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;

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                       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