Output from partcorr.sas

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0 Graphs 
                   Simple, Partial & Canonical Correlations                  1
              Simple Correlations among GRADES (ignoring TESTS)

                             Correlation Analysis

             4 'VAR' Variables:  MAT_GRAD ENG_GRAD SCI_GRAD HIS_GRAD


                 Pearson Correlation Coefficients  / N = 50
                        MAT_GRAD       ENG_GRAD       SCI_GRAD       HIS_GRAD

MAT_GRAD                 1.00000        0.15763        0.44541       -0.07662
Mathematics grade
ENG_GRAD                 0.15763        1.00000        0.00298        0.17121
English grade
SCI_GRAD                 0.44541        0.00298        1.00000       -0.03901
Science grade
HIS_GRAD                -0.07662        0.17121       -0.03901        1.00000
History grade
                   Simple, Partial & Canonical Correlations                  2
             Partial Correlations among GRADES, partialling TESTS

                             Correlation Analysis

           3 'PARTIAL' Variables:  MAT_TEST VER_TEST CRE_TEST
           4 'VAR'     Variables:  MAT_GRAD ENG_GRAD SCI_GRAD HIS_GRAD


             Pearson Partial Correlation Coefficients  / N = 50
                        MAT_GRAD       ENG_GRAD       SCI_GRAD       HIS_GRAD

MAT_GRAD                 1.00000        0.11425       -0.00304        0.03030
Mathematics grade
ENG_GRAD                 0.11425        1.00000       -0.03787       -0.00143
English grade
SCI_GRAD                -0.00304       -0.03787        1.00000        0.10511
Science grade
HIS_GRAD                 0.03030       -0.00143        0.10511        1.00000
History grade
                   Simple, Partial & Canonical Correlations                  3
             Method 2:  using PROC GLM with MANOVA / PRINTE stmt

                       General Linear Models Procedure

                   Number of observations in data set = 50



                            E = Error SS&CP Matrix

                  MAT_GRAD         ENG_GRAD         SCI_GRAD         HIS_GRAD

 MAT_GRAD     39.945669804     5.4932028612      -0.11447415     1.3501152358
 ENG_GRAD     5.4932028612     57.871730079     -1.716235631     -0.076452955
 SCI_GRAD      -0.11447415     -1.716235631     35.494092973     4.4142218239
 HIS_GRAD     1.3501152358     -0.076452955     4.4142218239     49.688528497
                   Simple, Partial & Canonical Correlations                  4
             Method 2:  using PROC GLM with MANOVA / PRINTE stmt

                       General Linear Models Procedure
                      Multivariate Analysis of Variance

  Partial Correlation Coefficients from the Error SS&CP Matrix / Prob > |r|
              DF = 46     MAT_GRAD  ENG_GRAD  SCI_GRAD  HIS_GRAD

              MAT_GRAD    1.000000  0.114250 -0.003040  0.030305
                            0.0001    0.4445    0.9838    0.8398

              ENG_GRAD    0.114250  1.000000 -0.037867 -0.001426
                            0.4445    0.0001    0.8005    0.9924

              SCI_GRAD   -0.003040 -0.037867  1.000000  0.105111
                            0.9838    0.8005    0.0001    0.4820

              HIS_GRAD    0.030305 -0.001426  0.105111  1.000000
                            0.8398    0.9924    0.4820    0.0001



                        Canonical correlation analysis                       5

                        Canonical Correlation Analysis

                                Adjusted       Approx       Squared
                 Canonical      Canonical     Standard     Canonical
                Correlation    Correlation     Error      Correlation

           1      0.820391       0.773486     0.046708      0.673041
           2      0.785258        .           0.054767      0.616630
           3      0.236033       0.203002     0.134898      0.055711

                                Eigenvalues of INV(E)*H
                                  = CanRsq/(1-CanRsq)

                 Eigenvalue    Difference    Proportion    Cumulative

            1       2.0585        0.4500       0.5525        0.5525
            2       1.6084        1.5494       0.4317        0.9842
            3       0.0590         .           0.0158        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    0.11836295     11.7882          12    114.0588    0.0001
          2    0.36201196      9.7098           6          88    0.0001
          3    0.94428854      1.3275           2          45    0.2753


                 Multivariate Statistics and F Approximations


                             S=3    M=0    N=20.5




 Statistic                     Value          F      Num DF    Den DF  Pr > F



 Wilks' Lambda              0.11836295    11.7882        12  114.0588  0.0001
 Pillai's Trace             1.34538271     9.1475        12       135  0.0001
 Hotelling-Lawley Trace     3.72593449    12.9373        12       125  0.0001
 Roy's Greatest Root        2.05849046    23.1580         4        45  0.0001

         NOTE: F Statistic for Roy's Greatest Root is an upper bound.




                        Canonical correlation analysis                       6



                        Canonical Correlation Analysis

          Raw Canonical Coefficients for the High School Test Scores



                  TEST1          TEST2          TEST3

MAT_TEST   0.8958230355   0.0498755273   -0.236289322   Math test score
VER_TEST   -0.462740932   0.8471481098   0.0346844107   Verbal test score
CRE_TEST   0.2736605845   0.2370780991   1.0502644845   Creativity test score




              Raw Canonical Coefficients for the College Grades



                  GRADE1          GRADE2          GRADE3

MAT_GRAD    0.5231092484    -0.084172117    0.4664745785    Mathematics grade
ENG_GRAD    0.0499705412    0.5565643153    -0.196020265    English grade
SCI_GRAD    0.3640056772    -0.056129593     -0.53287337    Science grade
HIS_GRAD    -0.104758658     0.140872712     0.766586091    History grade




     Standardized Canonical Coefficients for the High School Test Scores



                 TEST1         TEST2         TEST3

MAT_TEST        1.0682        0.0595       -0.2818      Math test score
VER_TEST       -0.5328        0.9755        0.0399      Verbal test score
CRE_TEST        0.2481        0.2149        0.9521      Creativity test score




          Standardized Canonical Coefficients for the College Grades



                  GRADE1        GRADE2        GRADE3

  MAT_GRAD        0.7359       -0.1184        0.6563      Mathematics grade
  ENG_GRAD        0.0869        0.9677       -0.3408      English grade
  SCI_GRAD        0.3882       -0.0599       -0.5683      Science grade
  HIS_GRAD       -0.1122        0.1508        0.8208      History grade




                        Canonical correlation analysis                       7



                             Canonical Structure

Correlations Between the High School Test Scores and Their Canonical Variables



                 TEST1         TEST2         TEST3

MAT_TEST        0.8259        0.4642       -0.3200      Math test score
VER_TEST       -0.1052        0.9756       -0.1928      Verbal test score
CRE_TEST        0.2488        0.0965        0.9637      Creativity test score




    Correlations Between the College Grades and Their Canonical Variables



                  GRADE1        GRADE2        GRADE3

  MAT_GRAD        0.9311       -0.0041        0.2865      Mathematics grade
  ENG_GRAD        0.1848        0.9746       -0.0985      English grade
  SCI_GRAD        0.7206       -0.1156       -0.3090      Science grade
  HIS_GRAD       -0.1688        0.3279        0.7344      History grade




               Correlations Between the High School Test Scores
              and the Canonical Variables of the College Grades



                GRADE1        GRADE2        GRADE3

MAT_TEST        0.6776        0.3645       -0.0755      Math test score
VER_TEST       -0.0863        0.7661       -0.0455      Verbal test score
CRE_TEST        0.2041        0.0757        0.2275      Creativity test score




          Correlations Between the College Grades and the Canonical
                   Variables of the High School Test Scores



                   TEST1         TEST2         TEST3

  MAT_GRAD        0.7639       -0.0032        0.0676      Mathematics grade
  ENG_GRAD        0.1516        0.7653       -0.0233      English grade
  SCI_GRAD        0.5912       -0.0908       -0.0729      Science grade
  HIS_GRAD       -0.1385        0.2575        0.1733      History grade




                        Canonical correlation analysis                       8



                        Canonical Redundancy Analysis

                 Raw Variance of the High School Test Scores
                                 Explained by
                  Their Own                               The Opposite
             Canonical Variables                       Canonical Variables

                        Cumulative     Canonical                  Cumulative
          Proportion    Proportion     R-Squared    Proportion    Proportion



     1        0.2901        0.2901        0.6730        0.1952        0.1952
     2        0.4415        0.7316        0.6166        0.2723        0.4675
     3        0.2684        1.0000        0.0557        0.0150        0.4824






                      Raw Variance of the College Grades
                                 Explained by
                  Their Own                               The Opposite
             Canonical Variables                       Canonical Variables

                        Cumulative     Canonical                  Cumulative
          Proportion    Proportion     R-Squared    Proportion    Proportion



     1        0.3353        0.3353        0.6730        0.2256        0.2256
     2        0.4131        0.7484        0.6166        0.2547        0.4804
     3        0.1261        0.8745        0.0557        0.0070        0.4874






             Standardized Variance of the High School Test Scores
                                 Explained by
                  Their Own                               The Opposite
             Canonical Variables                       Canonical Variables

                        Cumulative     Canonical                  Cumulative
          Proportion    Proportion     R-Squared    Proportion    Proportion



     1        0.2517        0.2517        0.6730        0.1694        0.1694
     2        0.3922        0.6439        0.6166        0.2418        0.4112
     3        0.3561        1.0000        0.0557        0.0198        0.4311




                        Canonical correlation analysis                       9



                        Canonical Redundancy Analysis

                 Standardized Variance of the College Grades
                                 Explained by
                  Their Own                               The Opposite
             Canonical Variables                       Canonical Variables

                        Cumulative     Canonical                  Cumulative
          Proportion    Proportion     R-Squared    Proportion    Proportion



     1        0.3622        0.3622        0.6730        0.2438        0.2438
     2        0.2677        0.6300        0.6166        0.1651        0.4089
     3        0.1816        0.8116        0.0557        0.0101        0.4190




      Squared Multiple Correlations Between the High School Test Scores
         and the First 'M' Canonical Variables of the College Grades

M                    1             2             3



MAT_TEST        0.4591        0.5920        0.5977      Math test score
VER_TEST        0.0074        0.5943        0.5964      Verbal test score
CRE_TEST        0.0417        0.0474        0.0992      Creativity test score




       Squared Multiple Correlations Between the College Grades and the
         First 'M' Canonical Variables of the High School Test Scores

  M                    1             2             3



  MAT_GRAD        0.5835        0.5836        0.5881      Mathematics grade
  ENG_GRAD        0.0230        0.6088        0.6093      English grade
  SCI_GRAD        0.3495        0.3577        0.3631      Science grade
  HIS_GRAD        0.0192        0.0855        0.1155      History grade




                        Canonical correlation analysis                      10
                             Canonical variables



  OBS  MAT_TEST  VER_TEST  CRE_TEST  MAT_GRAD  ENG_GRAD  SCI_GRAD  HIS_GRAD


    1  -0.12148  -0.26498  -0.22226   0.04009   0.15556  -1.52466   0.70583
    2   0.46181  -1.15750   0.44887   0.48615   0.72248   0.65446   0.24797
    3   0.60643   1.15498   0.72810   0.35593   2.05593  -1.00126   0.87395
    4   2.57884  -0.39437  -1.55640   1.08713  -1.71634   1.61845  -1.67299
    5   0.21827  -0.20116  -0.77319  -0.62364  -0.92800  -0.43022  -0.61638
    6   0.05884  -1.29567   1.61567   1.43204  -2.23690   0.21990   1.22402
    7  -1.36043  -1.54180   0.61034  -0.94770  -3.92644   0.14892  -0.36647
    8  -1.69801  -0.70359   1.41937  -1.28251  -0.05041   0.80740   0.64893
    9  -0.18101   0.61814  -0.79731   0.88708  -0.18838  -0.42703  -0.04812
   10   1.01408   0.28803   0.69760  -0.74616  -0.30609   1.22953  -0.06061
   11  -0.84220   0.38580  -0.05007  -1.61917  -1.46745  -1.63747  -0.00662
   12   1.38572   0.95101   0.20284  -0.32739   1.50584   0.19520   0.08989
   13   0.11347   2.39724   1.44692  -0.29034   2.52676  -1.11256   0.56944
   14   2.61849   1.37668  -0.64543   1.03630   2.66650  -0.82862  -1.41540
   15  -1.34077  -1.13100   0.77366   0.01310   0.66451   0.09958  -0.04096
   16   1.07471   0.79961   0.04430   1.36468   1.57244   0.19778   1.49217
   17  -0.84557  -0.25564  -0.71871  -1.52152  -2.07502  -0.18180   0.04253
   18   0.43368   1.07738   1.23229   0.98620   1.44479  -0.42837   1.33077
   19  -0.14641   0.29082  -0.68471  -1.62831  -1.17836  -2.06673  -2.68526
   20  -0.26282  -1.68632   0.52271   0.99889  -0.16661  -1.59407  -1.93739
   21  -1.96853  -3.52053  -0.48246   1.27807  -4.41169   0.57281  -1.73335
   22  -2.14604  -1.08381  -0.17716  -1.99084  -0.41981  -1.57576  -0.26524
   23   0.14594  -0.97163  -1.07973   1.45087  -0.17313   0.52584   0.35761



  OBS    TEST1       TEST2       TEST3      GRADE1      GRADE2      GRADE3


    1   0.08003    -0.26756    -0.25851    -0.44114     0.29323     1.38658
    2   1.19922    -0.83546     0.27758     0.66170     0.38441    -0.02865
    3   0.33511     1.19698     0.61688    -0.00806     1.31863     1.01137
    4   2.19381    -0.55879    -2.30225     1.40634    -1.34826    -1.25652
    5   0.20408    -0.32716    -0.91520    -0.30560    -0.50166    -0.30742
    6   1.22147    -0.69598     1.59345     0.74819    -1.18041     1.97247
    7  -0.21117    -1.21362     0.86440    -0.44032    -2.14051     0.01213
    8  -0.68006    -0.32856     1.82295    -0.28846     0.15101    -0.47631
    9  -0.53932     0.34127    -0.81776     0.46326    -0.13730     0.68623
   10   1.09312     0.47564     0.45845     0.20732    -0.16008    -0.94487
   11  -0.81963     0.28863     0.11521    -1.35665    -0.56444     0.44468
   12   0.98385     0.93852    -0.12600     0.12466     0.89238    -0.43816
   13  -0.48463     2.39518     1.53140    -0.33121     1.59843     0.44349
   14   1.65908     1.15950    -1.29344     0.68103     1.26899    -0.63791
   15  -0.33895    -0.82591     1.04554     0.23963     0.38240    -0.16377
   16   0.73192     0.75717    -0.22427     0.86717     0.98442     1.41168
   17  -0.70880    -0.41346    -0.60849    -0.81120    -0.98559    -0.12869
   18   0.35424     1.24215     1.18453     0.45178     0.95765     1.47009
   19  -0.32605     0.09241    -0.71903    -1.22263    -0.75603    -1.44092
   20   0.81499    -1.30208     0.50801     0.29595    -0.33524    -0.09228
   21  -0.13934    -3.17931    -0.20827     0.99724    -2.81428    -0.12819
   22  -1.34237    -1.05151     0.23884    -1.44917     0.01003    -0.16519
   23   0.41192    -1.05615    -1.24678     1.06330    -0.17260     0.74950




                        Canonical correlation analysis                      11
                             Canonical variables



  OBS  MAT_TEST  VER_TEST  CRE_TEST  MAT_GRAD  ENG_GRAD  SCI_GRAD  HIS_GRAD


   24   0.37483  -0.36685   0.91624   1.67103  -0.53175  -0.06917   1.25433
   25   0.16563  -1.62245   0.54067   0.45677  -0.08141   0.58942  -0.76273



  OBS    TEST1       TEST2       TEST3      GRADE1      GRADE2      GRADE3


   24   0.88333    -0.05919     0.81641     0.85002    -0.23100     1.92698
   25   1.17417    -1.22234     0.42784     0.68836    -0.19927    -0.62491




                        Canonical correlation analysis                      12
                    Correlations among canonical variates



                             Correlation Analysis



    6 'VAR' Variables:  TEST1    TEST2    TEST3    GRADE1   GRADE2   GRADE3




                              Simple Statistics

  Variable          N       Mean    Std Dev        Sum    Minimum    Maximum



  TEST1            50          0     1.0000          0    -2.1037     2.1938
  TEST2            50          0     1.0000          0    -3.1793     2.3952
  TEST3            50          0     1.0000          0    -2.3022     1.8697
  GRADE1           50          0     1.0000          0    -2.3150     2.3594
  GRADE2           50          0     1.0000          0    -2.8143     1.9141
  GRADE3           50          0     1.0000          0    -2.7488     1.9725




                 Pearson Correlation Coefficients  / N = 50


             TEST1       TEST2       TEST3      GRADE1      GRADE2      GRADE3

TEST1      1.00000     0.00000     0.00000     0.82039     0.00000     0.00000

TEST2      0.00000     1.00000     0.00000     0.00000     0.78526     0.00000

TEST3      0.00000     0.00000     1.00000     0.00000     0.00000     0.23603

GRADE1     0.82039     0.00000     0.00000     1.00000     0.00000     0.00000

GRADE2     0.00000     0.78526     0.00000     0.00000     1.00000     0.00000

GRADE3     0.00000     0.00000     0.23603     0.00000     0.00000     1.00000