Athletes are constantly seeking measures of the degree of their cardiovascular fitness prior to a major race. Athletes want to know when their training is at a level that will produce a peak performance. One such measure of fitness is the time to exhaustion from running on a treadmill at a specified angle and speed. The important question is then €œ Does this measure of cardiovascular fitness translate into performance in a 10- km running race?€ Twenty experienced distance runners who professed to be at top condition were evaluated on the treadmill and then had their times recorded in a 10- km race. The data are given here.

a. Plot the data in a scatterplot.
b. Fit a regression model to the data. Does a linear model seem appropriate?
c. Obtain the estimated linear regression model = β0 + β1.

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Treadmill time (minutes) 75 78 7.9 81 83 87 8.9 9.2 9.4 98 10-km time (minutes) 435 45.2 44.9 41.1 438 44.4 38.7 43.1 418 43.7 Treadmill time (minutes) 10.1 10.3 10.5 10.7 10.8 109 112 115 117 18 10-km time (minutes) 35 38.2 43.9 37 37.7 39.2 35.7 372 34.8 38.5