12.26 Sit-ups and the 40-yard dash Is there a relationship between x = how many sit-ups you can do and y = how fast you can run 40 yards (in seconds)? The MINITAB output of a regression analysis based on the female athlete strength study is shown here.

a. Find the predicted time in the 40-yard dash for a subject who can do (i) 10 sit-ups and (ii) 40 sit-ups.
(The minimum and maximum in the study were 10 and 39.) Relate the difference in predicted times to the slope.

b. The correlation between these two variables equals −0.46 (the negative square root of the R-Sq value shown, because the estimated slope has a negative sign).
Predict by how many standard deviations the time of the 40-yard dash decreases for a one standard deviation increase in the number of sit-ups the athlete can do.

c. The number of sit-ups had mean 27.175 and standard deviation 6.887. The time in the 40-yard dash had mean 6.045 and standard deviation 0.365. Show how the correlation relates to the slope and verify the value given in part b.

d. The time difference for the 40-yard run between two athletes that are one standard deviation apart in the number of sit-ups they can do is predicted to be how much? First, answer in terms of standard deviations of the time for the 40-yard dash. Then, using the standard deviation given in part

c, answer in absolute terms (i.e., in seconds).

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Coefficients Term Coef SE Coef T-Value P-Value Constant 6.707 0.178 37.70 0.000 SIT-UP -0.02435 0.00635 -3.83 0.000 Model Summary S R-sq 0.327208 21.10%