R backward elimination output for NCAA Data > bes.leaps(x=ncaa2[,1:19],y=ncaa2[,20]) Backward elimination sequence in reverse order Remove variables from bottom of list to top p s rem.var pval pvmin 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 0.0025 32.019 31.575 672.564 61.490 5 5 4 4 0.0053 0.0025 24.095 23.678 668.850 56.952 6 6 5 7 0.0025 0.0025 15.360 14.971 663.561 51.879 7 7 6 9 0.1045 0.0049 14.438 14.077 665.240 50.900 8 8 7 8 0.0049 0.0049 8.101 7.768 661.096 46.946 9 9 8 6 0.0778 0.0778 6.989 6.684 662.179 45.782 10 10 9 17 0.1613 0.1613 7.061 6.784 664.513 45.251 11 11 10 18 0.2268 0.2248 7.639 7.389 667.392 44.993 12 12 11 13 0.3199 0.2248 8.678 8.456 670.794 44.992 13 13 12 12 0.2248 0.2248 9.251 9.057 673.617 44.721 14 14 13 10 0.2581 0.2581 10.018 9.851 676.648 44.557 15 15 14 15 0.2713 0.2713 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 rem.var=next variable to remove, current model includes this variable and all variables above it pval=p-value to remove variable pvmin=min p-value from below, BS(alpha)=move down until pvmin > 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 Conclusions: Here Mallows Cp method chooses a 9 variables model that is different from the 9 variable model chosen from the FAS. The adjusted Cp leads to a model with only 8 variables, the same as the min BIC model.