## Output from phys8.sas

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```                           Eight physical variables                          1
SEE PP 154-155 of Harman: Modern Factor Analysis, 2nd Ed.
```
```Initial Factor Method: Principal Factors

Prior Communality Estimates: NUMERIC```
```                         VAR1      VAR2      VAR3      VAR4
0.854000  0.897000  0.833000  0.783000

VAR5      VAR6      VAR7      VAR8
0.870000  0.687000  0.521000  0.579000
```
`Eigenvalues of the Reduced Correlation Matrix:  Total = 6.024  Average = 0.753`
```                                1           2           3           4
Eigenvalue        4.4558      1.5127      0.1305      0.0587
Difference        2.9430      1.3823      0.0718      0.0252
Proportion        0.7397      0.2511      0.0217      0.0097
Cumulative        0.7397      0.9908      1.0124      1.0222

5           6           7           8
Eigenvalue        0.0335     -0.0314     -0.0440     -0.0917
Difference        0.0649      0.0126      0.0477
Proportion        0.0056     -0.0052     -0.0073     -0.0152
Cumulative        1.0277      1.0225      1.0152      1.0000
```
`             2 factors will be retained by the NFACTOR criterion.`

`                                Factor Pattern`
```                      FACTOR1   FACTOR2

VAR1         86 *     -33       HEIGHT
VAR2         85 *     -41       ARM SPAN
VAR3         81 *     -41       LENGTH OF FOREARM
VAR4         83 *     -34       LENGTH OF LOWER LEG
VAR5         75 *      56       WEIGHT
VAR6         64 *      51       BITROCHANTERIC DIAMETER
VAR7         56        49       CHEST GIRTH
VAR8         62 *      37       CHEST WIDTH
```
```NOTE: Printed values are multiplied by 100 and rounded to the nearest
integer.  Values greater than 0.610763 have been flagged by an '*'.```

`                      Variance explained by each factor`
```                                FACTOR1   FACTOR2
4.455751  1.512747```

```                           Eight physical variables                          2
SEE PP 154-155 of Harman: Modern Factor Analysis, 2nd Ed.
```
```Initial Factor Method: Principal Factors

Final Communality Estimates: Total = 5.968498```

`                         VAR1      VAR2      VAR3      VAR4`
```                     0.844344  0.892132  0.825951  0.795884
```
`                         VAR5      VAR6      VAR7      VAR8`
```                     0.873330  0.663143  0.552635  0.521080

```
`            Residual Correlations With Uniqueness on the Diagonal`
```               VAR1      VAR2      VAR3      VAR4

VAR1         16 *      -2        -3         4       HEIGHT
VAR2         -2        11 *       2        -1       ARM SPAN
VAR3         -3         2        17 *      -1       LENGTH OF FOREARM
VAR4          4        -1        -1        20 *     LENGTH OF LOWER LEG
VAR5          2        -3         1         1       WEIGHT
VAR6          2        -1         1        -3       BITROCHANTERIC DIAMETER
VAR7         -2         0        -2         3       CHEST GIRTH
VAR8         -3         4         0        -2       CHEST WIDTH

VAR5      VAR6      VAR7      VAR8

VAR1          2         2        -2        -3       HEIGHT
VAR2         -3        -1         0         4       ARM SPAN
VAR3          1         1        -2         0       LENGTH OF FOREARM
VAR4          1        -3         3        -2       LENGTH OF LOWER LEG
VAR5         13 *       0         4        -4       WEIGHT
VAR6          0        34 *      -2        -1       BITROCHANTERIC DIAMETER
VAR7          4        -2        45 *       1       CHEST GIRTH
VAR8         -4        -1         1        48 *     CHEST WIDTH
```
```NOTE: Printed values are multiplied by 100 and rounded to the nearest
integer.  Values greater than 0.10417 have been flagged by an '*'.```

```
Root Mean Square Off-diagonal Residuals: Over-all = 0.02222258```

`                         VAR1      VAR2      VAR3      VAR4`
```                     0.024764  0.022662  0.015430  0.023492
```
`                         VAR5      VAR6      VAR7      VAR8`
```                     0.024516  0.015301  0.022280  0.026504
```

```                           Eight physical variables                          3
SEE PP 154-155 of Harman: Modern Factor Analysis, 2nd Ed.
```
```Initial Factor Method: Principal Factors

Partial Correlations Controlling Factors```
```               VAR1      VAR2      VAR3      VAR4

VAR1        100 *     -14       -15        22       HEIGHT
VAR2        -14       100 *      17       -10       ARM SPAN
VAR3        -15        17       100 *      -4       LENGTH OF FOREARM
VAR4         22       -10        -4       100 *     LENGTH OF LOWER LEG
VAR5         12       -22         5         6       WEIGHT
VAR6          8        -3         5       -10       BITROCHANTERIC DIAMETER
VAR7         -8         1        -6        10       CHEST GIRTH
VAR8        -10        19        -1        -7       CHEST WIDTH

VAR5      VAR6      VAR7      VAR8

VAR1         12         8        -8       -10       HEIGHT
VAR2        -22        -3         1        19       ARM SPAN
VAR3          5         5        -6        -1       LENGTH OF FOREARM
VAR4          6       -10        10        -7       LENGTH OF LOWER LEG
VAR5        100 *       1        16       -17       WEIGHT
VAR6          1       100 *      -6        -1       BITROCHANTERIC DIAMETER
VAR7         16        -6       100 *       2       CHEST GIRTH
VAR8        -17        -1         2       100 *     CHEST WIDTH
```
```NOTE: Printed values are multiplied by 100 and rounded to the nearest
integer.  Values greater than 0.368461 have been flagged by an '*'.```

```
Root Mean Square Off-diagonal Partials: Over-all = 0.11090890```

`                         VAR1      VAR2      VAR3      VAR4`
```                     0.135918  0.142418  0.093332  0.111822
```
`                         VAR5      VAR6      VAR7      VAR8`
```                     0.131547  0.056024  0.081374  0.106628
```

```                           Eight physical variables                          4
SEE PP 154-155 of Harman: Modern Factor Analysis, 2nd Ed.
```
```Initial Factor Method: Principal Factors
```
```                Plot of Factor Pattern for FACTOR1 and FACTOR2

FACTOR1
1

.9
B DA
C           .8
E
.7
F
.6          H
G
.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

VAR1    =A    VAR2    =B    VAR3    =C    VAR4    =D    VAR5    =E
VAR6    =F    VAR7    =G    VAR8    =H```

```                           Eight physical variables                          5
Output data set from Proc FACTOR
```
```-------------------------- Type of Observation=MEAN --------------------------
```
```    _
N
A        V        V        V        V        V        V        V        V
O M        A        A        A        A        A        A        A        A
B E        R        R        R        R        R        R        R        R
S _        1        2        3        4        5        6        7        8```
```  1     0.0000   0.0000   0.0000   0.0000   0.0000   0.0000   0.0000   0.0000

```
```-------------------------- Type of Observation=STD ---------------------------
```
```    _
N
A        V        V        V        V        V        V        V        V
O M        A        A        A        A        A        A        A        A
B E        R        R        R        R        R        R        R        R
S _        1        2        3        4        5        6        7        8```
```  2     1.0000   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000

```
```--------------------------- Type of Observation=N ----------------------------
```
```    _
N
A        V        V        V        V        V        V        V        V
O M        A        A        A        A        A        A        A        A
B E        R        R        R        R        R        R        R        R
S _        1        2        3        4        5        6        7        8```
`  3   305.0000 305.0000 305.0000 305.0000 305.0000 305.0000 305.0000 305.0000`

```                           Eight physical variables                          6
Output data set from Proc FACTOR
```
```-------------------------- Type of Observation=CORR --------------------------
```
`        OBS    _NAME_        VAR1        VAR2        VAR3        VAR4`
```          4     VAR1       1.0000      0.8460      0.8050      0.8590
5     VAR2       0.8460      1.0000      0.8810      0.8260
6     VAR3       0.8050      0.8810      1.0000      0.8010
7     VAR4       0.8590      0.8260      0.8010      1.0000
8     VAR5       0.4730      0.3760      0.3800      0.4360
9     VAR6       0.3980      0.3260      0.3190      0.3290
10     VAR7       0.3010      0.2770      0.2370      0.3270
11     VAR8       0.3820      0.4150      0.3450      0.3650
```
`        OBS        VAR5        VAR6        VAR7        VAR8`
```          4      0.4730      0.3980      0.3010      0.3820
5      0.3760      0.3260      0.2770      0.4150
6      0.3800      0.3190      0.2370      0.3450
7      0.4360      0.3290      0.3270      0.3650
8      1.0000      0.7620      0.7300      0.6290
9      0.7620      1.0000      0.5830      0.5770
10      0.7300      0.5830      1.0000      0.5390
11      0.6290      0.5770      0.5390      1.0000

```
```------------------------ Type of Observation=COMMUNAL ------------------------
```
```    _
N
A        V        V        V        V        V        V        V        V
O M        A        A        A        A        A        A        A        A
B E        R        R        R        R        R        R        R        R
S _        1        2        3        4        5        6        7        8```
``` 12     0.8443   0.8921   0.8260   0.7959   0.8733   0.6631   0.5526   0.5211

```
```------------------------- Type of Observation=PRIORS -------------------------
```
```    _
N
A        V        V        V        V        V        V        V        V
O M        A        A        A        A        A        A        A        A
B E        R        R        R        R        R        R        R        R
S _        1        2        3        4        5        6        7        8```
` 13     0.8540   0.8970   0.8330   0.7830   0.8700   0.6870   0.5210   0.5790`

```                           Eight physical variables                          7
Output data set from Proc FACTOR
```
```------------------------ Type of Observation=EIGENVAL ------------------------
```
```    _
N
A        V        V        V        V        V        V        V        V
O M        A        A        A        A        A        A        A        A
B E        R        R        R        R        R        R        R        R
S _        1        2        3        4        5        6        7        8```
``` 14     4.4558   1.5127   0.1305   0.0587   0.0335  -0.0314  -0.0440  -0.0917

```
```------------------------ Type of Observation=RESIDUAL ------------------------
```
`        OBS    _NAME_        VAR1        VAR2        VAR3        VAR4`
```         15     VAR1       0.1557     -0.0186     -0.0254      0.0395
16     VAR2      -0.0186      0.1079      0.0227     -0.0149
17     VAR3      -0.0254      0.0227      0.1740     -0.0070
18     VAR4       0.0395     -0.0149     -0.0070      0.2041
19     VAR5       0.0167     -0.0255      0.0073      0.0099
20     VAR6       0.0176     -0.0053      0.0123     -0.0253
21     VAR7      -0.0198      0.0029     -0.0155      0.0295
22     VAR8      -0.0276      0.0427     -0.0033     -0.0205
```
`        OBS        VAR5        VAR6        VAR7        VAR8`
```         15      0.0167      0.0176     -0.0198     -0.0276
16     -0.0255     -0.0053      0.0029      0.0427
17      0.0073      0.0123     -0.0155     -0.0033
18      0.0099     -0.0253      0.0295     -0.0205
19      0.1267      0.0013      0.0370     -0.0418
20      0.0013      0.3369     -0.0218     -0.0057
21      0.0370     -0.0218      0.4474      0.0107
22     -0.0418     -0.0057      0.0107      0.4789

```
```------------------------ Type of Observation=PATTERN -------------------------
```
`        OBS    _NAME_         VAR1        VAR2        VAR3        VAR4`
```         23    FACTOR1      0.8583      0.8492      0.8098      0.8255
24    FACTOR2     -0.3282     -0.4136     -0.4126     -0.3384
```
`        OBS        VAR5        VAR6        VAR7        VAR8`
```         23      0.7466      0.6371      0.5605      0.6192
24      0.5621      0.5071      0.4883      0.3711```

```                           Eight physical variables                          8
Varimax rotation:  Harman, page 309
```
```Rotation Method: Varimax

Orthogonal Transformation Matrix```
```                                       1         2

1      0.78298   0.62205
2     -0.62205   0.78298
```
`                            Rotated Factor Pattern`
```                      FACTOR1   FACTOR2

VAR1       0.87616   0.27693    HEIGHT
VAR2       0.92214   0.20441    ARM SPAN
VAR3       0.89067   0.18070    LENGTH OF FOREARM
VAR4       0.85680   0.24854    LENGTH OF LOWER LEG
VAR5       0.23489   0.90452    WEIGHT
VAR6       0.18341   0.79341    BITROCHANTERIC DIAMETER
VAR7       0.13515   0.73101    CHEST GIRTH
VAR8       0.25393   0.67572    CHEST WIDTH
```
`                      Variance explained by each factor`
```                                FACTOR1   FACTOR2
3.316972  2.651526
```
```
Final Communality Estimates: Total = 5.968498```

`                         VAR1      VAR2      VAR3      VAR4`
```                     0.844344  0.892132  0.825951  0.795884
```
`                         VAR5      VAR6      VAR7      VAR8`
```                     0.873330  0.663143  0.552635  0.521080
```

```                           Eight physical variables                          9
Varimax rotation:  Harman, page 309
```
```Rotation Method: Varimax
```
```                Plot of Factor Pattern for FACTOR1 and FACTOR2

FACTOR1
1

.9    CB A
D
.8

.7

.6

.5

.4

.3
H      E
.2                      F
G          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

VAR1    =A    VAR2    =B    VAR3    =C    VAR4    =D    VAR5    =E
VAR6    =F    VAR7    =G    VAR8    =H```

```                           Eight physical variables                         10
Minres / Unweighted least squares solution k=2
See page 205 of Harman: Modern Factor Analysis, 2nd Ed.
```
```Initial Factor Method: Unweighted Least Squares

Prior Communality Estimates: SMC```
```                         VAR1      VAR2      VAR3      VAR4
0.816201  0.849314  0.800578  0.788437

VAR5      VAR6      VAR7      VAR8
0.748831  0.604149  0.562191  0.477792
```
`      Preliminary Eigenvalues:  Total = 5.64749154  Average = 0.70593644`
```                                1           2           3           4
Eigenvalue        4.4098      1.4609      0.0702      0.0266
Difference        2.9489      1.3907      0.0435      0.0457
Proportion        0.7809      0.2587      0.0124      0.0047
Cumulative        0.7809      1.0395      1.0520      1.0567

5           6           7           8
Eigenvalue       -0.0190     -0.0731     -0.0994     -0.1285
Difference        0.0541      0.0263      0.0291
Proportion       -0.0034     -0.0129     -0.0176     -0.0228
Cumulative        1.0533      1.0404      1.0228      1.0000
```
`             2 factors will be retained by the NFACTOR criterion.`

`      Iter Criterion    Ridge   Change   Communalities`
```        1    0.01206    0.000  0.13802   0.83857 0.88778 0.82054 0.80797
0.88685 0.63969 0.58252 0.49298

2    0.01205    0.000  0.00247   0.83804 0.88879 0.82047 0.80768
0.88932 0.63993 0.58309 0.49196

3    0.01205    0.000  0.00004   0.83802 0.88882 0.82048 0.80765
0.88936 0.63992 0.58309 0.49193
```
```
Convergence criterion satisfied.```

```                Eigenvalues of the Reduced Correlation Matrix:
Total = 5.95928119  Average = 0.74491015```
```                                1           2           3           4
Eigenvalue        4.4490      1.5103      0.1017      0.0546
Difference        2.9388      1.4085      0.0471      0.0394
Proportion        0.7466      0.2534      0.0171      0.0092
Cumulative        0.7466      1.0000      1.0171      1.0262```

```                           Eight physical variables                         11
Minres / Unweighted least squares solution k=2
See page 205 of Harman: Modern Factor Analysis, 2nd Ed.
```
```Initial Factor Method: Unweighted Least Squares
```
```                                5           6           7           8
Eigenvalue        0.0153     -0.0370     -0.0603     -0.0744
Difference        0.0523      0.0233      0.0141
Proportion        0.0026     -0.0062     -0.0101     -0.0125
Cumulative        1.0288      1.0226      1.0125      1.0000
```
`                                Factor Pattern`
```                      FACTOR1   FACTOR2

VAR1       0.85602  -0.32442    HEIGHT
VAR2       0.84824  -0.41149    ARM SPAN
VAR3       0.80820  -0.40901    LENGTH OF FOREARM
VAR4       0.83091  -0.34241    LENGTH OF LOWER LEG
VAR5       0.75035   0.57125    WEIGHT
VAR6       0.63065   0.49214    BITROCHANTERIC DIAMETER
VAR7       0.56873   0.50954    CHEST GIRTH
VAR8       0.60740   0.35071    CHEST WIDTH
```
`                      Variance explained by each factor`
```                                FACTOR1   FACTOR2
4.449027  1.510254
```
```
Final Communality Estimates: Total = 5.959281```

`                         VAR1      VAR2      VAR3      VAR4`
```                     0.838018  0.888825  0.820485  0.807653
```
`                         VAR5      VAR6      VAR7      VAR8`
```                     0.889358  0.639921  0.583088  0.491933
```

```                           Eight physical variables                         12
See page 228 of Harman: Modern Factor Analysis, 2nd Ed.
```
```Initial Factor Method: Maximum Likelihood

Prior Communality Estimates: SMC```
```                         VAR1      VAR2      VAR3      VAR4
0.816201  0.849314  0.800578  0.788437

VAR5      VAR6      VAR7      VAR8
0.748831  0.604149  0.562191  0.477792
```
`       Preliminary Eigenvalues:  Total = 24.524864  Average = 3.065608`
```                                1           2           3           4
Eigenvalue       20.5305      4.8514      0.2991      0.0760
Difference       15.6791      4.5523      0.2231      0.1407
Proportion        0.8371      0.1978      0.0122      0.0031
Cumulative        0.8371      1.0349      1.0471      1.0502

5           6           7           8
Eigenvalue       -0.0648     -0.3015     -0.3619     -0.5038
Difference        0.2367      0.0603      0.1420
Proportion       -0.0026     -0.0123     -0.0148     -0.0205
Cumulative        1.0476      1.0353      1.0205      1.0000
```
`             3 factors will be retained by the NFACTOR criterion.`

`      Iter Criterion    Ridge   Change   Communalities`
```        1    0.08715    0.000  0.15623   0.86321 0.97085 0.79342 0.85463
0.90507 0.64169 0.57516 0.50662

2    0.07902    0.000  0.02915   0.86732 1.00000 0.79046 0.84992
0.90383 0.64309 0.58037 0.50028

3    0.07572    0.000  0.01565   0.87275 1.00000 0.80611 0.84367
0.90967 0.64113 0.58760 0.50903

4    0.07571    0.000  0.00190   0.87247 1.00000 0.80596 0.84370
0.90950 0.64080 0.58951 0.50901

5    0.07571    0.000  0.00015   0.87259 1.00000 0.80598 0.84355
0.90959 0.64072 0.58945 0.50902
```
```
Convergence criterion satisfied.```

```                           Eight physical variables                         13
See page 228 of Harman: Modern Factor Analysis, 2nd Ed.
```
```Initial Factor Method: Maximum Likelihood

Significance tests based on 305 observations:
```
```          Test of H0: No common factors.
vs HA: At least one common factor.

Chi-square = 2085.740   df = 28   Prob>chi**2 = 0.0001

Test of H0: 3 Factors are sufficient.
vs HA: More factors are needed.

Chi-square = 22.598   df = 7   Prob>chi**2 = 0.0020

Chi-square without Bartlett's correction = 23.014756958
Akaike's Information Criterion = 9.0147569578
Schwarz's Bayesian Criterion = -17.02742548
Tucker and Lewis's Reliability Coefficient = 0.9696786418
```
`                        Squared Canonical Correlations`
```                           FACTOR1   FACTOR2   FACTOR3
1.000000  0.924345  0.679242
```
```           Eigenvalues of the Weighted Reduced Correlation Matrix:
Total = 14.3354277  Average = 2.04791825```
```                                1           2           3           4
Eigenvalue         .         12.2178      2.1176      0.2469
Difference         .         10.1002      1.8707      0.1265
Proportion         .          0.8523      0.1477      0.0172
Cumulative         .          0.8523      1.0000      1.0172

5           6           7           8
Eigenvalue        0.1205      0.0024     -0.1356     -0.2341
Difference        0.1180      0.1381      0.0985
Proportion        0.0084      0.0002     -0.0095     -0.0163
Cumulative        1.0256      1.0258      1.0163      1.0000
```
`                                Factor Pattern`
```                 FACTOR1   FACTOR2   FACTOR3

VAR1       0.84600   0.18900  -0.34807    HEIGHT
VAR2       1.00000   0.00000   0.00000    ARM SPAN
VAR3       0.88100   0.05512  -0.16364    LENGTH OF FOREARM
VAR4       0.82600   0.15976  -0.36844    LENGTH OF LOWER LEG
VAR5       0.37600   0.87593   0.03117    WEIGHT
VAR6       0.32600   0.72507   0.09330    BITROCHANTERIC DIAMETER
VAR7       0.27700   0.70419   0.12983    CHEST GIRTH
VAR8       0.41500   0.54317   0.20432    CHEST WIDTH```

```                           Eight physical variables                         14
See page 228 of Harman: Modern Factor Analysis, 2nd Ed.
```
```Initial Factor Method: Maximum Likelihood

Variance explained by each factor```
```                                FACTOR1   FACTOR2   FACTOR3
Weighted   16.376025 12.217818  2.117611
Unweighted  3.670759  2.148187  0.351956
```
```               Final Communality Estimates and Variable Weights
Total Communality: Weighted = 30.711453   Unweighted = 6.170901```
```                               VAR1      VAR2      VAR3      VAR4
Communality   0.872591  1.000000  0.805975  0.843544
Weight        7.848724   .        5.154134  6.391671

VAR5      VAR6      VAR7      VAR8
Communality   0.909593  0.640714  0.589472  0.509012
Weight       11.061128  2.783326  2.435739  2.036731```