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?