Question

can you answer question 9 please

Problems 473 results from parts (a), (b), and (c). What model seems most plausible? How do the data limit your conclusions? tle the data from Freund (1979), presented in Problem 22 in Chapter 14. Taking be model discussed there as the maximum model, repeat parts (a) through (h) of Problem 6. In part (h), note the possible role of collinearity. A random sample of data was collected on residential sales in a large city. The accompanying table shows the selling price (Y, in $1.000s), area (X, in hundreds of square 8. feet), number of bedrooms (X), total number of rooms (X), house age . in years), and location (Z-0 for in-town and inner suburbs, Z- 1 for outer (X suburbs) In parts (a) through (e), use variables X, .X, X, X, and Z as the predictor variables. Use the accompanying computer output to answer parts (a)-(d). a. Use the all possible regressions procedure to suggest a best model. b. Use the stepwise regression algorithm to suggest a best model. c. Use the backward-elimination algorithm to suggest a best model. d. Which of the models selected in parts (a), (b), and (c) seems to be the best model, and why? House x, x, 19.0 10.0 15 12 83.1 85.2 12.0 15.0 12.0 12 85.2 85.2 84.3 84.3 77.4 12.5 12.5 12.0 12 13 14 15 16 17 17.9 9.5 88.5 8.0 81.6 86.7 89.7 21 16.8 15 78.9 16.5 15.1 91.0 16.5 90.9 91.9 Edited SAS Output (PROC REG) for Problem 9 Regression Models for Dependent Variable: Y N 30 Number in Model Variables in Model MSE 32.78751 X3 R-Square C(p) 0.7417 06392 26.5059 45.79629 x1 0.3728 65.2771 0.1103 103 4723 112.92725 X2 0.0145 117.4173 25.09024 Z 17 11.5912 79.61294 x4 0.8069 40972 25.41440 X1 X3 25.49052 X3 X4 32.44298 X3Z 33.99634 X2 x3 0.8063 4.1814 0 7635 11,8678 324298x3z 0.741713.58513 0.70551 0.8936 20.5949 40.33682 x1 x2 0.6445 27.7395 46.79920 X1 X4 18.8517 38.76009 x1 z 0 5723 38.260 56 2947 xx 56.29347 X2 X4 0.4051 62.568378.30242 x4Z 0.1147 104.8398 116.53767 x2z 0 82243.8492 24.28032 X1 x3 x4 0.8190 4.3407 24.74191 X2 X3 X4 0 8104 5.5917 25.91700 x1x2x3 0.808658488 26.15849 X3 X42 0.8080 5.938926.24314 X1 X3 z 0.7535 13.8675 33 69053 0.7406 15.752135.46078 X1 x2Z 0.7231 18.3003 37.85424 X1 X2 X4 0.709820.2356 39.67213 X1 x4Z 0.5851 38.3797 56.71498 x2 x4 Z X2 X3 z 0.8346 4.070023.51341 x1 x2 x3 x4 08227 5.8014 2520478 X1 x3 x4Z 08209 6.0632 25.46058 x2 x3 X4 08118 7.3871 26.75380 x1x2 x3 Z 0.7627 14 5337 33.73516 x1 x2 X4 Z 0.8351 6.0000 24.42193 x1 X2 X3 x4 Z Problems 475 Dependent Variable Y Stepwise Selection: Ste iariable X3 Entered: R-Square red: R-Square 0.7417 and C(p) 11.5912 ANALYSIS OF VARIANCE Sum of DF F Value Pr>F Model Error Corrected Total 2635 95947 263595047 8040 0001 28 918.05019 29 354.00967 32.78751 Parameter VariableEstimate Standard Intercept X3 Type ISS F VauPr> F 17.08438 1126624 75.3618 230 0.1408 14.71918 1.64160 2635 95947 8040 0001 Bounds on condition number: 1, 1 Stepwise Selection: Step 2 Variable X1 Entered: R-Square = 0.8069 and C(p) = 4.0972 ANALYSIS OF VARIANCE Sum of Squares Square F Value Pr> F 867 82088 1433.91044 56.42 0001 27 686.18878 29 3554.00967 Error 25.41440 Corrected Total Parameter Standard Type II SS F Value Pr>F Variable Intercept X1 x3 Estimate Error 015 0.6994 1.30268 0.43128 231.86141 912 0.0055 11 596 10738 2346 0001 10.79550 3.87161 10.14196 Bounds on condition number: 2.0994, 8.3975 Stepwise Selection: Step 3 le X4 Entered: R-Square- o.8224 and C(p) 38492 ANALYSIS OF VARIANCE Sum of F Value Pr>F Square 2922 72134 974.24045 4012 .0001 631.28833 3554.00967 DFI Squares 2428032 26 Corrected Total (continued) 29 476 Selecting the Best Regression Equation Chapter 16 Parameter Standard Estimate Type lI SS F Value Pr>F 022 0.6451 Variable 5.27391 4 92269 10.56242 081476 0.5319756.96559 10.526382.06276 632 29012 26.0 5,0001 226 0.1447 x3 54 90046 045797 0.30456 X4 Bounds on condition number: 3.3432, 22.38 Stepwise Selection: Step4 All variables left in the model are significant at the 0.1500 level. No other variable met the 0.1500 significance level for entry into the model. SUMMARY OF STEPWISE SELECTION Variable Variable Number Step Entered Removed Vars in R Partial R-Square R-Square C(p) F Value Pr> 8040 000 0.8069 4.0972912 0 0055 226 0.1447 0.7417 115912 0.7417 0.0652 08224 3.8492 x4 10. In Problem 9, the first-order interactions between Z and the predictor variables X X, and X, were not included in the model selection process. Investigate whether this was appropriate, as follows (using the accompanying computer output). a. Conduct a test to investigate the importance of the interactions, given that X, X X, X,, and Zare in the model. b. In view of your answer in part (a) and in light of the model selected in Problem c. Why is it necessary to ignore the interaction termX, X Z was it appropriate to exclude the interactions? Edited SAS Output (PROC REG) for Problem 10 ANALYSIS OF VARIANCE Sum of DFI squares F Value Pr>F 8 3100 73978 387.59247 21 453 26991 21.58428 29 3554.00067 17.96

Answer 1

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