Question

n an analysis of leg strength for 57 female athletes, with y = maximum leg press and x = number of 200-pound leg presses until fatigue, the regression equation is ý = 240.85 +4.81x. Complete parts a through c using the software output shown below for observations at x = 25. Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 361.10 5.22 (350.66,371.54) (282.28,439.92) 1 a. Show how the software got the "Fit" of 361.10. O A. The "Fit" is y evaluated at x = 25 or y = 240.85 +4.81(25). 57 - 240.85 O B. The "Fit" is x evaluated at y = 57 or x = 4.81 O C. The "Fit" is y evaluated at x = 25 or y = 240.85 +4.81(25). OD. The "Fit" is evaluated at y = 57 or 8 = 57 - 240.85 4.81 b. Using the predicted value and se value, explain how the software got the interval listed under "95% CI." Choose the correct answer below. O A. The 95% confidence interval is labeled as "95% CI." These bounds are given by ý + se. OB. The 95% confidence interval is labeled as "95% CI." These bounds are given by ý +2se. OC. The 95% confidence interval is labeled as "95% CI." These bounds are given by se + 2º Interpret the interval listed under "95% CI." Choose the correct answer below. O A. For all female high school athletes who can do 25 leg presses, there is 95% confidence that the mean of their maximum leg press is between about 351 and 372 pounds. OB. For all female high school athletes who can do 25 leg presses, predict that 95% of them have a maximum leg press between about 351 and 372 pounds. O C. For the female high school athletes in this sample who can do 25 leg presses, there is 95% confidence that the mean of their maximum leg press is between about 351 and 372 pounds. OD. For the female high school athletes in this sample who can do 25 leg presses, predict that 95% of them have a maximum leg press between about 351 and 372 pounds c. Interpret the interval listed under "95% PL." O A. For all female high school athletes who can do 25 leg presses, there is 95% confidence that the mean of their maximum leg press is between about 282 and 440 pounds. OB. For the female high school athletes in this sample who can do 25 leg presses, predict that 95% of them have a maximum leg press between about 282 and 440 pounds. O c. For all female high school athletes who can do 25 leg presses, predict that 95% of them have a maximum leg press between about 282 and 440 pounds. OD. For the female high school athletes in this sample who can do 25 leg presses, there is 95% confidence that the mean of their maximum leg press is between about 282 and 440 pounds.

Answer 1

a. The software got the "Fit" of 361.10 by evaluating the regression equation at x = 25, which gives:

y = 240.85 + 4.81(25) = 361.10

Therefore, the predicted maximum leg press for a female athlete who can do 25 leg presses until fatigue is 361.10 pounds.

b. The 95% confidence interval listed under "95% CI" is given by the formula:

95% CI = (Fit - 1.96 SE, Fit + 1.96 SE)

where "Fit" is the predicted maximum leg press and "SE" is the standard error of the estimate, which is given as 5.22 in the software output.

Therefore, the 95% confidence interval is:

95% CI = (361.10 - 1.96(5.22), 361.10 + 1.96(5.22)) = (350.66, 371.54)

c. The 95% prediction interval listed under "95% PI" is the range of values within which we can predict with 95% confidence that a new observation will fall.

In this case, the 95% prediction interval is given by the formula:

95% PI = (Fit - 1.96 SE, Fit + 1.96 SE)

where "Fit" is the predicted maximum leg press and "SE" is the standard error of the estimate, which is given as 5.22 in the software output.

Therefore, the 95% prediction interval is:

95% PI = (361.10 - 1.96(5.22), 361.10 + 1.96(5.22)) = (282.28, 439.92)

Thus, we can predict with 95% confidence that a new female athlete who can do 25 leg presses until fatigue will have a maximum leg press between about 282 and 440 pounds.