5. (The dataset can be downloaded from: https:letles.umn.edu/usersinacht00 1lwwwfnachtsheimeutner/Chapte/BZO%206%20Data%20 Sets/CH06PR05 .txt} a. Prepare an added-variable plot for each of the predictor variables. b. Do you plots in part (a) suggest that the regression relationships in the tted regression function in Problem 4a in Homework 3 are inappropriate for any of the predictor variables? Explain. c. Obtain the tted regression function in Problem 4a in Homework 3 by separately regressing both Y and X2 on X1, and then regressing the residuals in an appropriate fashion. I 1 2 3 14 15 16 X\": 4 4 4 10 10 10 Xr2-' 2 4 2 4 2 4 YE: 64 73 61 95 94 100 Refer to Brand preference a. Obtain the studentized deleted residuals and identify and outlying Y observations. Use the Bonferroni outlier test procedure with u = .10. State the decision rule and conclusion. b. Obtain the diagonal elements of the hat matrix, and provide an explanation for the pattern in these elements. c. Are any of the observations outlying with regard to their X values according to the rule of thumb stated in the chapter? d. Management wishes to estimate the mean degree of brand liking for moisture content X1 = 10 and sweetness X2 = 3. Construct a scatter plot of X2 against X1 and determine visually whether this prediction involves an extrapolation beyond the range of the data. Also, use (10.29} to determine whether an extrapolation is involved. Do your conclusions from the two methods agree? Hmm = X'm(X'X)"Xm (10-29) e. The largest absolute studentized deleted residual is for case 14. Obtain the DFFITS, DFBETAS, and Cook's distance values for this case to assess the inuence of this case. What do you conclude? f. Calculate the average absolute percent difference in the tted values with and without case 14. What does this measure indicate about the inuence of case 14? g. Calculate Cook's distance D.- for each case and prepare an index plot. Are any cases inuential according to this measure