> allsub(x=ncaa2[,1:19],y=ncaa2$y) Best Subsets of Size s p s X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 1 2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 2 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 3 2 4 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 5 4 2 3 4 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 6 5 2 3 4 5 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 7 6 2 3 4 5 7 17 0 0 0 0 0 0 0 0 0 0 0 0 0 7 8 7 2 3 4 5 7 8 9 0 0 0 0 0 0 0 0 0 0 0 0 8 9 8 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 9 10 9 2 3 4 5 6 7 8 9 17 0 0 0 0 0 0 0 0 0 0 10 11 10 2 3 4 5 6 7 8 9 15 17 0 0 0 0 0 0 0 0 0 11 12 11 2 3 4 5 6 7 8 9 12 15 17 0 0 0 0 0 0 0 0 12 13 12 2 3 4 5 6 7 8 9 10 12 15 17 0 0 0 0 0 0 0 13 14 13 2 3 4 5 6 7 8 9 10 12 13 17 18 0 0 0 0 0 0 14 15 14 2 3 4 5 6 7 8 9 10 12 13 15 17 18 0 0 0 0 0 15 16 15 2 3 4 5 6 7 8 9 10 11 12 13 15 17 18 0 0 0 0 16 17 16 1 2 3 4 5 6 7 8 9 10 11 12 13 15 17 18 0 0 0 17 18 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 0 0 18 19 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 0 19 20 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Model Summary Statistics p s Cp Cp.adj BIC MSE RSQ RSQ.adj 1 1 0 422.995 422.467 797.425 259.665 0.000 0.000 2 2 1 60.941 60.441 686.605 76.933 0.707 0.704 3 3 2 38.730 38.257 674.714 65.303 0.754 0.749 4 4 3 30.304 29.860 671.187 60.596 0.774 0.767 5 5 4 24.095 23.678 668.850 56.952 0.790 0.781 6 6 5 15.360 14.971 663.561 51.879 0.811 0.800 7 7 6 12.871 12.510 663.667 50.056 0.820 0.807 8 8 7 8.101 7.768 661.096 46.946 0.833 0.819 9 9 8 6.989 6.684 662.179 45.782 0.839 0.824 10 10 9 7.061 6.784 664.513 45.251 0.843 0.826 11 11 10 7.450 7.200 667.169 44.886 0.846 0.827 12 12 11 8.087 7.864 670.085 44.654 0.848 0.828 13 13 12 8.992 8.798 673.301 44.571 0.850 0.828 14 14 13 10.018 9.851 676.648 44.557 0.852 0.828 15 15 14 10.855 10.716 679.742 44.431 0.855 0.829 16 16 15 12.408 12.296 683.722 44.732 0.856 0.828 17 17 16 14.186 14.102 687.984 45.178 0.856 0.826 18 18 17 16.046 15.990 692.350 45.686 0.856 0.824 19 19 18 18.015 17.987 696.854 46.276 0.856 0.822 20 20 19 20.000 20.000 701.379 46.891 0.856 0.819 p=number of effects in model, p=1 is just the intercept s=number of independent variables in model 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 MSE=unbiased estimate of error variance RSQ=usual R^2, 1-SSE/SST RSQ.adj=adjusted R^2, 1-(n-1)(1-R^2)/(n-p)