## Output from faccorr.sas

Source
0 Graphs

```            Demonstration of Partial Linear Independence principle           1
Simple Correlations among TESTS
```
```                             Correlation Analysis
```
```             4 'VAR' Variables:  MAT_TEST ENG_TEST SCI_TEST HIS_TEST
```
```
Pearson Correlation Coefficients  / N = 800```
```                        MAT_TEST       ENG_TEST       SCI_TEST       HIS_TEST

MAT_TEST                1.00000       -0.00417        0.41370       -0.21101
Mathematics test
ENG_TEST               -0.00417        1.00000       -0.14758        0.26917
English test
SCI_TEST                0.41370       -0.14758        1.00000       -0.24453
Science test
HIS_TEST               -0.21101        0.26917       -0.24453        1.00000
History test```

```            Demonstration of Partial Linear Independence principle           2
Partial Correlations among TESTS, partialling Factors
```
```                             Correlation Analysis
```
```           2 'PARTIAL' Variables:  MATH     VERBAL
4 'VAR'     Variables:  MAT_TEST ENG_TEST SCI_TEST HIS_TEST
```
```
Pearson Partial Correlation Coefficients  / N = 800```
```                        MAT_TEST       ENG_TEST       SCI_TEST       HIS_TEST

MAT_TEST                1.00000        0.06096       -0.00293       -0.02595
Mathematics test
ENG_TEST                0.06096        1.00000        0.02505       -0.06677
English test
SCI_TEST               -0.00293        0.02505        1.00000       -0.00846
Science test
HIS_TEST               -0.02595       -0.06677       -0.00846        1.00000
History test```

```            Demonstration of Partial Linear Independence principle           3
Retrieving the factor structure
```
```Initial Factor Method: Principal Components

Prior Communality Estimates: ONE```

`        Eigenvalues of the Correlation Matrix:  Total = 4  Average = 1`
```                                1           2           3           4
Eigenvalue        1.6709      1.0695      0.7019      0.5577
Difference        0.6014      0.3675      0.1443
Proportion        0.4177      0.2674      0.1755      0.1394
Cumulative        0.4177      0.6851      0.8606      1.0000
```
`             2 factors will be retained by the NFACTOR criterion.`

`                                Factor Pattern`
```                          FACTOR1   FACTOR2

MAT_TEST   0.67941   0.53070    Mathematics test
ENG_TEST  -0.43800   0.76245    English test
SCI_TEST   0.75789   0.27954    Science test
HIS_TEST  -0.66564   0.35827    History test
```
`                      Variance explained by each factor`
```                                FACTOR1   FACTOR2
1.670908  1.069471
```
```
Final Communality Estimates: Total = 2.740378```

`                     MAT_TEST  ENG_TEST  SCI_TEST  HIS_TEST`
```                     0.743241  0.773164  0.652543  0.571431
```

```            Demonstration of Partial Linear Independence principle           4
Retrieving the factor structure
```
```Rotation Method: Varimax

Orthogonal Transformation Matrix```
```                                       1         2

1      0.81299  -0.58228
2      0.58228   0.81299
```
`                            Rotated Factor Pattern`
```                          FACTOR1   FACTOR2

MAT_TEST   0.86137   0.03585    Mathematics test
ENG_TEST   0.08788   0.87490    English test
SCI_TEST   0.77893  -0.21405    Science test
HIS_TEST  -0.33254   0.67886    History test
```
`                      Variance explained by each factor`
```                                FACTOR1   FACTOR2
1.466988  1.273391
```
```
Final Communality Estimates: Total = 2.740378```

`                     MAT_TEST  ENG_TEST  SCI_TEST  HIS_TEST`
```                     0.743241  0.773164  0.652543  0.571431
```