Example 13.4 gave data on x 5 treadmill run time to exhaustion and y 5 20-km ski time for a sample of 11 biathletes. Use the accompanying Minitab output to answer the following questions.

The regression equation is ski = 88.8

– 2.33tread Predictor Coef Stdev t-ratio p Constant 88.796 5.750 15.44 0.000 tread –2.3335 0.5911 –3.95 0.003 s = 2.188 R-sq = 63.4% R-sq(adj) = 59.3%

Analysis of Variance Source DF SS MS F Regression 1 74.630 74.630 15.58 Error 9 43.097 4.789 Total 10 117.727

a. Carry out a test at significance level .01 to decide whether the simple linear regression model is useful.

b. Estimate the average change in ski time associated with a 1-minute increase in treadmill time, and do so in a way that conveys information about the precision of estimation.

c. Minitab reported that sa1b1102 5 .689. Predict ski time for a single biathlete whose treadmill time is 10 minutes, and do so in a way that conveys information about the precision of prediction.

d. Minitab also reported that sa1b1112 5 1.029. Why is this larger than sa1b1102? x