In Chapter 12, we analyzed strength data for a sample of female high school athletes. When we predict the maximum number of pounds the athlete can bench press using the number of times she can do a 60-pound bench press (BP_60), we get r2 = 0.643. When we add the number of times an athlete can perform a 200-pound leg press (LP_200) to the model, we get y = 60.6 + 1.33(BP_60) + 0.21 (LP_200) and R2 = 0.656.
a. Find the predicted value and residual for an athlete who has BP = 85, BP60 = 10, and LP200 = 20.
b. Find the prediction equation for athletes who have LP200 = 20, and explain how to interpret the slope for BP_60.
c. R2 = 0.656 for the multiple regression model is not much larger than r2 = 0.643 for the bivariate model with LP200 as the only explanatory variable. What does this suggest?