Using the data in GPA3.RAW, the following equation was estimated for the fall and second semester students:

Here, trmgpa is term GPA, crsgpa is a weighted average of overall GPA in courses taken, cumgpa is GPA prior to the current semester, tothrs is total credit hours prior to the semester, sat is SAT score, hsperc is graduating percentile in high school class, female is a gender dummy, and season is a dummy variable equal to unity if the student's sport is in season during the fall. The usual and heteroskedasticity robust standard errors are reported in parentheses and brackets, respectively.
(i) Do the variables crsgpa, cumgpa, and tothrs have the expected estimated effects? Which of these variables are statistically significant at the 5% level? Does it matter which standard errors are used?
(ii) Why does the hypothesis H0: (crsgpa - 1 make sense? Test this hypothesis against the two-sided alternative at the 5% level, using both standard errors. Describe your conclusions.
(iii) Test whether there is an in-season effect on term GPA, using both standard errors. Does the significance level at which the null can be rejected depend on the standard error used?

rmgpa-2.12900 crsgpa 193 cumgpa0014 tothrs (.55) (175) L55 L166 (064) 1.074] (0012) [.0012] +0018 sat 0039 hsperc .351 female .157 season 0002) .0018) .0002 [0019] (.085) .079] (.098) 1.080 n 269, R 465.