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.

a. Which explanatory variable gives by itself the best predictions of weight? Explain.
b. With height as the sole predictor, yÌ‚ = -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, yÌ‚ = -121 + 3.50(HGT) + 1.35(%BF) and R² = 0.66. When you add age to the model, yÌ‚ = -97.7 + 3.43(HGT) + 1.36(%BF) - 0.960(AGE) 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.

TBW HGT %BF AGE TBW 0.74 0.39 -0.19 0.10 HGT 0.74 -0.12 %BF 0.39 0.10 0.02 -0.19 AGE -0.12 0.02