Refer to the kinesiology data in Example 12.6 and the models fit to this data set in Exercises 12.23 and 12.24.
a. Predict the maximal oxygen uptake for a person having a weight of 150 kg, an age of 20 years, a time to walk 1 mile of 17 minutes, and a heart rate of 140 beats per minute using the fitted first- order model. Generate a 95% prediction interval for your prediction.
b. Predict the maximal oxygen uptake for a person having a weight of 150 kg, an age of 20 years, a time to walk 1 mile of 17 minutes, and a heart rate of 140 beats per minute using the fitted second- order model. Generate a 95% prediction interval for your prediction.
c. Predict the maximal oxygen uptake for a person having a weight of 150 kg, an age of 20 years, a time to walk 1 mile of 17 minutes, and a heart rate of 140 beats per minute using the fitted second- order model with cross- product terms. Generate a 95% prediction interval for your prediction.
d. Compare the widths of the three prediction intervals. Did the added complexity of models 2 and 3 provide a substantial reduction in the widths of the intervals?