Canonical Correlation Example 3 data canman3; input group y1 y2 y3 x1 x2; cards; 1 19.6 5.15 9.5 1 1 1 15.4 5.75 9.1 1 1 1 22.3 4.35 3.3 1 1 1 24.3 7.55 5.0 1 1 1 22.5 8.50 6.0 1 1 1 20.5 10.25 5.0 1 1 1 14.1 5.95 18.8 1 1 1 13.0 6.30 16.5 1 1 1 14.1 5.45 8.9 1 1 1 16.7 3.75 6.0 1 1 1 16.8 5.10 7.4 1 1 2 17.1 9.00 7.5 -1 1 2 15.7 5.30 8.5 -1 1 2 14.9 9.85 6.0 -1 1 2 19.7 3.60 2.9 -1 1 2 17.2 4.05 0.2 -1 1 2 16.0 4.40 2.6 -1 1 2 12.8 7.15 7.0 -1 1 2 13.6 7.25 3.2 -1 1 2 14.2 5.30 6.2 -1 1 2 13.1 3.10 5.5 -1 1 2 16.5 2.40 6.6 -1 1 3 16.0 4.55 2.9 0 -2 3 12.5 2.65 0.7 0 -2 3 18.5 6.50 5.3 0 -2 3 19.2 4.85 8.3 0 -2 3 12.0 8.75 9.0 0 -2 3 13.0 5.20 10.3 0 -2 3 11.9 4.75 8.5 0 -2 3 12.0 5.85 9.5 0 -2 3 19.8 2.85 2.3 0 -2 3 16.5 6.55 3.3 0 -2 3 17.4 6.60 1.9 0 -2 ; proc cancorr all vprefix=dv vname='dependent variables' wprefix=iv wname='indpendent variables'; var y1 y2 y3; with x1 x2; run; --------------------------------------------------------------------------------- Means and Standard Deviations 3 dependent variables 2 indpendent variables 33 Observations Variable Mean Std Dev Y1 16.330303 3.292462 Y2 5.715152 2.017598 Y3 6.475758 3.985131 X1 0 0.829156 X2 0 1.436141 Correlations Among the Original Variables Correlations Among the dependent variables Y1 Y2 Y3 Y1 1.0000 0.0978 -0.3411 Y2 0.0978 1.0000 0.1978 Y3 -0.3411 0.1978 1.0000 Correlations Among the indpendent variables X1 X2 X1 1.0000 0.0000 X2 0.0000 1.0000 Correlations Among the Original Variables Correlations Between the dependent variables and the indpendent variables X1 X2 Y1 0.3262 0.2148 Y2 0.1252 0.1219 Y3 0.3717 0.1512 Adjusted Approx Squared Canonical Canonical Standard Canonical Correlation Correlation Error Correlation 1 0.686626 0.656071 0.093434 0.471455 2 0.072213 -.139365 0.175855 0.005215 Eigenvalues of INV(E)*H = CanRsq/(1-CanRsq) Eigenvalue Difference Proportion Cumulative 1 0.8920 0.8867 0.9942 0.9942 2 0.0052 . 0.0058 1.0000 Test of H0: The canonical correlations in the current row and all that follow are zero Likelihood Ratio Approx F Num DF Den DF Pr > F 1 0.52578837 3.5382 6 56 0.0049 2 0.99478527 0.0760 2 29 0.9270 Multivariate Statistics and F Approximations S=2 M=0 N=13 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.52578837 3.5382 6 56 0.0049 Pillai's Trace 0.47667015 3.0248 6 58 0.0122 Hotelling-Lawley Trace 0.89723004 4.0375 6 54 0.0021 Roy's Greatest Root 0.89198797 8.6226 3 29 0.0003 NOTE: F Statistic for Roy's Greatest Root is an upper bound. NOTE: F Statistic for Wilks' Lambda is exact. Raw Canonical Coefficients for the dependent variables DV1 DV2 Y1 0.2636265875 0.0813957795 Y2 -0.007656089 0.3886764475 Y3 0.2210547696 -0.14785517 Raw Canonical Coefficients for the indpendent variables IV1 IV2 X1 1.0690954306 -0.558193886 X2 0.3222733906 0.6172425347 Standardized Canonical Coefficients for the dependent variables DV1 DV2 Y1 0.8680 0.2680 Y2 -0.0154 0.7842 Y3 0.8809 -0.5892 Standardized Canonical Coefficients for the indpendent variables IV1 IV2 X1 0.8864 -0.4628 X2 0.4628 0.8864 Canonical Structure Correlations Between the dependent variables and Their Canonical Variables DV1 DV2 Y1 0.5660 0.5457 Y2 0.2437 0.6939 Y3 0.5818 -0.5255 Correlations Between the indpendent variables and Their Canonical Variables IV1 IV2 X1 0.8864 -0.4628 X2 0.4628 0.8864 Canonical Structure Correlations Between the dependent variables and the Canonical Variables of the indpendent variables IV1 IV2 Y1 0.3886 0.0394 Y2 0.1673 0.0501 Y3 0.3995 -0.0379 Correlations Between the indpendent variables and the Canonical Variables of the dependent variables DV1 DV2 X1 0.6087 -0.0334 X2 0.3178 0.0640 Canonical Redundancy Analysis Raw Variance of the dependent variables Explained by Their Own The Opposite Canonical Variables Canonical Variables Cumulative Canonical Cumulative Proportion Proportion R-Squared Proportion Proportion 1 0.2952 0.2952 0.4715 0.1392 0.1392 2 0.3109 0.6061 0.0052 0.0016 0.1408 The SAS System 19 17:11 Monday, May 6, 1996 Canonical Redundancy Analysis Raw Variance of the indpendent variables Explained by Their Own The Opposite Canonical Variables Canonical Variables Cumulative Canonical Cumulative Proportion Proportion R-Squared Proportion Proportion 1 0.3571 0.3571 0.4715 0.1684 0.1684 2 0.6429 1.0000 0.0052 0.0034 0.1717 The SAS System 20 17:11 Monday, May 6, 1996 Canonical Redundancy Analysis Standardized Variance of the dependent variables Explained by Their Own The Opposite Canonical Variables Canonical Variables Cumulative Canonical Cumulative Proportion Proportion R-Squared Proportion Proportion 1 0.2394 0.2394 0.4715 0.1129 0.1129 2 0.3518 0.5912 0.0052 0.0018 0.1147 Canonical Redundancy Analysis Standardized Variance of the indpendent variables Explained by Their Own The Opposite Canonical Variables Canonical Variables Cumulative Canonical Cumulative Proportion Proportion R-Squared Proportion Proportion 1 0.5000 0.5000 0.4715 0.2357 0.2357 2 0.5000 1.0000 0.0052 0.0026 0.2383 The SAS System 22 17:11 Monday, May 6, 1996 Canonical Redundancy Analysis Squared Multiple Correlations Between the dependent variables and the First 'M' Canonical Variables of the indpendent variables M 1 2 Y1 0.1510 0.1526 Y2 0.0280 0.0305 Y3 0.1596 0.1610 Squared Multiple Correlations Between the indpendent variables and the First 'M' Canonical Variables of the dependent variables M 1 2 X1 0.3705 0.3716 X2 0.1010 0.1051