Use the data in GPA2.RAW for this exercise.(i) Consider the equationwhere colgpa is cumula...

Use the data in GPA2.RAW for this exercise.

(i) Consider the equation

where colgpa is cumulative college grade point average, hsize is size of high school graduating class, in hundreds, hsperc is academic percentile in graduating class, sat is combined SAT score, female is a binary gender variable, and athlete is a binary variable, which is one for tudent-athletes. What are your expectations for the coefficients in this equation? Which ones are you unsure about?

(ii) Estimate the equation in part (i) and report the results in the usual form. What is the estimated GPA differential between athletes and nonathletes? Is it statistically significant?

(iii) Drop sat from the model and reestimate the equation. Now, what is the estimated effect of being an athlete? Discuss why the estimate is different than that obtained in part (ii).

(iv) In the model from part (i), allow the effect of being an athlete to differ by gender and test the null hypothesis that there is no ceteris paribus difference between women athletes and women nonathletes.

(v) Does the effect of sat on colgpa differ by gender? Justify your answer.