## Output from gcandis2.sas

Source
1 Graph

```                  Canonical Discriminant Analysis: Iris Data                 1
```
```                       Canonical Discriminant Analysis
```
```                 150 Observations        149 DF Total
4 Variables           147 DF Within Classes
3 Classes               2 DF Between Classes

```
```                           Class Level Information

SPECIES        Frequency        Weight     Proportion
```
```            Setosa                50       50.0000       0.333333
Versicolor            50       50.0000       0.333333
Virginica             50       50.0000       0.333333```

```                  Canonical Discriminant Analysis: Iris Data                 2
```
```                       Canonical Discriminant Analysis

Multivariate Statistics and F Approximations```

`                             S=2    M=0.5    N=71`

``` Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.02343863    199.145         8       288  0.0001
Pillai's Trace             1.19189883     53.466         8       290  0.0001
Hotelling-Lawley Trace    32.47732024    580.532         8       286  0.0001
Roy's Greatest Root       32.19192920   1166.957         4       145  0.0001

NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.```

```                  Canonical Discriminant Analysis: Iris Data                 3
```
```                       Canonical Discriminant Analysis

Canonical      Canonical     Standard     Canonical
Correlation    Correlation     Error      Correlation
```
```           1      0.984821       0.984508     0.002468      0.969872
2      0.471197       0.461445     0.063734      0.222027
```
```                                Eigenvalues of INV(E)*H
= CanRsq/(1-CanRsq)

Eigenvalue    Difference    Proportion    Cumulative
```
```            1      32.1919       31.9065       0.9912        0.9912
2       0.2854         .           0.0088        1.0000
```
```                     Test of H0: The canonical correlations in the
current row and all that follow are zero

Likelihood
Ratio      Approx F      Num DF      Den DF    Pr > F
```
```          1    0.02343863    199.1453           8         288    0.0001
2    0.77797337     13.7939           3         145    0.0001
```
```
Total Canonical Structure

CAN1              CAN2
```
```    SEPALLEN          0.791888          0.217593      Sepal length in mm.
SEPALWID         -0.530759          0.757989      Sepal width  in mm.
PETALLEN          0.984951          0.046037      Petal length in mm.
PETALWID          0.972812          0.222902      Petal width  in mm.
```
```
Between Canonical Structure

CAN1              CAN2
```
```    SEPALLEN          0.991468          0.130348      Sepal length in mm.
SEPALWID         -0.825658          0.564171      Sepal width  in mm.
PETALLEN          0.999750          0.022358      Petal length in mm.
PETALWID          0.994044          0.108977      Petal width  in mm.```

```                  Canonical Discriminant Analysis: Iris Data                 4
```
```                       Canonical Discriminant Analysis

Pooled Within Canonical Structure

CAN1              CAN2
```
```    SEPALLEN          0.222596          0.310812      Sepal length in mm.
SEPALWID         -0.119012          0.863681      Sepal width  in mm.
PETALLEN          0.706065          0.167701      Petal length in mm.
PETALWID          0.633178          0.737242      Petal width  in mm.
```
```
Total-Sample Standardized Canonical Coefficients

CAN1              CAN2
```
```    SEPALLEN      -0.686779533       0.019958173      Sepal length in mm.
SEPALWID      -0.668825075       0.943441829      Sepal width  in mm.
PETALLEN       3.885795047      -1.645118866      Petal length in mm.
PETALWID       2.142238715       2.164135931      Petal width  in mm.
```
```
Pooled Within-Class Standardized Canonical Coefficients

CAN1              CAN2
```
```    SEPALLEN      -.4269548486      0.0124075316      Sepal length in mm.
SEPALWID      -.5212416758      0.7352613085      Sepal width  in mm.
PETALLEN      0.9472572487      -.4010378190      Petal length in mm.
PETALWID      0.5751607719      0.5810398645      Petal width  in mm.
```
```
Raw Canonical Coefficients

CAN1              CAN2
```
```    SEPALLEN      -.0829377642      0.0024102149      Sepal length in mm.
SEPALWID      -.1534473068      0.2164521235      Sepal width  in mm.
PETALLEN      0.2201211656      -.0931921210      Petal length in mm.
PETALWID      0.2810460309      0.2839187853      Petal width  in mm.
```
```
Class Means on Canonical Variables

SPECIES                 CAN1              CAN2
```
```                Setosa          -7.607599927       0.215133017
Versicolor       1.825049490      -0.727899622
Virginica        5.782550437       0.512766605```

```                  Canonical Discriminant Analysis: Iris Data                 5
```
```---------------------------------- SPEC_NO=1 ---------------------------------

```
`       Variable          Mean       Std Dev       Minimum       Maximum`
```       ----------------------------------------------------------------
CAN1        -7.6075999     0.8474608    -9.8498430    -5.6618807
CAN2         0.2151330     0.9137836    -1.9343552     2.7375965
----------------------------------------------------------------```
```---------------------------------- SPEC_NO=2 ---------------------------------

```
`       Variable          Mean       Std Dev       Minimum       Maximum`
```       ----------------------------------------------------------------
CAN1         1.8250495     1.0361701    -0.4759738     4.4984664
CAN2        -0.7278996     0.8734757    -2.6434099     1.1915677
----------------------------------------------------------------```
```---------------------------------- SPEC_NO=3 ---------------------------------

```
`       Variable          Mean       Std Dev       Minimum       Maximum`
```       ----------------------------------------------------------------
CAN1         5.7825504     1.0991641     3.8151597     9.1714749
CAN2         0.5127666     1.1840776    -2.1557372     2.7175896
----------------------------------------------------------------```

```                  Canonical Discriminant Analysis: Iris Data                 6
```
`OBS  SPECIES     _TYPE_     _NAME_    SEPALLEN  SEPALWID   PETALLEN   PETALWID`
```  1              N                      150.00    150.00     150.00     150.00
2  Setosa      N                       50.00     50.00      50.00      50.00
3  Versicolor  N                       50.00     50.00      50.00      50.00
4  Virginica   N                       50.00     50.00      50.00      50.00
5              MEAN                    58.43     30.57      37.58      11.99
6  Setosa      MEAN                    50.06     34.28      14.62       2.46
7  Versicolor  MEAN                    59.36     27.70      42.60      13.26
8  Virginica   MEAN                    65.88     29.74      55.52      20.26
9  Setosa      CSSCP     SEPALLEN     608.82    486.16      80.14      50.62
10  Setosa      CSSCP     SEPALWID     486.16    704.08      57.32      45.56
11  Setosa      CSSCP     PETALLEN      80.14     57.32     147.78      29.74
12  Setosa      CSSCP     PETALWID      50.62     45.56      29.74      54.42
13  Versicolor  CSSCP     SEPALLEN    1305.52    417.40     896.20     273.32
14  Versicolor  CSSCP     SEPALWID     417.40    482.50     405.00     201.90
15  Versicolor  CSSCP     PETALLEN     896.20    405.00    1082.00     358.20
16  Versicolor  CSSCP     PETALWID     273.32    201.90     358.20     191.62
17  Virginica   CSSCP     SEPALLEN    1981.28    459.44    1486.12     240.56
18  Virginica   CSSCP     SEPALWID     459.44    509.62     349.76     233.38
19  Virginica   CSSCP     PETALLEN    1486.12    349.76    1492.48     239.24
20  Virginica   CSSCP     PETALWID     240.56    233.38     239.24     369.62
21              PSSCP     SEPALLEN    3895.62   1363.00    2462.46     564.50
22              PSSCP     SEPALWID    1363.00   1696.20     812.08     480.84
23              PSSCP     PETALLEN    2462.46    812.08    2722.26     627.18
24              PSSCP     PETALWID     564.50    480.84     627.18     615.66
25              BSSCP     SEPALLEN    6321.21  -1995.27   16524.84    7127.93
26              BSSCP     SEPALWID   -1995.27   1134.49   -5723.96   -2293.27
27              BSSCP     PETALLEN   16524.84  -5723.96   43710.28   18677.40
28              BSSCP     PETALWID    7127.93  -2293.27   18677.40    8041.33
29              CSSCP     SEPALLEN   10216.83   -632.27   18987.30    7692.43
30              CSSCP     SEPALWID    -632.27   2830.69   -4911.88   -1812.43
31              CSSCP     PETALLEN   18987.30  -4911.88   46432.54   19304.58
32              CSSCP     PETALWID    7692.43  -1812.43   19304.58    8656.99
33              RSQUARED                 0.62      0.40       0.94       0.93
34  Setosa      COV       SEPALLEN      12.42      9.92       1.64       1.03
35  Setosa      COV       SEPALWID       9.92     14.37       1.17       0.93
36  Setosa      COV       PETALLEN       1.64      1.17       3.02       0.61
37  Setosa      COV       PETALWID       1.03      0.93       0.61       1.11
38  Versicolor  COV       SEPALLEN      26.64      8.52      18.29       5.58
39  Versicolor  COV       SEPALWID       8.52      9.85       8.27       4.12
40  Versicolor  COV       PETALLEN      18.29      8.27      22.08       7.31
41  Versicolor  COV       PETALWID       5.58      4.12       7.31       3.91
42  Virginica   COV       SEPALLEN      40.43      9.38      30.33       4.91
43  Virginica   COV       SEPALWID       9.38     10.40       7.14       4.76
44  Virginica   COV       PETALLEN      30.33      7.14      30.46       4.88
45  Virginica   COV       PETALWID       4.91      4.76       4.88       7.54
46              PCOV      SEPALLEN      26.50      9.27      16.75       3.84
47              PCOV      SEPALWID       9.27     11.54       5.52       3.27
48              PCOV      PETALLEN      16.75      5.52      18.52       4.27
49              PCOV      PETALWID       3.84      3.27       4.27       4.19
50              BCOV      SEPALLEN      63.21    -19.95     165.25      71.28
51              BCOV      SEPALWID     -19.95     11.34     -57.24     -22.93```

```                  Canonical Discriminant Analysis: Iris Data                 7
```
` OBS  SPECIES     _TYPE_    _NAME_    SEPALLEN  SEPALWID  PETALLEN  PETALWID`
```  52              BCOV      PETALLEN   165.248  -57.2396   437.103   186.774
53              BCOV      PETALWID    71.279  -22.9327   186.774    80.413
54              COV       SEPALLEN    68.569   -4.2434   127.432    51.627
55              COV       SEPALWID    -4.243   18.9979   -32.966   -12.164
56              COV       PETALLEN   127.432  -32.9656   311.628   129.561
57              COV       PETALWID    51.627  -12.1639   129.561    58.101
58  Setosa      STD                    3.525    3.7906     1.737     1.054
59  Versicolor  STD                    5.162    3.1380     4.699     1.978
60  Virginica   STD                    6.359    3.2250     5.519     2.747
61              PSTD                   5.148    3.3969     4.303     2.047
62              BSTD                   7.951    3.3682    20.907     8.967
63              STD                    8.281    4.3587    17.653     7.622
64  Setosa      CORR      SEPALLEN     1.000    0.7425     0.267     0.278
65  Setosa      CORR      SEPALWID     0.743    1.0000     0.178     0.233
66  Setosa      CORR      PETALLEN     0.267    0.1777     1.000     0.332
67  Setosa      CORR      PETALWID     0.278    0.2328     0.332     1.000
68  Versicolor  CORR      SEPALLEN     1.000    0.5259     0.754     0.546
69  Versicolor  CORR      SEPALWID     0.526    1.0000     0.561     0.664
70  Versicolor  CORR      PETALLEN     0.754    0.5605     1.000     0.787
71  Versicolor  CORR      PETALWID     0.546    0.6640     0.787     1.000
72  Virginica   CORR      SEPALLEN     1.000    0.4572     0.864     0.281
73  Virginica   CORR      SEPALWID     0.457    1.0000     0.401     0.538
74  Virginica   CORR      PETALLEN     0.864    0.4010     1.000     0.322
75  Virginica   CORR      PETALWID     0.281    0.5377     0.322     1.000
76              PCORR     SEPALLEN     1.000    0.5302     0.756     0.365
77              PCORR     SEPALWID     0.530    1.0000     0.378     0.471
78              PCORR     PETALLEN     0.756    0.3779     1.000     0.484
79              PCORR     PETALWID     0.365    0.4705     0.484     1.000
80              BCORR     SEPALLEN     1.000   -0.7451     0.994     1.000
81              BCORR     SEPALWID    -0.745    1.0000    -0.813    -0.759
82              BCORR     PETALLEN     0.994   -0.8128     1.000     0.996
83              BCORR     PETALWID     1.000   -0.7593     0.996     1.000
84              CORR      SEPALLEN     1.000   -0.1176     0.872     0.818
85              CORR      SEPALWID    -0.118    1.0000    -0.428    -0.366
86              CORR      PETALLEN     0.872   -0.4284     1.000     0.963
87              CORR      PETALWID     0.818   -0.3661     0.963     1.000
88  Setosa      STDMEAN               -1.011    0.8504    -1.301    -1.251
89  Versicolor  STDMEAN                0.112   -0.6592     0.284     0.166
90  Virginica   STDMEAN                0.899   -0.1912     1.016     1.085
91  Setosa      PSTDMEAN              -1.627    1.0912    -5.335    -4.658
92  Versicolor  PSTDMEAN               0.180   -0.8459     1.167     0.619
93  Virginica   PSTDMEAN               1.447   -0.2453     4.169     4.039
94              CANCORR   CAN1         0.985    0.9848     0.985     0.985
95              CANCORR   CAN2         0.471    0.4712     0.471     0.471
96              STRUCTUR  CAN1         0.792   -0.5308     0.985     0.973
97              STRUCTUR  CAN2         0.218    0.7580     0.046     0.223
98              BSTRUCT   CAN1         0.991   -0.8257     1.000     0.994
99              BSTRUCT   CAN2         0.130    0.5642     0.022     0.109
100              PSTRUCT   CAN1         0.223   -0.1190     0.706     0.633
101              PSTRUCT   CAN2         0.311    0.8637     0.168     0.737
102              SCORE     CAN1        -0.687   -0.6688     3.886     2.142```

```                  Canonical Discriminant Analysis: Iris Data                 8
```
`  OBS  SPECIES     _TYPE_    _NAME_  SEPALLEN  SEPALWID  PETALLEN  PETALWID`
```  103              SCORE      CAN2    0.01996   0.94344  -1.64512   2.16414
104              PSCORE     CAN1   -0.42695  -0.52124   0.94726   0.57516
105              PSCORE     CAN2    0.01241   0.73526  -0.40104   0.58104
106              RAWSCORE   CAN1   -0.08294  -0.15345   0.22012   0.28105
107              RAWSCORE   CAN2    0.00241   0.21645  -0.09319   0.28392
108  Setosa      CANMEAN    CAN1   -7.60760  -7.60760  -7.60760  -7.60760
109  Setosa      CANMEAN    CAN2    0.21513   0.21513   0.21513   0.21513
110  Versicolor  CANMEAN    CAN1    1.82505   1.82505   1.82505   1.82505
111  Versicolor  CANMEAN    CAN2   -0.72790  -0.72790  -0.72790  -0.72790
112  Virginica   CANMEAN    CAN1    5.78255   5.78255   5.78255   5.78255
113  Virginica   CANMEAN    CAN2    0.51277   0.51277   0.51277   0.51277```

```                  Canonical Discriminant Analysis: Iris Data                 9
```
```---------------------------------- SPEC_NO=1 ---------------------------------

```
`    Variable    N          Mean       Std Dev       Minimum       Maximum`
```    ---------------------------------------------------------------------
CAN1       50    -7.6075999     0.8474608    -9.8498430    -5.6618807
CAN2       50     0.2151330     0.9137836    -1.9343552     2.7375965
---------------------------------------------------------------------```
```---------------------------------- SPEC_NO=2 ---------------------------------

```
`    Variable    N          Mean       Std Dev       Minimum       Maximum`
```    ---------------------------------------------------------------------
CAN1       50     1.8250495     1.0361701    -0.4759738     4.4984664
CAN2       50    -0.7278996     0.8734757    -2.6434099     1.1915677
---------------------------------------------------------------------```
```---------------------------------- SPEC_NO=3 ---------------------------------

```
`    Variable    N          Mean       Std Dev       Minimum       Maximum`
```    ---------------------------------------------------------------------
CAN1       50     5.7825504     1.0991641     3.8151597     9.1714749
CAN2       50     0.5127666     1.1840776    -2.1557372     2.7175896
---------------------------------------------------------------------```

```                  Canonical Discriminant Analysis: Iris Data                10
Multiple & Canonical Vector Regression
```
```           Univariate Multiple Regression Statistics for Predicting
the VARIABLES from the CANONICALS

Standardized Regression Coefficients
```
```                   SEPALLEN      SEPALWID      PETALLEN      PETALWID

CAN1        0.7919       -0.5308        0.9850        0.9728
CAN2        0.2176        0.7580        0.0460        0.2229
```
```
Raw Regression Coefficients
```
```               SEPALLEN          SEPALWID          PETALLEN          PETALWID

CAN1       1.145900392      -0.404267515       3.038442708       1.295798783
CAN2       1.600025916       2.933818135       0.721676861       1.508766056```

```                  Canonical Discriminant Analysis: Iris Data                11
Multiple & Canonical Vector Regression
```
```                        Canonical Correlation Analysis

Canonical      Canonical     Standard     Canonical
Correlation    Correlation     Error      Correlation
```
```           1      1.000000        .           0.000000      1.000000
2      1.000000        .           0.000000      1.000000
```
```                                Eigenvalues of INV(E)*H
= CanRsq/(1-CanRsq)

Eigenvalue    Difference    Proportion    Cumulative
```
```            1        .             .            .             .
2        .             .            .             .
```
```                     Test of H0: The canonical correlations in the
current row and all that follow are zero

Likelihood
Ratio      Approx F      Num DF      Den DF    Pr > F
```
```          1    0.00000000       .               8         288    0.0001
2    0.00000000       .               3         145    0.0001

```
`                 Multivariate Statistics and F Approximations`

`                             S=2    M=0.5    N=71`

``` Statistic                     Value          F      Num DF    Den DF  Pr > F
```
``` Wilks' Lambda              0.00000000      .             8       288  0.0001
Pillai's Trace             2.00000000      .             8       290  0.0001
Hotelling-Lawley Trace      .              .             8       286  0.0001
Roy's Greatest Root         .              .             4       145  0.0001

NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.```

```                  Canonical Discriminant Analysis: Iris Data                12
Multiple & Canonical Vector Regression
```
```                        Canonical Correlation Analysis

Raw Canonical Coefficients for the CANONICALS
```
```                                       C1                C2

CAN1      0.1165150204      -0.130238082
CAN2      0.6618149985      0.5920801876
```
```
Raw Canonical Coefficients for the VARIABLES
```
```                            W1                W2

SEPALLEN      -0.008068379      0.0122286958      Sepal length in mm.
SEPALWID      0.1253723457      0.1481416968      Sepal width  in mm.
PETALLEN      -0.036028521      -0.083845367      Petal length in mm.
PETALWID      0.2206477945      0.1314997916      Petal width  in mm.
```
```
Standardized Canonical Coefficients for the CANONICALS
```
```                                       C1            C2

CAN1        0.6668       -0.7453
CAN2        0.7453        0.6668
```
```
Standardized Canonical Coefficients for the VARIABLES
```
```                            W1            W2

SEPALLEN       -0.0668        0.1013      Sepal length in mm.
SEPALWID        0.5465        0.6457      Sepal width  in mm.
PETALLEN       -0.6360       -1.4801      Petal length in mm.
PETALWID        1.6819        1.0023      Petal width  in mm.```

```                  Canonical Discriminant Analysis: Iris Data                13
Multiple & Canonical Vector Regression
```
```                             Canonical Structure

Correlations Between the CANONICALS and Their Canonical Variables
```
```                                       C1            C2

CAN1        0.6668       -0.7453
CAN2        0.7453        0.6668
```
```
Correlations Between the VARIABLES and Their Canonical Variables
```
```                            W1            W2

SEPALLEN        0.6902       -0.4451      Sepal length in mm.
SEPALWID        0.2110        0.9010      Sepal width  in mm.
PETALLEN        0.6910       -0.7034      Petal length in mm.
PETALWID        0.8147       -0.5764      Petal width  in mm.
```
```
Correlations Between the CANONICALS and
the Canonical Variables of the VARIABLES
```
```                                       W1            W2

CAN1        0.6668       -0.7453
CAN2        0.7453        0.6668
```
```
Correlations Between the VARIABLES and the
Canonical Variables of the CANONICALS
```
```                            C1            C2

SEPALLEN        0.6902       -0.4451      Sepal length in mm.
SEPALWID        0.2110        0.9010      Sepal width  in mm.
PETALLEN        0.6910       -0.7034      Petal length in mm.
PETALWID        0.8147       -0.5764      Petal width  in mm.```

```                  Canonical Discriminant Analysis: Iris Data                14
Multiple & Canonical Vector Regression
```
`  OBS _TYPE_   _NAME_       CAN1    CAN2 SEPALLEN SEPALWID PETALLEN PETALWID`
```    1 MEAN                 0.000   0.000   58.433   30.573   37.580   11.993
2 STD                  5.722   1.126    8.281    4.359   17.653    7.622
3 N                  150.000 150.000  150.000  150.000  150.000  150.000
4 CORR     CAN1        1.000   0.000    0.792   -0.531    0.985    0.973
5 CORR     CAN2        0.000   1.000    0.218    0.758    0.046    0.223
6 CORR     SEPALLEN    0.792   0.218    1.000   -0.118    0.872    0.818
7 CORR     SEPALWID   -0.531   0.758   -0.118    1.000   -0.428   -0.366
8 CORR     PETALLEN    0.985   0.046    0.872   -0.428    1.000    0.963
9 CORR     PETALWID    0.973   0.223    0.818   -0.366    0.963    1.000
10 STB      SEPALLEN    0.792   0.218     .        .        .        .
11 STB      SEPALWID   -0.531   0.758     .        .        .        .
12 STB      PETALLEN    0.985   0.046     .        .        .        .
13 STB      PETALWID    0.973   0.223     .        .        .        .
14 B        SEPALLEN    1.146   1.600     .        .        .        .
15 B        SEPALWID   -0.404   2.934     .        .        .        .
16 B        PETALLEN    3.038   0.722     .        .        .        .
17 B        PETALWID    1.296   1.509     .        .        .        .
18 CANCORR              1.000   1.000     .        .        .        .
19 SCORE    C1          0.667   0.745    0.000    0.000    0.000    0.000
20 SCORE    C2         -0.745   0.667    0.000    0.000    0.000    0.000
21 SCORE    W1          0.000   0.000   -0.067    0.546   -0.636    1.682
22 SCORE    W2          0.000   0.000    0.101    0.646   -1.480    1.002
23 RAWSCORE C1          0.117   0.662    0.000    0.000    0.000    0.000
24 RAWSCORE C2         -0.130   0.592    0.000    0.000    0.000    0.000
25 RAWSCORE W1          0.000   0.000   -0.008    0.125   -0.036    0.221
26 RAWSCORE W2          0.000   0.000    0.012    0.148   -0.084    0.131
27 STRUCTUR C1          0.667   0.745    0.690    0.211    0.691    0.815
28 STRUCTUR C2         -0.745   0.667   -0.445    0.901   -0.703   -0.576
29 STRUCTUR W1          0.667   0.745    0.690    0.211    0.691    0.815
30 STRUCTUR W2         -0.745   0.667   -0.445    0.901   -0.703   -0.576```

```                  Canonical Discriminant Analysis: Iris Data                15
Multiple & Canonical Vector Regression
```
`        OBS     _NAME_           _LABEL_            CAN1        CAN2`
```         1     SEPALLEN    Sepal length in mm.     0.79189    0.21759
2     SEPALWID    Sepal width  in mm.    -0.53076    0.75799
3     PETALLEN    Petal length in mm.     0.98495    0.04604
4     PETALWID    Petal width  in mm.     0.97281    0.22290```

`                                                                            16`

### Graphic output from gcandis2.sas

 PLOT OF CAN2 * CAN1 = SPECIES [ GPLOT 09/27/99 ]