Consider the solar thermal energy test data in Table B.2.

a. Use forward selection to specify a subset regression model.
b. Use backward elimination to specify a subset regression model.
c. Use stepwise regression to specify a subset regression model.
d. Apply all possible regressions to the data. Evaluate \(R_{p}^{2}, C_{p}\), and \(M S_{\text {Res }}\) for each model. Which subset model do you recommend?
e. Compare and contrast the models produced by the variable selection strategies in parts a-d.

y X 12 X3 X4 271.8 783.35 33.53 40.55 16.66 13.20 264.0 748.45 36.50 36.19 16.46 14.11 238.8 684.45 34.66 37.31 1766 15.68 230.7 827.80 33.13 32.52 1750 10.53 251.6 860.45 35.75 33.71 16.40 11.00 257.9 875.15 34.46 34.14 16.28 11.31 263.9 909.45 34.60 34.85 16.06 11.96 266.5 905.55 35.38 35.89 15.93 12.58 229.1 756.00 35.85 33.53 16.60 10.66 239.3 769.35 35.68 33.79 16.41 10.85 258.0 793.50 35.35 34.72 16.17 11.41 257.6 801.65 35.04 35.22 15.92 11.91 267.3 819.65 34.07 36.50 16.04 12.85 267.0 808.55 32.20 37.60 16.19 13.58 259.6 774.95 34.32 37.89 16.62 14.21 240.4 711.85 31.08 37.71 17.37 15.56 227.2 694.85 35.73 37.00 18.12 15.83 196.0 638.10 34.11 36.76 18.53 16.41 278.7 774.55 34.79 34.62 15.54 13.10 272.3 757.90 35.77 35.40 15.70 13.63 267.4 753.35 36.44 35.96 16.45 14.51 254.5 704.70 37.82 36.26 17.62 15.38 224.7 666.80 35.07 36.34 18.12 16.10 181.5 568.55 35.26 35.90 19.05 16.73 227.5 653.10 35.56 31.84 16.51 10.58 253.6 704.05 35.73 33.16 16.02 11.28 263.0 709.60 36.46 33.83 15.89 11.91 265.8 726.90 36.26 34.89 15.83 12.65 263.8 697.15 37.20 36.27 16.71 14.06