Use the all-possible-regressions method to select a subset regression model for the Belle Ayr liquefaction data in Table B.5. Evaluate the subset models using the \(C_{p}\) criterion. Justify your choice of final model using the standard checks for model adequacy.

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Run No. y X x2 X3 X4 Xs X6 1234567890 36.98 5.1 400 51.37 4.24 1484.83 2227.25 2.06 13.74 26.4 400 72.33 30.87 289.94 434.90 1.33 10.08 23.8 400 71.44 33.01 320.79 481.19 0.97 8.53 46.4 400 79.15 44.61 164.76 247.14 0.62 36.42 7.0 450 80.47 33.84 1097.26 1645.89 0.22 26.59 12.6 450 89.90 41.26 605.06 90759 0.76 19.07 18.9 450 91.48 41.88 405.37 608.05 1.71 5.96 30.2 450 98.6 70.79 253.70 380.55 3.93 15.52 53.8 450 98.05 66.82 142.27 213.40 1.97 56.61 5.6 400 55.69 8.92 1362.24 2043.36 5.08 11 26.72 15.1 400 66.29 17.98 507.65 761.48 0.60 12 20.80 20.3 400 58.94 17.79 377.60 566.40 0.90 13 6.99 48.4 400 74.74 33.94 158.05 23708 0.63 14 45.93 5.8 425 63.71 11.95 130.66 1961.49 2.04 15 43.09 11.2 425 67.14 14.73 682.59 1023.89 1.57 16 15.79 27.9 425 77.65 34.49 274.20 411.30 2.38 17 21.60 5.1 450 67.22 14.48 1496.51 2244.77 0.32 18 35.19 11.7 450 81.48 29.69 652.43 978.64 0.44 19 26.14 16.7 450 83.88 26.33 458.42 687.62 8.82 20 8.60 24.8 450 89.38 37.98 312.25 468.28 0.02 21 11.63 24.9 450 79.77 25.66 307.08 460.62 1.72 22 9.59 39.5 450 87.93 22.36 193.61 290.42 1.88 23 4.42 29.0 450 79.50 21.52 155.96 233.95 1.43 24 38.89 5.5 460 72.73 17.86 1392.08 2088.12 1.35 25 11.19 11.5 450 77.88 25.20 663.09 994.63 1.61 26 75.62 5.2 470 75.50 8.66 1464.11 2196.17 4.78 27 36.03 10.6 470 83.15 22.39 720.07 1080.11 5.88