C9.8 Use the data in TWOYEAR.RAW for this exercise. (i) The variable stotal is a standardized test variable, which can act as a proxy variable for unobserved ability. Find the sample mean and stan- dard deviation of stotal. (ii) Run simple regressions of jc and univ on stotal. Are both college educa- tion variables statistically related to stotal? Explain.

(iii) Add stotal to equation (4.17) and test the hypothesis that the returns to two- and four-year colleges are the same against the alternative that the return to four-year colleges is greater. How do your findings compare with those from Section 4.4? (iv) Add stotal to the equation estimated in part (iii). Does a quadratic in the test score variable seem necessary? GON LENG (v) Add the interaction terms stotal-jc and stotal-univ to part (iii). Are these terms jointly significant? (vi) What would be your final model that controls for ability through the use of stotal? Justify your answer.