12.47 Stride Rate One measure of form for a runner is stride rate, defined as the number of steps per second. A runner is considered to be efficient if the stride rate is close to optimum. The stride rate is related to speed; the greater the speed, the greater the stride rate. In a study of some top female runners, research- ers measured the stride rate for different speeds. The following table gives the average stride rate of these women versus the speed (in metres per second)."

a. What is the least-squares line relating the stride rate to speed?

b. What proportion of the total variation is explained by the regression of stride rate (y) on the speed (x)?

c. If they are available, examine the diagnostic plots to check the validity of the regression assumptions.

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Speed 4.83 5.15 5.33 5.68 6.09 6.42 6.74 Stride rate 3.05 3.12 3.17 3.25 3.36 3.46 3.55