The article “Predicting Marathon Time from Anaerobic Threshold Measurements” (The Physic...

The article “Predicting Marathon Time from Anaerobic Threshold Measurements” (The Physician and Sports Medicine [1984]: 95– 98) gave data on y = maximum heart rate (beats/min), x₁ = age, and x₂ = weight (kg) for n = 18 marathon runners. The estimated regression equation for the model

and SSRegr = 649.75, SSResid = 538.03.

a. Is the model useful for predicting maximum heart rate? Use a significance level of .10.

b. Using , calculate and interpret a 95% confidence interval for b1. c. Predict the maximum heart rate of a particular runner who is 43 years old and weighs 65 kg, using a 99% interval. The estimated standard deviation of the statistic a + b₁ (43)+ b₂ (65) is 3.52.

d. Use a 90% interval to estimate the average maximum heart rate for all marathon runners who are 30 years old and weigh 77.2 kg. The estimated standard deviation of a + b₁ (30)+ b₂ (77.2) is 2.97.

e. Would a 90% prediction interval for a single 30-yearold runner weighing 77.2 kg be wider or narrower than the interval computed in Part (d)? Explain. (You need not compute the interval.)