fu "twa" rdv t ra e Problem 1 19 . . r 0 ra e 01n ave V e e p g a. Obtain the residuals ei. DO they sum to zero in accord With (1.17)? b. Estimate 02 and a. In what units is 0' expressed? 1" 11 4 anChapter 1 Linear Regression with One Predictor Variable 35 i: 1 2 3 118 119 120 "MN-"'- X,: 21 14 28 28 16 28 Y,: 3.897 3.885 3.778 3.914 1.860 2.948 a. Obtain the least squares estimates of fig and ,81 , 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?fu "twa" rdv t ra e Problem 1 19 . . r 0 ra e 01n ave V e e p g a. Obtain the residuals ei. DO they sum to zero in accord With (1.17)? b. Estimate 02 and a. In what units is 0' expressed? 1" 11 4 an.. .v wa 54111LLJ "VU Chill; 2.4 Refer to Grade point average Problem 1.19. a. Obtain a 99 percent confidence interval for ,81. Interpret your confidence interval. Does it include zero? Why might the director of admissions be interested in Whether the confidence interval includes zero?95 percent prediction interval. Interpret your prediction interval. C. IS the prediction interval in part (b) Wider than the confidence interval in part (a)? Should it be? d. Determine the boundary values of the 95 percent confidence band for the regression line When Xh = 28. Is your confidence band Wider at this point than the confidence interval in part (a)? Should it be?"Mi. Refer to Grade point average Problem 1.19. it. Would it be more reasonable to consider the Xi as known constants or as random variables here? Explain. b. If the Xi were considered to be random variables, would this have any effect on prediction intervals for new applicants? Explain. 4 'A 4- - vr 11.' -"A'-- ----.C.J-..AA -..- - 4- A A A - 4