Refer to the kinesiology data in Example 12.6. In this example, a first- order model was fit to relate y, maximal oxygen uptake, to the explanatory variables: x1, weight; x2, age; x3, time to walk 1 mile; and x4, heart rate at the end of a 1- mile walk.
a. Provide the kinesiologist with an interpretation of the fitted model having an R2 of 58.2%.
b. Fit a quadratic model to the data with the squared values of the four predictors in the model. How much of an increase in R2 was obtained by this fitting this model?
c. The quadratic model now has eight partial slope coefficients. How many of them are significant at the .05 level?
d. At the .05 level, are the quadratic terms significant taken as a group of four terms?
e. Which of the two model— just first- order terms or first- and second- order terms— would you recommend?