middle;\n }\n\n .dataframe tbody tr th {\n vertical-align: top;\n }\n\n .dataframe thead th {\n text-align: right;\n }\n<\/style>\n<table border=\"1\" class=\"dataframe\">\n<thead>\n<tr style=\"text-align: right;\">\n<th><\/th>\n<th>SE(intercept)<\/th>\n<th>SE(slope)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>Huber<\/th>\n<td>5.927090<\/td>\n<td>0.197058<\/td>\n<\/tr>\n<tr>\n<th>OLS<\/th>\n<td>6.061590<\/td>\n<td>0.201530<\/td>\n<\/tr>\n<tr>\n<th>bootstrap<\/th>\n<td>6.636223<\/td>\n<td>0.223418<\/td>\n<\/tr>\n<tr>\n<th>Huber-White<\/th>\n<td>6.739135<\/td>\n<td>0.226801<\/td>\n<\/tr>\n<tr>\n<th>quantile<\/th>\n<td>7.644932<\/td>\n<td>0.254171<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>The standard errors we get from different methods are notably different, but the differences probably don’t matter.<\/p>\n<p>First, I am skeptical of the results from Huber regression.\nWith this kind of heteroskedasticity, the standard errors should be larger than what we get from OLS.\nI’m not sure what’s the problem is, and I haven’t bothered to find out, because I don’t think Huber regression is necessary in the first place.<\/p>\n<p>The results from bootstrapping and the Huber-White estimator are the most reliable — which suggests that the standard errors from quantile regression are too big.<\/p>\n<p>In my opinion, we don’t need esoteric methods to deal with heteroskedasticity.\nIf heteroskedasticity is extreme, consider using wild bootstrap.\nOtherwise, just use ordinary least squares.<\/p>\n<p>Now let’s address OP’s headline question, “Is it correct to use logarithmic transformation in order to mitigate heteroskedasticity?”<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<h2 id=\"Log-transform-help?\">Log transform help?<a class=\"anchor-link\" href=\"#Log-transform-help?\">\u00b6<\/a><\/h2><p>In some cases, a log transform can reduce or eliminate heteroskedasticity.\nHowever, there are several reasons this is not a good idea in general:<\/p>\n<ul>\n<li><p>As we’ve seen, heteroskedasticity is not a big problem, so it usually doesn’t require any mitigation.<\/p>\n<\/li>\n<li><p>Taking a log transform of one or more variables in a regression model changes the meaning of the model — it hypothesizes a relationship between the variables that might not make sense in context.<\/p>\n<\/li>\n<li><p>Anyway, taking a log transform doesn’t always help.<\/p>\n<\/li>\n<\/ul>\n<p>To demonstrate the last point, let’s see what happens if we apply a log transform to the dependent variable:<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [22]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">log_ys<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">log10<\/span><span class=\"p\">(<\/span><span class=\"n\">ys<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Here’s what the scatter plot looks like after the transform.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [23]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">log_ys<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'log10 y'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Here’s what we get if we fit a model to the data.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [24]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">ols_model_log<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sm<\/span><span class=\"o\">.<\/span><span class=\"n\">OLS<\/span><span class=\"p\">(<\/span><span class=\"n\">log_ys<\/span><span class=\"p\">,<\/span> <span class=\"n\">X<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ols_results_log<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ols_model_log<\/span><span class=\"o\">.<\/span><span class=\"n\">fit<\/span><span class=\"p\">()<\/span>\n\n<span class=\"n\">intercept<\/span><span class=\"p\">,<\/span> <span class=\"n\">slope<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ols_results_log<\/span><span class=\"o\">.<\/span><span class=\"n\">params<\/span>\n<span class=\"n\">intercept<\/span><span class=\"p\">,<\/span> <span class=\"n\">slope<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[24]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>(1.072059757295944, 0.013315487289434717)<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>And here’s the fitted line.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [25]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">log_fys<\/span> <span class=\"o\">=<\/span> <span class=\"n\">intercept<\/span> <span class=\"o\">+<\/span> <span class=\"n\">slope<\/span> <span class=\"o\">*<\/span> <span class=\"n\">xs<\/span>\n\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">log_ys<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">log_fys<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'log10 y'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>If we plot the absolute values of the residuals, we can see that the log transform did not entirely remove the heteroskedasticity.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [26]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">log_resid<\/span> <span class=\"o\">=<\/span> <span class=\"n\">log_ys<\/span> <span class=\"o\">-<\/span> <span class=\"n\">log_fys<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">xs<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">abs<\/span><span class=\"p\">(<\/span><span class=\"n\">log_resid<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'.'<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">decorate<\/span><span class=\"p\">(<\/span><span class=\"n\">xlabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'x'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span><span class=\"o\">=<\/span><span class=\"s1\">'absolute residual on log y'<\/span><span class=\"p\">)<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\"><\/div>\n<div class=\"jp-RenderedImage jp-OutputArea-output\" tabindex=\"0\">\n<img decoding=\"async\" alt=\"No description has been provided for this image\" class=\"\" 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\"\/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>Which we can confirm by running the tests again (which we should never do).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [27]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">p_value<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">het_breuschpagan<\/span><span class=\"p\">(<\/span><span class=\"n\">log_resid<\/span><span class=\"p\">,<\/span> <span class=\"n\">ols_model_log<\/span><span class=\"o\">.<\/span><span class=\"n\">exog<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">p_value<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[27]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>0.002154782205265498<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [28]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span><span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">p_value<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">het_white<\/span><span class=\"p\">(<\/span><span class=\"n\">log_resid<\/span><span class=\"p\">,<\/span> <span class=\"n\">ols_model_log<\/span><span class=\"o\">.<\/span><span class=\"n\">exog<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">p_value<\/span>\n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell-outputWrapper\">\n<div class=\"jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser\">\n<\/div>\n<div class=\"jp-OutputArea jp-Cell-outputArea\">\n<div class=\"jp-OutputArea-child jp-OutputArea-executeResult\">\n<div class=\"jp-OutputPrompt jp-OutputArea-prompt\">Out[28]:<\/div>\n<div class=\"jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult\" data-mime-type=\"text\/plain\" tabindex=\"0\">\n<pre>0.006069762292696221<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p>The p-values are bigger, which suggests that the log transform mitigated the heteroskedasticity a little.\nBut if the goal was to eliminate heteroskedasticity, the log transform didn’t do it.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<h2 id=\"Discussion\">Discussion<a class=\"anchor-link\" href=\"#Discussion\">\u00b6<\/a><\/h2><p>To summarize:<\/p>\n<ul>\n<li><p>Heteroskedasticity is common in real datasets — if you test for it, you will often find it, provided you have enough data.<\/p>\n<\/li>\n<li><p>Either way, testing does not answer the question you really care about, which is whether the heteroskedasticity is extreme enough to be a problem.<\/p>\n<\/li>\n<li><p>Plain old linear regression is robust to heteroskedasticity, so unless it is really extreme, it is probably not a problem.<\/p>\n<\/li>\n<li><p>Even in the worst case, heteroskedasticity does not bias the estimated parameters — it only affects the standard errors — and we don’t need standard errors to be particularly precise anyway.<\/p>\n<\/li>\n<li><p>Although a log transform can sometimes mitigate heteroskedasticity, it doesn’t always succeed, and even if it does, it’s usually not necessary.<\/p>\n<\/li>\n<li><p>A log transform changes the meaning of the regression model in ways that might not make sense in context.<\/p>\n<\/li>\n<\/ul>\n<p>So, use a log transform if it makes sense in context, not to mitigate a problem that’s not much of a problem in the first place.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"jp-Cell jp-MarkdownCell jp-Notebook-cell\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\"><div class=\"jp-InputPrompt jp-InputArea-prompt\">\n<\/div><div class=\"jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput\" data-mime-type=\"text\/markdown\">\n<p><a href=\"https:\/\/allendowney.github.io\/DataQnA\/index.html\"><em>Data Q&A: Answering the real questions with Python<\/em><\/a><\/p>\n<p>Copyright 2024 <a href=\"https:\/\/allendowney.com\">Allen B. Downey<\/a><\/p>\n<p>License: <a href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/\">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div><div class=\"jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs\">\n<div class=\"jp-Cell-inputWrapper\" tabindex=\"0\">\n<div class=\"jp-Collapser jp-InputCollapser jp-Cell-inputCollapser\">\n<\/div>\n<div class=\"jp-InputArea jp-Cell-inputArea\">\n<div class=\"jp-InputPrompt jp-InputArea-prompt\">In [ ]:<\/div>\n<div class=\"jp-CodeMirrorEditor jp-Editor jp-InputArea-editor\" data-type=\"inline\">\n<div class=\"cm-editor cm-s-jupyter\">\n<div class=\"highlight hl-ipython3\"><pre><span><\/span> \n<\/pre><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/main>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Here’s another installment in Data Q&A: Answering the real questions with Python. Previous installments are available from the Data Q&A landing page. log_heterosked Logarithms and heteroskedasticity\u00b6 Here’s a question from the Reddit statistics forum. Is it correct to use logarithmic transformation in order to mitigate heteroskedasticity? For my studies I gathered data on certain preferences across a group of people. I am trying to figure out if I can pinpoint preferences to factors such as gender in this case. I…<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/www.allendowney.com\/blog\/2024\/05\/26\/logarithms-and-heteroskedasticity\/\"> Read More<span class=\"screen-reader-text\"> Read More<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-1292","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"\n<title>Logarithms and Heteroskedasticity - Probably Overthinking It<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.allendowney.com\/blog\/2024\/05\/26\/logarithms-and-heteroskedasticity\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Logarithms and Heteroskedasticity - Probably Overthinking It\" \/>\n<meta property=\"og:description\" content=\"Here’s another installment in Data Q&A: Answering the real questions with Python. 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Previous installments are available from the Data Q&A landing page. low_percentile Bootstrapping percentiles\u00b6Here's a question from the Reddit statistics forum. I'm trying to figure out how to determine the confidence interval for the .2 percentile temperature for specific\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1262,"url":"https:\/\/www.allendowney.com\/blog\/2024\/04\/09\/data-qa\/","url_meta":{"origin":1292,"position":1},"title":"Data Q&A","author":"AllenDowney","date":"April 9, 2024","format":false,"excerpt":"Today I'm starting a new project with the working title Data Q&A: Answering the real questions with Python. In each installment, I'll take a question from Reddit's statistics forum and answer it, using Python code to demonstrate. The first installment is a question about the harmonic mean, which is a\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1271,"url":"https:\/\/www.allendowney.com\/blog\/2024\/04\/21\/what-does-strength-mean\/","url_meta":{"origin":1292,"position":2},"title":"What does “strength” mean?","author":"AllenDowney","date":"April 21, 2024","format":false,"excerpt":"Here's another installment in Data Q&A: Answering the real questions with Python. Previous installments are available from the Data Q&A landing page. corr_trend What does \"strength\" mean?\u00b6Here's a question from the Reddit statistics forum. 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I have two different samples (about 100 observations per sample) drawn from the same population (or that's what\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1278,"url":"https:\/\/www.allendowney.com\/blog\/2024\/05\/03\/the-mean-of-a-likert-scale\/","url_meta":{"origin":1292,"position":4},"title":"The mean of a Likert scale?","author":"AllenDowney","date":"May 3, 2024","format":false,"excerpt":"Here's another installment in Data Q&A: Answering the real questions with Python. Previous installments are available from the Data Q&A landing page. likert_mean Likert scale analysis\u00b6Here's a question from the Reddit statistics forum. I have collected data regarding how individuals feel about a particular program. They reported their feelings on\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1281,"url":"https:\/\/www.allendowney.com\/blog\/2024\/05\/07\/destructive-testing\/","url_meta":{"origin":1292,"position":5},"title":"Destructive Testing","author":"AllenDowney","date":"May 7, 2024","format":false,"excerpt":"Here's another installment in Data Q&A: Answering the real questions with Python. Previous installments are available from the Data Q&A landing page. sample_size Sample Size Selection\u00b6Here's a question from the Reddit statistics forum. Hi Redditors, I am a civil engineer trying to solve a statistical problem for a current project\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/1292","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/comments?post=1292"}],"version-history":[{"count":2,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/1292\/revisions"}],"predecessor-version":[{"id":1294,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/1292\/revisions\/1294"}],"wp:attachment":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/media?parent=1292"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/categories?post=1292"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/tags?post=1292"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}