Using the data on 1, 500 uaf students, the following equation was estimated by ols: colgpa = 1.392 - 0.0135 hsperc + 0.001 48 sat n = 1, 500, r^2 = 0.073 where colgpa is measured on a four-point scale, hsperc is the percentile in the high school graduating class (defined so that, for example, hsperc = 5 means the top five percent of the class), and sat is the combined math and verbal scores on the student achievement test. (a) interpret the intercept. does it have a useful meaning? (b) why does it make sense for the coefficient on hsperc to be negative? (c) what is the predicted college gpa when on hsperc = 21 and sat = 1100? (d) suppose that two high school graduates, a and b, graduated in the same percentile from west valley high school, but student a's sat score was 130 points higher (about one standard deviation in the sample). what is the predicted difference in college gpa for these two students? (e) holding hsperc fixed, what difference in sat scores leads to a predicted colgpa difference of 0.50, or one-half of a grade point? (f) would you say hsperc and sat explain much of the variation in colgpa? why or why not? explain clearly.