13.13 Predicting weight Let’s use multiple regression to predict total body weight (TBW, in pounds) using data from a study of female college athletes. Possible predictors are HGT = height (in inches), %BF = percent body fat, and age. The display shows the correlation matrix for these variables.

TBW HGT %BF AGE TBW – 0.74 0.39 −0.19 HGT 0.74 – 0.10 −0.12

%BF 0.39 0.10 – 0.02 AGE −0.19 −0.12 0.02 –

a. Which explanatory variable gives by itself the best predictions of weight? Explain.

b. With height as the sole predictor, yn = -106 + 3.65

(HGT) and r2 = 0.55. If you add %BF as a predictor, you know that R2 will be at least 0.55. Explain why.

c. When you add % body fat to the model, yn = -121 +

3.501HGT2 + 1.351%BF2 and R2 = 0.66. When you add age to the model, yn = -97.7 + 3.431HGT2 +

1.361%BF2 - 0.9601AGE2 and R2 = 0.67. Once you know height and % body fat, does age seem to help you in predicting weight? Explain, based on comparing the R2 values.