## Output from partcorr.sas

Source
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

```                   Simple, Partial & Canonical Correlations                  2
Partial Correlations among GRADES, partialling TESTS
```
```                             Correlation Analysis
```
```           3 'PARTIAL' Variables:  MAT_TEST VER_TEST CRE_TEST
```
```
Pearson Partial Correlation Coefficients  / N = 50```
```                        MAT_GRAD       ENG_GRAD       SCI_GRAD       HIS_GRAD

```                   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

```                   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

```                            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

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

```
```
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

```                        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

```
```
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

```                        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

```                        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```