R Forward Program Output for NCAA data > fas.leaps(x=ncaa2[,1:19],y=ncaa2[,20]) Forward addition sequence p s add.var pval pvmax Cp Cp.adj BIC MSE 1 1 0 0 NA NA 422.995 422.467 797.425 259.665 2 2 1 2 0.0000 0.0000 60.941 60.441 686.605 76.933 3 3 2 3 0.0001 0.0001 38.730 38.257 674.714 65.303 4 4 3 5 0.0116 0.0116 32.019 31.575 672.564 61.490 5 5 4 4 0.0053 0.0116 24.095 23.678 668.850 56.952 6 6 5 7 0.0025 0.0116 15.360 14.971 663.561 51.879 7 7 6 17 0.0433 0.0433 12.871 12.510 663.667 50.056 8 8 7 15 0.0527 0.0527 10.883 10.550 664.085 48.464 9 9 8 6 0.1056 0.1056 10.171 9.866 665.716 47.538 10 10 9 9 0.0826 0.1056 9.118 8.840 666.868 46.399 11 11 10 8 0.0536 0.1056 7.450 7.200 667.169 44.886 12 12 11 12 0.2350 0.2350 8.087 7.864 670.085 44.654 13 13 12 10 0.2864 0.2864 8.992 8.798 673.301 44.571 14 14 13 13 0.3163 0.3163 10.026 9.859 676.658 44.562 15 15 14 18 0.2697 0.3163 10.855 10.716 679.742 44.431 16 16 15 11 0.4953 0.4953 12.408 12.296 683.722 44.732 17 17 16 1 0.6326 0.6326 14.186 14.102 687.984 45.178 18 18 17 14 0.7056 0.7056 16.046 15.990 692.350 45.686 19 19 18 19 0.8605 0.8605 18.015 17.987 696.854 46.276 20 20 19 16 0.9032 0.9032 20.000 20.000 701.379 46.891 p=number of effects in model, p=1 is just the intercept s=number of independent variables in model add.var=next variable to add, current model includes this variable and all variables above it pval=p-value to add variable pvmax=max p-value from above, FS(alpha)=move down until pvmax > alpha Cp=usual Cp, note p=s+1 where s=number of x variables in model Cp.adj=adjusted Cp, choose smallest model with Cp.adj < p=s+1 BIC=official BIC, number of parameters=s+2, intercept & sigma^2 Some conclusions: Mallows (1973) Cp method would select a 9 variable model because Cp=9.118 < p=10 but Cp=10.171 is not less than p=9. Mallows rule is equivalent to finding the smallest model such that the mse is less than the full model mse. Gilmour's (1996) adjusted Cp gives the same result as Cp. Choosing the model with the smallest BIC results in a 5 variabel model.