To try to improve the prediction of FEV1, additional independent variables are included in the model. These new variables are Weight (in kg), the product (interaction) of Height and Weight, and the ambient temperature (in —¦C). The following MINITAB output presents results of fitting the model
FEV1 = β0 + β1 Last FEV1 + β2 Gender + β3 Height + β4 Weight + β5 Height · Weight + β6 Temperature + β7 Pressure + ε

a. The following MINITAB output, reproduced from Exercise 7 in Section 8.1, is for a reduced model in which Weight, Height · Weight, and Temp have been dropped. Compute the F statistic for testing the plausibility of the reduced model.

b. How many degrees of freedom does the F statistic have?
c. Find the P-value for the F statistic. Is the reduced model plausible?
d. Someone claims that since each of the variables being dropped had large P-values, the reduced model must be plausible, and it was not necessary to perform an F test. Is this correct? Explain why or why not.
e. The total sum of squares is the same in both models, even though the independent variables are different. Is there a mistake? Explain.

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The regression equation is FEV1-一0.257 + 0.778 Last FEV-0.105 Gender + 1.213 Height-0.00624 Weight +0.00386 Height*Weight0.00740 Temp 0.00148 Pressure Predictor Constant Last FEV Gender Height Weight Height*Weight Coef 0.2565 0.77818 -0.10479 1.2128 0.0062446 0.0038642 SE Coef 0.7602 0.05270 0.03647 0.4270 0.01351 0.008414 -0.34 14.77 -2.87 2.84 -0.46 0.46 0.736 0.000 0.005 0.005 0.645 0.647 Temp Pressure -0.007404 0.009313 0.0014773 0.0005170 -0.79 0.428 2.86 0.005 S- 0.22189 R-Sq -93.5% R-Sq ( adj) -93.2% Analysis of Variance Source Regression Residual Error 157 7.7302 0.049237 Total DF MS 7 111.35 15.907 323.06 0.000 164 119.08 The regression equation is FEV1--0. 219 + 0.779 Last FEV-0.108 Gender +1.354 Height-0.00134 Pressure Predictor Constant Last FEV Gender Height Pressure Coef -0.21947 0.779 0.10827 1.3536 0.0013431 SE Coef 0.4503 0.04909 0.0352 0.2880 0.0004722 0.49 15.87 -3.08 4.70 -2.84 0.627 0.000 0.002 0.000 0.005 S 0.22039 R-Sq-93.5% R-Sq ( adj) -93.3% Analysis of Variance DF Source Regression Residual Error Total MS 27.826 0.048572 0.000 111.31 7.7716 119.08 572.89 160 164