The students data set contains ACT and SAT scores, as well as high school and graduation GPAs, for a sample of 1000 students from a single undergraduate institution over a number of years.
a) At this institution, most students take the ACT. For the small number of students who take the SAT but not the ACT, it would be convenient to have a way of estimating what the ACT score would have been. Fit a model that can be used to predict ACT scores from SAT scores in the students data set.
b) Why don't the degrees of freedom for your model add up to 999?
c) Fit a model that can be used to predict ACT scores from SAT scores in the gpa data set. (Note: SAT is the sum of SATM and SATV.)
d) How do these two models compare?