# Question

Refer to the previous two exercises. The sample standard deviation of BP was 13.3. The residual standard deviation of BP when BP_60 and LP_200 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 BP are approximately bell shaped, explain why most maximum bench press values fall within about 16 pounds of the regression equation, when the predictors BP_60 and LP_200 are near their sample mean values.

c. At x1 = 11 and x2 = 22, which are close to the sample mean values, software reports = 80 and a 95% prediction interval of 80 {16, or (64, 96). Is this interval an inference about where the population BP values fall or where the population mean of the BP values fall (for subjects having x1 = 11 and x2 = 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?

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

b. If the conditional distributions of BP are approximately bell shaped, explain why most maximum bench press values fall within about 16 pounds of the regression equation, when the predictors BP_60 and LP_200 are near their sample mean values.

c. At x1 = 11 and x2 = 22, which are close to the sample mean values, software reports = 80 and a 95% prediction interval of 80 {16, or (64, 96). Is this interval an inference about where the population BP values fall or where the population mean of the BP values fall (for subjects having x1 = 11 and x2 = 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?

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