Output from stepiris.sas	Source 0 Graphs

                  Iris data: Stepwise discriminant analysis                  1

                        Stepwise Discriminant Analysis

            150 Observations          4 Variable(s) in the Analysis
              3 Class Levels          0 Variable(s) will be included

             The Method for Selecting Variables will be: STEPWISE

             Significance Level to Enter =  0.1500
             Significance Level to Stay  =  0.1500

                           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

                  Iris data: Stepwise discriminant analysis                  2

                        Stepwise Discriminant Analysis

Stepwise Selection:  Step 1

                      Statistics for Entry, DF = 2, 147

Variable       R**2         F      Prob > F   Tolerance   Label

SEPALLEN     0.6187      119.265     0.0001      1.0000   Sepal length in mm.
SEPALWID     0.4008       49.160     0.0001      1.0000   Sepal width  in mm.
PETALLEN     0.9414     1180.161     0.0001      1.0000   Petal length in mm.
PETALWID     0.9289      960.007     0.0001      1.0000   Petal width  in mm.

                      Variable PETALLEN will be entered

                 The following variable(s) have been entered:
                                   PETALLEN

                           Multivariate Statistics

 Wilks' Lambda  = 0.05862828    F( 2, 147) = 1180.161      Prob > F = 0.0001
 Pillai's Trace =   0.941372    F( 2, 147) = 1180.161      Prob > F = 0.0001

              Average Squared Canonical Correlation = 0.47068586

------------------------------------------------------------------------------

Stepwise Selection:  Step 2

                    Statistics for Removal,  DF = 2, 147

  Variable         R**2           F        Prob > F     Label

  PETALLEN       0.9414       1180.161       0.0001     Petal length in mm.


                         No variables can be removed

                  Iris data: Stepwise discriminant analysis                  3

                        Stepwise Discriminant Analysis

Stepwise Selection:  Step 2

                      Statistics for Entry, DF = 2, 146

            Partial
Variable       R**2         F      Prob > F   Tolerance   Label

SEPALLEN     0.3198       34.323     0.0001      0.2400   Sepal length in mm.
SEPALWID     0.3709       43.035     0.0001      0.8164   Sepal width  in mm.
PETALWID     0.2533       24.766     0.0001      0.0729   Petal width  in mm.

                      Variable SEPALWID will be entered

                 The following variable(s) have been entered:
                              SEPALWID PETALLEN

                           Multivariate Statistics

 Wilks' Lambda  = 0.03688411    F( 4, 292) =  307.105      Prob > F = 0.0001
 Pillai's Trace =   1.119908    F( 4, 294) =   93.528      Prob > F = 0.0001

              Average Squared Canonical Correlation = 0.55995394

------------------------------------------------------------------------------

Stepwise Selection:  Step 3

                    Statistics for Removal,  DF = 2, 146

                Partial
  Variable         R**2           F        Prob > F     Label

  SEPALWID       0.3709         43.035       0.0001     Sepal width  in mm.
  PETALLEN       0.9384       1112.954       0.0001     Petal length in mm.


                         No variables can be removed

                  Iris data: Stepwise discriminant analysis                  4

                        Stepwise Discriminant Analysis

Stepwise Selection:  Step 3

                      Statistics for Entry, DF = 2, 145

            Partial
Variable       R**2         F      Prob > F   Tolerance   Label

SEPALLEN     0.1447       12.268     0.0001      0.1323   Sepal length in mm.
PETALWID     0.3229       34.569     0.0001      0.0662   Petal width  in mm.

                      Variable PETALWID will be entered

                 The following variable(s) have been entered:
                          SEPALWID PETALLEN PETALWID

                           Multivariate Statistics

 Wilks' Lambda  = 0.02497554    F( 6, 290) =  257.503      Prob > F = 0.0001
 Pillai's Trace =   1.189914    F( 6, 292) =   71.485      Prob > F = 0.0001

              Average Squared Canonical Correlation = 0.59495691

------------------------------------------------------------------------------

Stepwise Selection:  Step 4

                    Statistics for Removal,  DF = 2, 145

                Partial
  Variable         R**2           F        Prob > F     Label

  SEPALWID       0.4295         54.577       0.0001     Sepal width  in mm.
  PETALLEN       0.3482         38.724       0.0001     Petal length in mm.
  PETALWID       0.3229         34.569       0.0001     Petal width  in mm.


                         No variables can be removed

                  Iris data: Stepwise discriminant analysis                  5

                        Stepwise Discriminant Analysis

Stepwise Selection:  Step 4

                      Statistics for Entry, DF = 2, 144

            Partial
Variable       R**2         F      Prob > F   Tolerance   Label

SEPALLEN     0.0615        4.721     0.0103      0.0320   Sepal length in mm.

                      Variable SEPALLEN will be entered

                       All variables have been entered

                           Multivariate Statistics

 Wilks' Lambda  = 0.02343863    F( 8, 288) =  199.145      Prob > F = 0.0001
 Pillai's Trace =   1.191899    F( 8, 290) =   53.466      Prob > F = 0.0001

              Average Squared Canonical Correlation = 0.59594941

------------------------------------------------------------------------------

Stepwise Selection:  Step 5

                    Statistics for Removal,  DF = 2, 144

                Partial
  Variable         R**2           F        Prob > F     Label

  SEPALLEN       0.0615          4.721       0.0103     Sepal length in mm.
  SEPALWID       0.2335         21.936       0.0001     Sepal width  in mm.
  PETALLEN       0.3308         35.590       0.0001     Petal length in mm.
  PETALWID       0.2570         24.904       0.0001     Petal width  in mm.


                         No variables can be removed

No further steps are possible

                  Iris data: Stepwise discriminant analysis                  6

                        Stepwise Discriminant Analysis

Stepwise Selection:  Summary

             Variable        Number  Partial        F        Prob >
  Step  Entered   Removed      In       R**2    Statistic      F
 ------------------------------------------------------------------

     1  PETALLEN                  1   0.9414     1180.161    0.0001
     2  SEPALWID                  2   0.3709       43.035    0.0001
     3  PETALWID                  3   0.3229       34.569    0.0001
     4  SEPALLEN                  4   0.0615        4.721    0.0103

             Variable        Number      Wilks'     Prob <
  Step  Entered   Removed      In        Lambda     Lambda
 ---------------------------------------------------------

     1  PETALLEN                  1  0.05862828     0.0001
     2  SEPALWID                  2  0.03688411     0.0001
     3  PETALWID                  3  0.02497554     0.0001
     4  SEPALLEN                  4  0.02343863     0.0001

                                         Average
                                         Squared
             Variable        Number    Canonical  Prob >
  Step  Entered   Removed      In    Correlation    ASCC  Label
 ----------------------------------------------------------------------------

     1  PETALLEN                  1   0.47068586  0.0001  Petal length in mm.
     2  SEPALWID                  2   0.55995394  0.0001  Sepal width  in mm.
     3  PETALWID                  3   0.59495691  0.0001  Petal width  in mm.
     4  SEPALLEN                  4   0.59594941  0.0001  Sepal length in mm.

                  Iris data: Stepwise discriminant analysis                  7
                             Size and elongation

           Plot of PETALLEN*PETALWID.  Symbol is value of SPEC_NO.

             |
             |
          70 +                                                3
             |                                          3   3
             |                                            3
             |                                      3   3
             |                                        3       3   3
        P 60 +                                      3     3   3   3
        e    |                                  3   3     3 3 3   3
        t    |                              3       3     3 3   3
        a    |                                        3   3   3
        l    |                                3 2   3 3 3     3 3
          50 +                                3   2 3 3 3
        l    |                          2   2 2 2   2
        e    |                            2 2 2 2 3
        n    |                          2 2 2
        g    |                      2   2 2   2
        t 40 +                      2 2 2 2 2
        h    |                      2 2
             |                      2     2
        i    |                      2
        n    |
          30 +                        2
        m    |
        m    |
        .    |
             |
          20 +      1   1
             |      1 1 1 1
             |    1 1 1 1   1
             |    1 1 1 1
             |    1 1
          10 +      1
             |
             ---+---------+---------+---------+---------+---------+--
                0         5        10        15        20        25

                                Petal width  in mm.

NOTE: 65 obs hidden.

                  Iris data: Stepwise discriminant analysis                  8
                             Size and elongation

              Plot of SIZE*ELONG.  Symbol is value of SPEC_NO.

SIZE |
   8 +
     |
     |
     |
     |                 3
     |         3 3 3   33
     |       3 3333333   33
   7 +        3   33     333
     |           33333 33   3
     |             23 2 2      3
     |             3 2222232
     |               2  2222
     |               2 222222 2
     |               2   22
   6 +                     2   22
     |              2    2 2 2
     |
     |
     |
     |
     |
   5 +
     |
     |
     |             1
     |                    1
     |                           1  1
     |                       1 1
   4 +                   1               1
     |                               1
     |                           1 1
     |                                              1  1
     |                                          1 1
     |                                      1 1
     |                                    1
   3 +                               1
     |
     |                                                              1
     |                                                            1
     |                                                     1
     |
     |
   2 +
     -+-------------+-------------+-------------+-------------+-------------+-
     0.5           1.0           1.5           2.0           2.5           3.0

                                       ELONG

NOTE: 62 obs hidden.

                  Iris data: Stepwise discriminant analysis                  9
                             Size and elongation

                        Stepwise Discriminant Analysis

            150 Observations          6 Variable(s) in the Analysis
              3 Class Levels          2 Variable(s) will be included

             The Method for Selecting Variables will be: STEPWISE

             Significance Level to Enter =  0.1500
             Significance Level to Stay  =  0.1500

                           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

                  Iris data: Stepwise discriminant analysis                 10
                             Size and elongation

                        Stepwise Discriminant Analysis

Stepwise Selection:  Step 0

                 The following variable(s) have been entered:
                              SIZE     ELONG

                           Multivariate Statistics

 Wilks' Lambda  = 0.03192219    F( 4, 292) =  335.579      Prob > F = 0.0001
 Pillai's Trace =   0.968321    F( 4, 294) =   68.986      Prob > F = 0.0001

              Average Squared Canonical Correlation = 0.48416035

                  Iris data: Stepwise discriminant analysis                 11
                             Size and elongation

                        Stepwise Discriminant Analysis

Stepwise Selection:  Step 1

                      Statistics for Entry, DF = 2, 145

            Partial
Variable       R**2         F      Prob > F   Tolerance   Label

PETALLEN     0.5627       93.295     0.0001      0.0139   Petal length in mm.
PETALWID     0.5415       85.636     0.0001      0.0580   Petal width  in mm.
SEPALLEN     0.2844       28.812     0.0001      0.1022   Sepal length in mm.
SEPALWID     0.3463       38.415     0.0001      0.1710   Sepal width  in mm.

                      Variable PETALLEN will be entered

                 The following variable(s) have been entered:
                          SIZE     ELONG    PETALLEN

                           Multivariate Statistics

 Wilks' Lambda  = 0.01395913    F( 6, 290) =  360.756      Prob > F = 0.0001
 Pillai's Trace =   1.505327    F( 6, 292) =  148.096      Prob > F = 0.0001

              Average Squared Canonical Correlation = 0.75266346

------------------------------------------------------------------------------

Stepwise Selection:  Step 2

                    Statistics for Removal,  DF = 2, 145

                Partial
  Variable         R**2           F        Prob > F     Label

  PETALLEN       0.5627         93.295       0.0001     Petal length in mm.


                         No variables can be removed

                  Iris data: Stepwise discriminant analysis                 12
                             Size and elongation

                        Stepwise Discriminant Analysis

Stepwise Selection:  Step 2

                      Statistics for Entry, DF = 2, 144

            Partial
Variable       R**2         F      Prob > F   Tolerance   Label

PETALWID     0.2417       22.955     0.0001      0.0125   Petal width  in mm.
SEPALLEN     0.1971       17.676     0.0001      0.0119   Sepal length in mm.
SEPALWID     0.2296       21.460     0.0001      0.0107   Sepal width  in mm.

                      Variable PETALWID will be entered

                 The following variable(s) have been entered:
                     SIZE     ELONG    PETALLEN PETALWID

                           Multivariate Statistics

 Wilks' Lambda  = 0.01058458    F( 8, 288) =  313.917      Prob > F = 0.0001
 Pillai's Trace =   1.611595    F( 8, 290) =  150.411      Prob > F = 0.0001

              Average Squared Canonical Correlation = 0.80579746

------------------------------------------------------------------------------

Stepwise Selection:  Step 3

                    Statistics for Removal,  DF = 2, 144

                Partial
  Variable         R**2           F        Prob > F     Label

  PETALLEN       0.2768         27.554       0.0001     Petal length in mm.
  PETALWID       0.2417         22.955       0.0001     Petal width  in mm.


                         No variables can be removed

                  Iris data: Stepwise discriminant analysis                 13
                             Size and elongation

                        Stepwise Discriminant Analysis

Stepwise Selection:  Step 3

                      Statistics for Entry, DF = 2, 143

            Partial
Variable       R**2         F      Prob > F   Tolerance   Label

SEPALLEN     0.1617       13.792     0.0001      0.0095   Sepal length in mm.
SEPALWID     0.2605       25.191     0.0001      0.0103   Sepal width  in mm.

                      Variable SEPALWID will be entered

                 The following variable(s) have been entered:
                 SIZE     ELONG    PETALLEN PETALWID SEPALWID

                           Multivariate Statistics

 Wilks' Lambda  = 0.00782693    F( 10, 286) =  294.674      Prob > F = 0.0001
 Pillai's Trace =   1.619403    F( 10, 288) =  122.541      Prob > F = 0.0001

              Average Squared Canonical Correlation = 0.80970166

------------------------------------------------------------------------------

Stepwise Selection:  Step 4

                    Statistics for Removal,  DF = 2, 143

                Partial
  Variable         R**2           F        Prob > F     Label

  PETALLEN       0.2458         23.302       0.0001     Petal length in mm.
  PETALWID       0.2722         26.738       0.0001     Petal width  in mm.
  SEPALWID       0.2605         25.191       0.0001     Sepal width  in mm.


                         No variables can be removed

                  Iris data: Stepwise discriminant analysis                 14
                             Size and elongation

                        Stepwise Discriminant Analysis

Stepwise Selection:  Step 4

                      Statistics for Entry, DF = 2, 142

            Partial
Variable       R**2         F      Prob > F   Tolerance   Label

SEPALLEN     0.0442        3.284     0.0403      0.0092   Sepal length in mm.

                      Variable SEPALLEN will be entered

                       All variables have been entered

                           Multivariate Statistics

 Wilks' Lambda  = 0.00748089    F( 12, 284) =  249.961      Prob > F = 0.0001
 Pillai's Trace =   1.628839    F( 12, 286) =  104.593      Prob > F = 0.0001

              Average Squared Canonical Correlation = 0.81441969

------------------------------------------------------------------------------

Stepwise Selection:  Step 5

                    Statistics for Removal,  DF = 2, 142

                Partial
  Variable         R**2           F        Prob > F     Label

  PETALLEN       0.2207         20.109       0.0001     Petal length in mm.
  PETALWID       0.2055         18.369       0.0001     Petal width  in mm.
  SEPALLEN       0.0442          3.284       0.0403     Sepal length in mm.
  SEPALWID       0.1569         13.212       0.0001     Sepal width  in mm.


                         No variables can be removed

No further steps are possible

                  Iris data: Stepwise discriminant analysis                 15
                             Size and elongation

                        Stepwise Discriminant Analysis

Stepwise Selection:  Summary

             Variable        Number  Partial        F        Prob >
  Step  Entered   Removed      In       R**2    Statistic      F
 ------------------------------------------------------------------

     0                            2    .             .        .
     1  PETALLEN                  3   0.5627       93.295    0.0001
     2  PETALWID                  4   0.2417       22.955    0.0001
     3  SEPALWID                  5   0.2605       25.191    0.0001
     4  SEPALLEN                  6   0.0442        3.284    0.0403

             Variable        Number      Wilks'     Prob <
  Step  Entered   Removed      In        Lambda     Lambda
 ---------------------------------------------------------

     0                            2  0.03192219     0.0001
     1  PETALLEN                  3  0.01395913     0.0001
     2  PETALWID                  4  0.01058458     0.0001
     3  SEPALWID                  5  0.00782693     0.0001
     4  SEPALLEN                  6  0.00748089     0.0001

                                         Average
                                         Squared
             Variable        Number    Canonical  Prob >
  Step  Entered   Removed      In    Correlation    ASCC  Label
 ----------------------------------------------------------------------------

     0                            2   0.48416035  0.0001
     1  PETALLEN                  3   0.75266346  0.0001  Petal length in mm.
     2  PETALWID                  4   0.80579746  0.0001  Petal width  in mm.
     3  SEPALWID                  5   0.80970166  0.0001  Sepal width  in mm.
     4  SEPALLEN                  6   0.81441969  0.0001  Sepal length in mm.

                  Iris data: Stepwise discriminant analysis                 16
                             Size and elongation

                            Discriminant Analysis

                 150 Observations        149 DF Total
                   4 Variables           147 DF Within Classes
                   3 Classes               2 DF Between Classes

                           Class Level Information

                                                                    Prior
    SPECIES        Frequency        Weight     Proportion     Probability

    Setosa                50       50.0000       0.333333        0.333333
    Versicolor            50       50.0000       0.333333        0.333333
    Virginica             50       50.0000       0.333333        0.333333

                  Iris data: Stepwise discriminant analysis                 17
                             Size and elongation

                            Discriminant Analysis

            Classification Summary for Calibration Data: WORK.IRIS

          Resubstitution Summary using Linear Discriminant Function

             Generalized Squared Distance Function:

              2         _       -1   _
             D (X) = (X-X )' COV  (X-X )
              j          j            j

             Posterior Probability of Membership in each SPECIES:

                                2                    2
             Pr(j|X) = exp(-.5 D (X)) / SUM exp(-.5 D (X))
                                j        k           k

                 Number of Observations and Percent Classified into SPECIES:

 From SPECIES            Setosa     Versicolor      Virginica          Total

      Setosa                 50              0              0             50
                         100.00           0.00           0.00         100.00

      Versicolor              0             48              2             50
                           0.00          96.00           4.00         100.00

      Virginica               0              1             49             50
                           0.00           2.00          98.00         100.00

      Total                  50             49             51            150
      Percent             33.33          32.67          34.00         100.00

      Priors             0.3333         0.3333         0.3333

                   Error Count Estimates for SPECIES:

                     Setosa     Versicolor     Virginica        Total

        Rate         0.0000         0.0400        0.0200       0.0200

        Priors       0.3333         0.3333        0.3333

                  Iris data: Stepwise discriminant analysis                 18
                             Size and elongation

                            Discriminant Analysis

                 150 Observations        149 DF Total
                   2 Variables           147 DF Within Classes
                   3 Classes               2 DF Between Classes

                           Class Level Information

                                                                    Prior
    SPECIES        Frequency        Weight     Proportion     Probability

    Setosa                50       50.0000       0.333333        0.333333
    Versicolor            50       50.0000       0.333333        0.333333
    Virginica             50       50.0000       0.333333        0.333333

                  Iris data: Stepwise discriminant analysis                 19
                             Size and elongation

                            Discriminant Analysis

            Classification Summary for Calibration Data: WORK.IRIS

          Resubstitution Summary using Linear Discriminant Function

             Generalized Squared Distance Function:

              2         _       -1   _
             D (X) = (X-X )' COV  (X-X )
              j          j            j

             Posterior Probability of Membership in each SPECIES:

                                2                    2
             Pr(j|X) = exp(-.5 D (X)) / SUM exp(-.5 D (X))
                                j        k           k

                 Number of Observations and Percent Classified into SPECIES:

 From SPECIES            Setosa     Versicolor      Virginica          Total

      Setosa                 50              0              0             50
                         100.00           0.00           0.00         100.00

      Versicolor              0             47              3             50
                           0.00          94.00           6.00         100.00

      Virginica               0              1             49             50
                           0.00           2.00          98.00         100.00

      Total                  50             48             52            150
      Percent             33.33          32.00          34.67         100.00

      Priors             0.3333         0.3333         0.3333

                   Error Count Estimates for SPECIES:

                     Setosa     Versicolor     Virginica        Total

        Rate         0.0000         0.0600        0.0200       0.0267

        Priors       0.3333         0.3333        0.3333