This exercise refers to the data in Example 7.2.4.

a) Derive each p-value that appears in Example 7.2.4 using a model comparison test.

b) Sometimes SAT scores are expressed as a single score which is obtained by adding SATV and SATM. Can we make better predictions of GPA if we know both sub scores than if we only know the combined score? Conduct the appropriate model comparison test to see.

c) As you might expect, predict() can produce interval estimates for the additive model as well as point estimates. Using an appropriate model, produce a 95% confidence interval for the mean GPA of students who have SATV and SATM scores of 550 and 650, respectively.

d) Many students do not have both ACT and SAT scores, so it can be handy to convert from one to the other for comparison purposes. Provide a formula that an admissions counselor could use to convert from SAT scores to ACT scores and provide some advice about the accuracy of this conversion.