Chapter 8.3, Problem 9E

(Continues Exercise 7 in Section 8.1.) 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

$\begin{array}{l}{\text{FEV}}_1={\beta }_0+{\beta }_1\text{Last}{\text{FEV}}_1+{\beta }_2\text{Gender}+{\beta }_3\text{Height}+{\beta }_4\text{Weight}+{\beta }_5\text{Height}\cdot \text{Weight}\\ +{\beta }_6\text{Temperature}+{\beta }_7\text{Pressure}+\epsilon \end{array}$

1. 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.

1. b. How many degrees of freedom does the F statistic have?
2. c. Find the P-value for the F statistic. Is the reduced model plausible?
3. 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.