Need help on 11.26. Thank you so much!
11.26. Refer to Computer-assisted learning Problem 11.6. d. Based on the weighted least squares fit in Problemi 11.6e, construct an approximate 95 per- cent confidence interval for B, by means of (6.50), using the estimated standard deviation s{b}. b. Using random X sampling, obtain 750 bootstrap samples of size 12. For each bootstrap sample, (1) use ordinary least squares to regress Y on X and obtain the residuals, (2) estimate the standard deviation function by regressing the absolute residuals on X and then use the fitted standard deviation function and (11.16a) to obtain weights, and (3) use weighted least squares to regress Y on X and obtain the bootstrap estimated regression coefficient b*. (Note that for each bootstrap sample, only one iteration of the iteratively reweighted least squares procedure is to be used.) c. Construct a histograh of the 750 bootstrap estimates bt. Does the bootstrap sampling distribution of b appear to approximate a normal distribution? d. Calculate the sample standard deviation of the 750 bootstrap estimates by. How does this value compare to the estimated standard deviation s{by} used in part (a)? e. Construct a 95 percent bootstrap confidence interval for B, using reflection method (11.59). How does this confidence interval compare with that obtained in part (a)? Does the ap- proximate interval in part (a) appear to be useful for this data set? 11.6. Computer-assisted learning. Data from a study of computer-assisted learning by 12 students, showing the total number of responses in completing a lesson (X) and the cost of computer time (Y, in cents), follow. i: 1 2 3 4 5 6 7 8 9 9 10 11 12 Xi: Yi: 16 77 14 70 22 85 10 50 14 62 17 70 10 55 13 63 19 88 12 57 18 81 11 51 11.26. Refer to Computer-assisted learning Problem 11.6. d. Based on the weighted least squares fit in Problemi 11.6e, construct an approximate 95 per- cent confidence interval for B, by means of (6.50), using the estimated standard deviation s{b}. b. Using random X sampling, obtain 750 bootstrap samples of size 12. For each bootstrap sample, (1) use ordinary least squares to regress Y on X and obtain the residuals, (2) estimate the standard deviation function by regressing the absolute residuals on X and then use the fitted standard deviation function and (11.16a) to obtain weights, and (3) use weighted least squares to regress Y on X and obtain the bootstrap estimated regression coefficient b*. (Note that for each bootstrap sample, only one iteration of the iteratively reweighted least squares procedure is to be used.) c. Construct a histograh of the 750 bootstrap estimates bt. Does the bootstrap sampling distribution of b appear to approximate a normal distribution? d. Calculate the sample standard deviation of the 750 bootstrap estimates by. How does this value compare to the estimated standard deviation s{by} used in part (a)? e. Construct a 95 percent bootstrap confidence interval for B, using reflection method (11.59). How does this confidence interval compare with that obtained in part (a)? Does the ap- proximate interval in part (a) appear to be useful for this data set? 11.6. Computer-assisted learning. Data from a study of computer-assisted learning by 12 students, showing the total number of responses in completing a lesson (X) and the cost of computer time (Y, in cents), follow. i: 1 2 3 4 5 6 7 8 9 9 10 11 12 Xi: Yi: 16 77 14 70 22 85 10 50 14 62 17 70 10 55 13 63 19 88 12 57 18 81 11 51
