Output from phys8.sas	Source 0 Graphs

                           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