In a physiology exercise, an objective measure of aerobic fitness is the oxygen consumption in volume per unit body weight per unit time. Thirty-one individuals were used in an experiment to model oxygen consumption against their age in years $\left(x_{1}\right),$ weight in kilograms $\left(x_{2}\right),$ time to run $1 \frac{1}{2}$ miles $\left(x_{3}\right),$ resting pulse rate $\left(x_{4}\right),$ pulse rate at the end of the run $\left(x_{5}\right),$ and maximum pulse rate during the run $\left(x_{6}\right)$.
(a) Do a stepwise regression at an input significance level of $0.25 .$ Quote the final model.
(b) Do all possible subsets using $s^{2}, C_{p}, R^{2},$ and $R_{a d j}^{2}$ Make a decision and quote the final model.
$$
\begin{array}{rccccccc}
\text { ID } & y & x_{1} & x_{2} & x_{3} & x_{4} & x_{5} & x_{6} \\
\hline 1 & 44.609 & 44 & 89.47 & 11.37 & 62 & 178 & 182 \\
2 & 45.313 & 40 & 75.07 & 10.07 & 62 & 185 & 185 \\
3 & 54.297 & 44 & 85.84 & 8.65 & 45 & 156 & 168 \\
4 & 59.571 & 42 & 68.15 & 8.17 & 40 & 166 & 172 \\
5 & 49.874 & 38 & 89.02 & 9.22 & 55 & 178 & 180 \\
6 & 44.811 & 47 & 77.45 & 11.63 & 58 & 176 & 176 \\
7 & 45.681 & 40 & 75.98 & 11.95 & 70 & 176 & 180 \\
8 & 49.091 & 43 & 81.19 & 10.85 & 64 & 162 & 170 \\
9 & 39.442 & 44 & 81.42 & 13.08 & 63 & 174 & 176 \\
10 & 60.055 & 38 & 81.87 & 8.63 & 48 & 170 & 186 \\
11 & 50.541 & 44 & 73.03 & 10.13 & 45 & 168 & 168 \\
12 & 37.388 & 45 & 87.66 & 14.03 & 56 & 186 & 192 \\
13 & 44.754 & 45 & 66.45 & 11.12 & 51 & 176 & 176 \\
14 & 47.273 & 47 & 79.15 & 10.6 & 47 & 162 & 164 \\
15 & 51.855 & 54 & 83.12 & 10.33 & 50 & 166 & 170\\
16 & 49.156 & 49 & 81.42 & 8.95 & 44 & 180 & 185 \\
17 & 40.836 & 51 & 69.63 & 10.95 & 57 & 168 & 172 \\
18 & 46.672 & 51 & 77.91 & 10 & 48 & 162 & 168 \\
19 & 46.774 & 48 & 91.63 & 10.25 & 48 & 162 & 164 \\
20 & 50.388 & 49 & 73.37 & 10.08 & 76 & 168 & 168 \\
21 & 39.407 & 57 & 73.37 & 12.63 & 58 & 174 & 176 \\
22 & 46.08 & 54 & 79.38 & 11.17 & 62 & 156 & 165 \\
23 & 45.441 & 52 & 76.32 & 9.63 & 48 & 164 & 166 \\
24 & 54.625 & 50 & 70.87 & 8.92 & 48 & 146 & 155 \\
25 & 45.118 & 51 & 67.25 & 11.08 & 48 & 172 & 172 \\
26 & 39.203 & 54 & 91.63 & 12.88 & 44 & 168 & 172 \\
27 & 45.79 & 51 & 73.71 & 10.47 & 59 & 186 & 188 \\
28 & 50.545 & 57 & 59.08 & 9.93 & 49 & 148 & 155 \\
29 & 48.673 & 49 & 76.32 & 9.4 & 56 & 186 & 188 \\
30 & 47.92 & 48 & 61.24 & 11.5 & 52 & 170 & 176 \\
31 & 47.467 & 52 & 82.78 & 10.5 & 53 & 170 & 172
\end{array}
$$