Using the data in GPA2.RAW on 4,137 college students, the following equation was estimated by OLS:

Where colgpa is measured on a four-point scale, hsperc s the percentile in the high school graduating class (defined so that, for example, hsperc = 5 means the top 5% of the calss),
(i) Why does it make sense for the coefficient on hsperc to be negative?
(ii) What is the predicted college GPA when hsperc = 20 and sat = 1,050?
(iii) Suppose that two high school graduates, A and B, graduated in the same percentile from high school, but Student A's SAT score was 140 points higher (about one standard deviation in the sample). What is the predicted difference in college GPA for these two students? Is the difference large?
(iv) Holding hsperc fixed, what difference in SAT scores leads to a predicted colgpa difference of .50, or one half of a grade point? Comment on your answer?

colgpa 1.392 0135 hsperc +.00148 sat 4,137, R 273,