Use the data in GPA1 to answer this question. We can compare multiple regression estimates, where we control for student achievement and background variables, and compare our findings with the difference-in-means estimate in Computer Exercise C11 in Chapter 2.

(i) In the simple regression equation

colGPA = β₀ +  β₁PC + u

obtain β̂₀ and β̂₁. Interpret these estimates.

(ii) Now add the controls hsGPA and ACT—that is, run the regression colGPA on PC, hsGPA, and ACT. Does the coefficient on PC change much from part (ii)? Does β̂_hsGPA make sense?

(iii) In the estimation from part (ii), what is worth more: Owning a PC or having 10 more points on the ACT score?

(iv) Now to the regression in part (ii) add the two binary indicators for the parents being college graduates. Does the estimate of b1 change much from part (ii)? How much variation are you explaining in colGPA?

(v) Suppose someone looking at your regression from part (iv) says to you, “The variables hsGPA and ACT are probably pretty highly correlated, so you should drop one of them from the regression.”

How would you respond?