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 which 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 "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. Treadmill Time (minutes) 7.57.87.98.18.38.78.99.2 9.49.8 10-km Time (minutes) 43.5 45.2 44.9 41.1 43.8 44.4 42.7 43.1 41.8 43.7 Treadmill Time (minutes) 10.110.3 10.5 10.7 10.8 10.9 11.2 11.511.7 11.8 10-km Time (minutes) 39.5 38.2 43.9 37.1 37.7 39.2 35.7 37.2 34.8 38.5 a) Find the relation between the variables. b) Fit a regression equation and check for its goodness of fit using coefficient of determination

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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 which 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
"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.
Treadmill Time (minutes) 7.57.87.98.18.38.78.99.2
9.49.8
10-km Time (minutes) 43.5 45.2 44.9 41.1 43.8 44.4
42.7 43.1 41.8 43.7
Treadmill Time (minutes) 10.1 10.3 10.5 10.7 10.8
10.9 11.211.511.711.8
10-km Time (minutes) 39.5 38.2 43.9 37.1 37.739.2
35.7 37.2 34.8 38.5
a) Find the relation between the variables.
b) Fit a regression equation and check for its
goodness of fit using coefficient of determination
Transcribed Image Text: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 which 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 "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. Treadmill Time (minutes) 7.57.87.98.18.38.78.99.2 9.49.8 10-km Time (minutes) 43.5 45.2 44.9 41.1 43.8 44.4 42.7 43.1 41.8 43.7 Treadmill Time (minutes) 10.1 10.3 10.5 10.7 10.8 10.9 11.211.511.711.8 10-km Time (minutes) 39.5 38.2 43.9 37.1 37.739.2 35.7 37.2 34.8 38.5 a) Find the relation between the variables. b) Fit a regression equation and check for its goodness of fit using coefficient of determination
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