4) Based on 107 students' scores on the first exam in a course in econometrics, the following model was estimated by OLS: score = 2.178 + .469expscore + 3.369study + 3.054gpa (0.090) (0.456) (1.457) n=107, R2 = 0.686 In this model, score is the actual score on an exam, expscore is the expected score, study is number of study hours per week, and gpa is the student's grade point average. The standard errors for each estimate are in parentheses below the estimate. Assume the regression model errors are heteroskedastic. a) (4 points) Mike is a student with an expected score of 50, who studies 10 hours per week, and has a gpa of 3.5. Steve has an expected score of 50, studies 14 hours per week, and has a gpa of 3.5. Construct a 95% confidence interval for the difference in their actual exam scores. b) (4 points) Using an F-test, test the null hypothesis that By = 0 against the alternative that it is not at the 5% level c) (4 points) Jointly test the null hypothesis that B1 -.6 and B2 =3 against the alternative that one or both of those restrictions is not true. Assume the t-statistics for testing each restriction individually have a correlation of 0.5