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Physical fitness testing is an important 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 middleaged 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. $$ \begin{array}{ccc} & y \text { , Maximum } & \text { x, Time } \\ \text { Subject } & \text { Volume of } \mathbf{O}_{2} & \text { in } \text { Seconds } \\ \hline 1 & 42.33 & 918 \\ 2 & 53.10 & 805 \\ 3 & 42.08 & 892 \\ 4 & 50.06 & 962 \\ 5 & 42.45 & 968 \end{array} $$ (Figure) $$ \begin{array}{ccc} & y, \text { Maximum } & x, \text { Time } \\ \text { Subject } & \text { Volume of } \mathrm{O}_{2} & \text { in } \text { Seconds } \\ \hline \mathbf{6} & 42.46 & 907 \\ 7 & 47.82 & 770 \\ \mathbf{8} & 49.92 & 743 \\ \mathbf{9} & 36.23 & 1045 \\ 10 & 49.66 & 810 \\ 11 & 41.49 & 927 \\ 12 & 46.17 & 813 \\ 13 & 46.18 & 858 \\ 14 & 43.21 & 860 \\ 15 & 51.81 & 760 \end{array} $$ $$ \begin{array}{ccc} & y \text { , Maximum } & x \text { , Time } \\ \text { Subject } & \text { Volume of } \mathrm{O}_{2} & \text { in } \text { Seconds } \\ \hline 16 & 53.28 & 747 \\ 17 & 53.29 & 743 \\ 18 & 47.18 & 803 \\ 19 & 56.91 & 683 \\ 20 & 47.80 & 844 \\ 21 & 48.65 & 755 \\ 22 & 53.67 & 700 \\ 23 & 60.62 & 748 \\ 24 & 56.73 & 775 \end{array} $$ (Figure) (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 uptake? Use $\begin{array}{ll}H_{0}: & 0=0 \\ H_{1}: & \beta \neq 0\end{array}$ (c) Plot the residuals on a graph against $x$ and comment on the appropriateness of the simple linear model.
Physical fitness is the ability and ability to do work efficiently without causing significant fatigue. Examples include jogging, swimming, riding, and fast strolling. Exercises for strength, often known as resistance training, make your muscles stronger. Lifting weights and utilizing a resistance band is a couple of examples. Exercises that improve balance can make it easier to navigate rocky terrain and reduce the risk of falling. Purpose of Physical Fitness
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