Factor Analysis

Obs _type_ x1 x2 x3 x4 x5 x6
1 CORR 1.000 0.439 0.410 0.288 0.329 0.248
2 CORR 0.439 1.000 0.351 0.354 0.320 0.329
3 CORR 0.410 0.351 1.000 0.164 0.190 0.181
4 CORR 0.288 0.354 0.164 1.000 0.595 0.470
5 CORR 0.329 0.320 0.190 0.595 1.000 0.464
6 CORR 0.248 0.329 0.181 0.470 0.464 1.000

(Score Data): Principal Factor Method with Varimax Rotation

The FACTOR Procedure
Initial Factor Method: Principal Components


Prior Communality Estimates: ONE

Eigenvalues of the Correlation Matrix: Total
= 6 Average = 1
  Eigenvalue Difference Proportion Cumulative
1 2.73288407 1.60311371 0.4555 0.4555
2 1.12977037 0.51459650 0.1883 0.6438
3 0.61517387 0.01395199 0.1025 0.7463
4 0.60122188 0.07642497 0.1002 0.8465
5 0.52479691 0.12864401 0.0875 0.9340
6 0.39615290   0.0660 1.0000


2 factors will be retained by the NFACTOR criterion.

Factor Pattern
  Factor1 Factor2
x1 Gaelic 0.65782 0.44905
x2 English 0.68842 0.29039
x3 History 0.51737 0.63734
x4 Artimethic 0.73831 -0.41303
x5 Algebra 0.74388 -0.37545
x6 Geometry 0.67831 -0.35501

Variance Explained by Each
Factor
Factor1 Factor2
2.7328841 1.1297704

Final Communality Estimates: Total = 3.862654
x1 x2 x3 x4 x5 x6
0.63437428 0.55824594 0.67387364 0.71570325 0.69431309 0.58614424

Residual Correlations With Uniqueness on the Diagonal
  x1 x2 x3 x4 x5 x6
x1 Gaelic 0.36563 -0.14426 -0.21653 -0.01221 0.00826 -0.03879
x2 English -0.14426 0.44175 -0.19024 -0.03433 -0.08307 -0.03487
x3 History -0.21653 -0.19024 0.32613 0.04526 0.04443 0.05633
x4 Artimethic -0.01221 -0.03433 0.04526 0.28430 -0.10929 -0.17744
x5 Algebra 0.00826 -0.08307 0.04443 -0.10929 0.30569 -0.17387
x6 Geometry -0.03879 -0.03487 0.05633 -0.17744 -0.17387 0.41386

Root Mean Square Off-Diagonal Residuals: Overall = 0.11423990
x1 x2 x3 x4 x5 x6
0.11782884 0.11514955 0.13436892 0.09675217 0.10111151 0.11628388

Partial Correlations Controlling Factors
  x1 x2 x3 x4 x5 x6
x1 Gaelic 1.00000 -0.35894 -0.62707 -0.03786 0.02470 -0.09972
x2 English -0.35894 1.00000 -0.50122 -0.09687 -0.22606 -0.08155
x3 History -0.62707 -0.50122 1.00000 0.14865 0.14073 0.15333
x4 Artimethic -0.03786 -0.09687 0.14865 1.00000 -0.37072 -0.51730
x5 Algebra 0.02470 -0.22606 0.14073 -0.37072 1.00000 -0.48884
x6 Geometry -0.09972 -0.08155 0.15333 -0.51730 -0.48884 1.00000

Root Mean Square Off-Diagonal Partials: Overall = 0.32267554
x1 x2 x3 x4 x5 x6
0.32681445 0.29906281 0.37678621 0.29595406 0.29930154 0.33065500

(Score Data): Principal Factor Method with Varimax Rotation

The FACTOR Procedure
Initial Factor Method: Principal Components

Plot of Factor Pattern for Factor1 and Factor2                                                  
                                                                                                
                                             Factor1                                            
                                                1                                               
                                                                                                
                                               .9                                               
                                                                                                
                                               .8                                               
                                   DE                                                           
                                     F         .7       B                                       
                                                             A                                  
                                               .6                                               
                                                                                                
                                               .5                  C                            
                                                                                                
                                               .4                                               
                                                                                                
                                               .3                                               
                                                                                                
                                               .2                                               
                                                                                F               
                                               .1                               a               
                                                                                c               
                -1 -.9-.8-.7-.6-.5-.4-.3-.2-.1  0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0t               
                                                                                o               
                                              -.1                               r               
                                                                                2               
                                              -.2                                               
                                                                                                
                                              -.3                                               
                                                                                                
                                              -.4                                               
                                                                                                
                                              -.5                                               
                                                                                                
                                              -.6                                               
                                                                                                
                                              -.7                                               
                                                                                                
                                              -.8                                               
                                                                                                
                                              -.9                                               
                                                                                                
                                               -1                                               
                                                                                                
        x1=A          x2=B          x3=C          x4=D          x5=E          x6=F

(Score Data): Principal Factor Method with Varimax Rotation

The FACTOR Procedure
Rotation Method: Varimax

Orthogonal Transformation Matrix
  1 2
1 0.77441 0.63269
2 -0.63269 0.77441

Rotated Factor Pattern
  Factor1 Factor2
x1 Gaelic 0.22531 0.76394
x2 English 0.34939 0.66044
x3 History -0.00259 0.82089
x4 Artimethic 0.83308 0.14727
x5 Algebra 0.81360 0.17989
x6 Geometry 0.74990 0.15424

Variance Explained by Each
Factor
Factor1 Factor2
2.0911641 1.7714904

Final Communality Estimates: Total = 3.862654
x1 x2 x3 x4 x5 x6
0.63437428 0.55824594 0.67387364 0.71570325 0.69431309 0.58614424

(Score Data): Principal Factor Method with Varimax Rotation

The FACTOR Procedure
Rotation Method: Varimax

Plot of Factor Pattern for Factor1 and Factor2                                                  
                                                                                                
                                             Factor1                                            
                                                1                                               
                                                                                                
                                               .9                                               
                                                    D                                           
                                               .8    E                                          
                                                    F                                           
                                               .7                                               
                                                                                                
                                               .6                                               
                                                                                                
                                               .5                                               
                                                                                                
                                               .4                                               
                                                                   B                            
                                               .3                                               
                                                                      A                         
                                               .2                                               
                                                                                F               
                                               .1                               a               
                                                                                c               
                -1 -.9-.8-.7-.6-.5-.4-.3-.2-.1  0 .1 .2 .3 .4 .5 .6 .7 .C .9 1.0t               
                                                                                o               
                                              -.1                               r               
                                                                                2               
                                              -.2                                               
                                                                                                
                                              -.3                                               
                                                                                                
                                              -.4                                               
                                                                                                
                                              -.5                                               
                                                                                                
                                              -.6                                               
                                                                                                
                                              -.7                                               
                                                                                                
                                              -.8                                               
                                                                                                
                                              -.9                                               
                                                                                                
                                               -1                                               
                                                                                                
        x1=A          x2=B          x3=C          x4=D          x5=E          x6=F