Grade point average. The director of admissions of a small college selected 120 students at random from the new freshman class in a study to determine whether a student's grade point average (GPA) at the end of the freshman year (Y) can be predicted from the ACT test score (X). The results of the study follow. Assume that first-order regression model (1.1) is appropriate. a. Obtain the least squares estimates of beta_0 and beta_1, and state the estimated regression function. b. Plot the estimated regression function and the data. Does the estimated regression function appear to fit the data well? c. Obtain a point estimate of the mean freshman GPA for students with ACT test score X = 30. d. What is the point estimate of the change in the mean response when the entrance test $core increases by one point? e. Obtain the residuals eh Do they sum to zero in accord with (1.17)? f. Estimate sigma^2 and sigma. In what units is o expressed?