Physical fitness testing is an important as aspect of athletic training. A common measure of the magnitude of cardiovascular fitness is the maximum volume of oxygen uptake during a strenuous exercise. A study was conducted on 24 middle aged men to study the influence of the time it takes to complete a two mile run. The oxygen uptake measure was accomplished with standard laboratory methods as the subjects performed on a treadmill. The work was published in "Maximal Oxygen Intake Prediction in Young and Middle Aged Males," Journal of Sports Medicine 9, 1969, 17-22. The data are as presented here.

(a) Estimate the parameters in a simple linear regression model.

(b) Does the time it takes to run two miles have a significant influence on maximum oxygen up-take? Use H_o: 0 = 0, H₁: β ≠ 0

(c) Plot the residuals on a graph against x and comment on the appropriateness of the simple linear model.

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у, Махimum Subject Volume of O2 in Seconds г, Time 1 42.33 53.10 42.08 50.06 918 805 892 962 968 3 4 5 42.45