Use the data set GPA1 for this exercise.

(i) Use OLS to estimate a model relating colGPA to hsGPA, ACT, skipped, and PC. Obtain the OLS residuals.

(ii) Compute the special case of the White test for heteroskedasticity. In the regression of u^

2 i on colGPAi

, colGPA2 i , obtain the fitted values, say h^

i

.

(iii) Verify that the fitted values from part (ii) are all strictly positive. Then, obtain the weighted least squares estimates using weights 1/h^
i . Compare the weighted least squares estimates for the effect of skipping lectures and the effect of PC ownership with the corresponding OLS estimates. What about their statistical significance?
(iv) In the WLS estimation from part (iii), obtain heteroskedasticity-robust standard errors. In other words, allow for the fact that the variance function estimated in part (ii) might be misspecified.
(See Question 8.4.) Do the standard errors change much from part (iii)?