The following table shows the results of fitting a linear regression model of starting annual salaries on a constant, GPA (4 point scale), and a variable (Metrics =1) indicating whether the recent economics graduate took an econometrics course for a random sample of 50 recent economics graduates from a large state university. Note that econometrics was not required at this university.
a. Can these results be used to predict what would happen if this university made econometrics a required course for economics students? (hint: consider the possibility of sample selection bias).
b. Suppose that econometrics is a very hard class, and the instructor is a very hard grader. What is the predicted change in starting salary for a student who has just taken econometrics, and this resulted in decreasing his GPA by .5 points. Give a 90% confidence interval for this prediction. The covariance matrix of the estimated parameters are:
c. Note that the standard errors in the above regression are calculated assuming homoskedasticity. Explain why we typically use heteroskedastic-consistent standard errors.