FOR REFERENCE

LOOKING SPECIFICALLY FOR WORKING-HOTELLING CONFIDENCE BAND

2.13. Refer to Grade point average Problem 1.19. d. Determine the boundary values of the 95 percent confidence band for the regression line when X = 28. Is your confidence band wider at this point than the confidence interval in part (a)? Should it be? 1.19. Grade poit 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. i: X: Yi: 1 21 3.897 2 14 3.885 3 28 3.778 ... ... ... 118 28 3.914 119 16 1.860 120 28 2.948 a. Obtain the least squares estimates of Bo and Bi, 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 score increases by one point