(Continues Exercise 7 in Section 8.1.) To try to improve

Chapter 8, Problem 9E

(choose chapter or problem)

(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 \({ }^{\circ} \mathrm{C}\)). The following MINITAB output presents results of fitting the model

     \(\mathrm{FEV}_{1}=\beta_{0}+\beta_{1} \text { Last } \mathrm{FEV}_{1}+\beta_{2} \text { Gender }+\beta_{3} \text { Height }+\beta_{4} \text { Weight }+\beta_{5} \text { Height } \cdot \text { Weight }+\beta_{6} \text { Temperature }+\beta_{7} \text { Pressure }+\varepsilon\)

a. The following MINITAB output, reproduced from Exercise 7 in Section 8.1, is for a reduced model in which Weight, \(\text {Height} \cdot \text{Weight}\), 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.

Equation Transcription:

Text Transcription:

FEV_1

^oC

FEV1=beta_0+beta_1 Last FEV_1+beta_2 Gender+beta_3 Height+beta_4 Weight+beta_5 Height{cdot}Weight

+beta_6 Temperature+beta_7 Pressure+varepsilon

Height{cdot}Weight