SAS Output

(Stock 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 = 5 Average = 1
	Eigenvalue	Difference	Proportion	Cumulative
1	2.43761478	1.03135359	0.4875	0.4875
2	1.40626120	0.90607546	0.2813	0.7688
3	0.50018573	0.10015292	0.1000	0.8688
4	0.40003281	0.14412732	0.0800	0.9488
5	0.25590548		0.0512	1.0000

2 factors will be retained by the NFACTOR criterion.

Factor Pattern
	Factor1	Factor2
x1	0.73258	-0.43614
x2	0.83096	-0.28039
x3	0.72635	-0.37403
x4	0.60474	0.69375
x5	0.56317	0.71850

Variance Explained by Each Factor
Factor1	Factor2
2.4376148	1.4062612

Final Communality Estimates: Total = 3.843876
x1	x2	x3	x4	x5
0.72689087	0.76910539	0.66748055	0.84699821	0.83340095

Residual Correlations With Uniqueness on the Diagonal
	x1	x2	x3	x4	x5
x1	0.27311	-0.09903	-0.18424	-0.02545	0.05580
x2	-0.09903	0.23089	-0.13444	0.01401	-0.05352
x3	-0.18424	-0.13444	0.33252	0.00323	0.00568
x4	-0.02545	0.01401	0.00323	0.15300	-0.15603
x5	0.05580	-0.05352	0.00568	-0.15603	0.16660

Root Mean Square Off-Diagonal Residuals: Overall = 0.09645329
x1	x2	x3	x4	x5
0.10898520	0.08794901	0.11408265	0.07937147	0.08711316

Partial Correlations Controlling Factors
	x1	x2	x3	x4	x5
x1	1.00000	-0.39436	-0.61137	-0.12448	0.26158
x2	-0.39436	1.00000	-0.48518	0.07452	-0.27286
x3	-0.61137	-0.48518	1.00000	0.01434	0.02414
x4	-0.12448	0.07452	0.01434	1.00000	-0.97729
x5	0.26158	-0.27286	0.02414	-0.97729	1.00000

Root Mean Square Off-Diagonal Partials: Overall = 0.43410706
x1	x2	x3	x4	x5
0.39153754	0.34311832	0.39049831	0.49405058	0.52405910

(Stock 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                                               
                                       B                                                        
                                               .8                                               
                                  A C                                                           
                                               .7                                               
                                                                                                
                                               .6                   D                           
                                                                     E                          
                                               .5                                               
                                                                                                
                                               .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

(Stock Data): Principal Factor Method with Varimax Rotation

The FACTOR Procedure

Rotation Method: Varimax

Orthogonal Transformation Matrix
	1	2
1	0.84070	0.54150
2	-0.54150	0.84070

Rotated Factor Pattern
	Factor1	Factor2
x1	0.85205	0.03002
x2	0.85042	0.21424
x3	0.81318	0.07886
x4	0.13275	0.91070
x5	0.08440	0.90900

Variance Explained by Each Factor
Factor1	Factor2
2.1352041	1.7086719

Final Communality Estimates: Total = 3.843876
x1	x2	x3	x4	x5
0.72689087	0.76910539	0.66748055	0.84699821	0.83340095

(Stock Data): Principal Factor Method with Varimax Rotation

The FACTOR Procedure

Rotation Method: Varimax

Plot of Factor Pattern for Factor1 and Factor2                                                  
                                                                                                
                                             Factor1                                            
                                                1                                               
                                                                                                
                                               .9                                               
                                                A     B                                         
                                               .8 C                                             
                                                                                                
                                               .7                                               
                                                                                                
                                               .6                                               
                                                                                                
                                               .5                                               
                                                                                                
                                               .4                                               
                                                                                                
                                               .3                                               
                                                                                                
                                               .2                                               
                                                                           D    F               
                                               .1                          E    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

#3b (Stock Data): Maximum Likelihood Method (k=2 factor)

The FACTOR Procedure

Initial Factor Method: Maximum Likelihood

Prior Communality Estimates: SMC
x1	x2	x3	x4	x5
0.45156689	0.53347907	0.36655825	0.51643642	0.47767780

Preliminary Eigenvalues: Total = 4.52808758 Average = 0.90561752
	Eigenvalue	Difference	Proportion	Cumulative
1	3.67372695	1.95722570	0.8113	0.8113
2	1.71650125	1.86845966	0.3791	1.1904
3	-.15195842	0.07024376	-0.0336	1.1568
4	-.22220217	0.26577786	-0.0491	1.1078
5	-.48798003		-0.1078	1.0000

2 factors will be retained by the NFACTOR criterion.

Iteration	Criterion	Ridge	Change	Communalities
1	0.0979665	0.0313	0.4836	0.52461	0.64776	0.42439	1.00000	0.23287
2	0.0195937	0.0000	0.2349	0.58313	0.72449	0.45774	1.00000	0.46775
3	0.0195920	0.0000	0.0010	0.58408	0.72379	0.45854	1.00000	0.46756

Convergence criterion satisfied.

Significance Tests Based on 10000 Observations
Test	DF	Chi-Square	Pr > ChiSq
H0: No common factors	10	17393.6805	<.0001
HA: At least one common factor
H0: 2 Factors are sufficient	1	195.8253	<.0001
HA: More factors are needed

Chi-Square without Bartlett's Correction	195.90039
Akaike's Information Criterion	193.90039
Schwarz's Bayesian Criterion	186.69005
Tucker and Lewis's Reliability Coefficient	0.88793

Squared Canonical Correlations
Factor1	Factor2
1.0000000	0.8149733

Eigenvalues of the Weighted Reduced Correlation Matrix: Total = 4.40462521 Average = 1.1011563
	Eigenvalue	Difference	Proportion	Cumulative
1	Infty	Infty
2	4.40462638	4.26529969	1.0000	1.0000
3	0.13932669	0.13939470	0.0316	1.0316
4	-.00006801	0.13919184	-0.0000	1.0316
5	-.13925985		-0.0316	1.0000

Factor Pattern
	Factor1	Factor2
x1	0.11500	0.75555
x2	0.32200	0.78747
x3	0.18300	0.65195
x4	1.00000	-0.00000
x5	0.68300	0.03281

Variance Explained by Each Factor
Factor	Weighted	Unweighted
Factor1	1.34516012	1.61688700
Factor2	4.40462638	1.61708744

Final Communality Estimates and Variable Weights
Total Communality: Weighted = 5.749786 Unweighted = 3.233974
Variable	Communality	Weight
x1	0.58408551	2.40432917
x2	0.72379091	3.62045851
x3	0.45853266	1.84686184
x4	1.00000000	Infty
x5	0.46756536	1.87813579

Residual Correlations With Uniqueness on the Diagonal
	x1	x2	x3	x4	x5
x1	0.41591	-0.00000	-0.00263	0.00000	0.05167
x2	-0.00000	0.27621	0.00168	0.00000	-0.03276
x3	-0.00263	0.00168	0.54147	0.00000	-0.00038
x4	0.00000	0.00000	0.00000	0.00000	0.00000
x5	0.05167	-0.03276	-0.00038	0.00000	0.53243

Root Mean Square Off-Diagonal Residuals: Overall = 0.01937176
x1	x2	x3	x4	x5
0.02586691	0.01640214	0.00157232	0.00000000	0.03058965

Partial Correlations Controlling Factors
	x1	x2	x3	x4	x5
x1	1.00000	-0.00001	-0.00554	0.00000	0.10979
x2	-0.00001	1.00000	0.00435	0.00000	-0.08543
x3	-0.00554	0.00435	1.00000	0.00000	-0.00070
x4	0.00000	0.00000	0.00000	0.00000	0.00000
x5	0.10979	-0.08543	-0.00070	0.00000	1.00000

Root Mean Square Off-Diagonal Partials: Overall = 0.04404878
x1	x2	x3	x4	x5
0.05496674	0.04276996	0.00353966	0.00000000	0.06955812

#3b (Stock Data): Maximum Likelihood Method (k=2 factor)

The FACTOR Procedure

Initial Factor Method: Maximum Likelihood

Plot of Factor Pattern for Factor1 and Factor2                                                  
                                                                                                
                                             Factor1                                            
                                                D                                               
                                                                                                
                                               .9                                               
                                                                                                
                                               .8                                               
                                                                                                
                                               .E                                               
                                                                                                
                                               .6                                               
                                                                                                
                                               .5                                               
                                                                                                
                                               .4                                               
                                                                                                
                                               .3                      B                        
                                                                                                
                                               .2                  C                            
                                                                                F               
                                               .1                     A         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

#3b (Stock Data): Maximum Likelihood Method (k=2 factor)

The FACTOR Procedure

Rotation Method: Varimax

Orthogonal Transformation Matrix
	1	2
1	0.11841	0.99297
2	0.99297	-0.11841

Rotated Factor Pattern
	Factor1	Factor2
x1	0.76385	0.02473
x2	0.82006	0.22649
x3	0.66904	0.10452
x4	0.11841	0.99297
x5	0.11345	0.67431

Variance Explained by Each Factor
Factor	Weighted	Unweighted
Factor1	4.68843713	1.73046567
Factor2	1.06134937	1.50350876

Final Communality Estimates and Variable Weights
Total Communality: Weighted = 5.749786 Unweighted = 3.233974
Variable	Communality	Weight
x1	0.58408551	2.40432917
x2	0.72379091	3.62045851
x3	0.45853266	1.84686184
x4	1.00000000	Infty
x5	0.46756536	1.87813579

#3b (Stock Data): Maximum Likelihood Method (k=2 factor)

The FACTOR Procedure

Rotation Method: Varimax

Plot of Factor Pattern for Factor1 and Factor2                                                  
                                                                                                
                                             Factor1                                            
                                                1                                               
                                                                                                
                                               .9                                               
                                                                                                
                                               .8     B                                         
                                                A                                               
                                               .7                                               
                                                   C                                            
                                               .6                                               
                                                                                                
                                               .5                                               
                                                                                                
                                               .4                                               
                                                                                                
                                               .3                                               
                                                                                                
                                               .2                                               
                                                                                F               
                                               .1                   E        D  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