13.25 Interpret strength variability Refer to the previous two exercises.

The sample standard deviation of maxBP was 13.3.

The residual standard deviation of maxBP when BP60 and LP200 are predictors in a multiple regression model is 7.9.

a. Explain the difference between the interpretations of these two standard deviations.

b. If the conditional distributions of maxBP are approximately bell shaped, explain why most maximum bench press values fall within about 16 pounds of the regression equation when the predictors BP60 and LP200 are near their sample mean values.

c. At BP60 = 11 and LP200 = 22, which are close to the sample mean values, software reports yn = 80 and a 95% prediction interval of 80 { 16, or (64, 96). Is this interval an inference about where the population maxBP values fall or where the population mean of the maxBP values fall (for subjects having BP60 = 11 and LP200 = 22)? Explain.

d. Refer to part

c. Would it be unusual for a female athlete with these predictor values to be able to bench press more than 100 pounds? Why?