Fit models

1.

Following the examples from class and the handout, fit three models to each dataset, linear, quadratic and log:

$$t = \alpha + \beta s$$ (1)

$$t = \alpha + \beta s^2$$ (2)

$$t = \alpha + \beta s \log s$$ (3)

where t is the run time, s is the problem size, and $\alpha$ and $\beta$ are the parameters you are going to estimate.

You can use either the matrix form or the summation form to do the computation.

2.

For each model, calculate the errors and the R² values. Which model seems to fit the data best?