Let’s use multiple regression to predict total body weight (in pounds) using data from a study of the University of Georgia female athletes. Possible predictors are HGT = height (in inches), % BF = percent body fat, and age. The display shows correlations among these explanatory variables.
a. Which explanatory variable gives by itself the best predictions of weight? Explain.
b. With height as the sole predictor, ŷ = -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, ŷ = -121 + 3.50(HGT) + 1.35(BF) and R2 = 0.66. When you add age to the model ŷ = – 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.