To further evaluate whether GPA is a linear function of SAT score, you decide to set up an appropriate regression model.

1. Write down your regression model taking care to define your notation clearly. Using appropriate software, estimate the regression model and report your results.
2. Use your regression results to give a one-sentence interpretation of the regression slope estimate.
3. Test whether SAT score is an effective predictor of GPA in the regression model you have estimated in question 6. Make sure you report your null and alternative hypotheses, the test statistic, decision rule, and conclusion to the test.
4. Briefly comment on the relationship between your results for the sample correlation test in question 2 and the regression model test in question 8.