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 (H can be predicted from the ACT test score (X). The results of the study are in the le HW3 3 . txt. a) Obtain the least squares estimates and state the estimated regression function. b) Plot the estimated regression function and the data. Does the estimated regression function appear to t the data well? c) Obtain an estimate of the mean GPA for students with ACT tests core X : 30. d) What is the point estimate of the change in the mean response when the entrance test sore increases by one point? e) Obtain a 99 percent condence interval for [31. Does it include zero? Why might the director of admissions be interested in whether the condence interval includes zero