The multiple regression relationships of SBP (Y) to AGE (X1), SMK (X2), and QUET (X3) are studied. Three regression models are considered, yielding least-squares estimates and ANOVA tables as shown in the accompanying SAS output.
a. Use the model that includes all three independent variables (X1, X2, and X3) to answer the following questions.
(1) What is the predicted SBP for a 50-year-old smoker with a quetelet index of 3.5?
(2) What is the predicted SBP for a 50-year-old nonsmoker with a quetelet index of 3.5?
(3) For 50-year-old smokers, estimate the change in SBP corresponding to an increase in quetelet index from 3.0 to 3.5.
b. Using the computer output, determine and compare the R2-values for the three models. If you use R2 and model simplicity as the criteria for selecting a model, which of the three models appears to be the best?
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Regression of SBP on AGE Source DF Sum of SquaresMean Square F Value Pr F 3861-630375 30 2564 338375 31 6425 968750 Model 3861,630375 45.18 <0001 85.477946 Corrected Total Portion of output omitted Parameter Intercept AGE Estimate Standard Error t Value Pr>t ,61 .0001 6,72 ,0001 59.09162500 12.81626145 1.60450000 0.23871593 Regression of SBP on AGE and SMK Source Model Error Corrected Total DF Sum of Squares Mean Square FValue Pr>F 3916 000 2 4689 684229 1736 284521 6425 958750 2344 842114 29 59.871880 31 IPortion of output omitted] Estimate | Standard Error | t Value | Pr> Parameter Intercept AGE SMK 11.12955962 0.20175872 4 .0001 2 76810685 372 0.0009 48.04960299 4.32 0.0002 1.70915965 Regression of SBP on AGE, SMK, and QUET DF Sum of Squares Mean Square F Value Prè F Model Error Corrected Total 2971 0001 4889 825697 28 1536143053 31 6425 968750 629 941899 54.662252 [Portion of output omitted Standard Error tValue Pr> t Parameter Intercept AGE SMK QUET Estimate 4.19 0.0003 032381922 375 08 74 0.0008 449868122191 0664 45 10319242 10 76487511 1 21271462 9.94558782 2 85605655 3 8,5924486