1. (30 points) Using the data, the following equation is estimated for the fall and second semester students: trmgpa=-2.12+ 0.900 crsgpa +0.0018sat- 0.0039 hsperc (0.0002) (0.0018) (0.55) (0.175) n=269, R = 0.465 where trmgpa is term GPA, crsgpa is a weighted average of overall GPA in courses taken, sat is SAT score and hsperc is graduating percentile in high school class (defined so that, for example, hsperc-5 means the top five percent of the class). (a) Interpret the coefficient on sat clearly. (b) Interpret the coefficient on hsperc clearly. (c) From (b), (i) State the null hypothesis that hsperc has no effect on term GPA against the alternative that hsperc has a negative effect. (ii) Carry out the test at the 5% significance level. Is hsperc statistically significant at the 5% level against a one-sided alternative? (d) Is crsgpa statistically significant at the 10% level against a two-sided alternative? Show your work. (e) Is sat statistically significant at the 1% level against a two-sided alternative? Show your work. (f) Obtain a 90% confidence interval for Basperc