The SAS System 09:34 Monday, April 1, 2002 128
Canonical Discriminant Analysis
22 Observations 21 DF Total
3 Variables 20 DF Within Classes
2 Classes 1 DF Between Classes
Class Level Information
G Frequency Weight Proportion
1 12 12.0000 0.545455
2 10 10.0000 0.454545
The SAS System 09:34 Monday, April 1, 2002 129
Canonical Discriminant Analysis
Multivariate Statistics and Exact F Statistics
S=1 M=0.5 N=8
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.53805541 5.1513 3 18 0.0096
Pillai's Trace 0.46194459 5.1513 3 18 0.0096
Hotelling-Lawley Trace 0.85854465 5.1513 3 18 0.0096
Roy's Greatest Root 0.85854465 5.1513 3 18 0.0096
The SAS System 09:34 Monday, April 1, 2002 130
Canonical Discriminant Analysis
Adjusted Approx Squared
Canonical Canonical Standard Canonical
Correlation Correlation Error Correlation
1 0.679665 0.650675 0.117413 0.461945
Eigenvalues of INV(E)*H
= CanRsq/(1-CanRsq)
Eigenvalue Difference Proportion Cumulative
1 0.8585 . 1.0000 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 0.53805541 5.1513 3 18 0.0096
NOTE: The F statistic is exact.
Total Canonical Structure
CAN1
X1 -0.391583
X2 0.890607
X3 -0.789274
Between Canonical Structure
CAN1
X1 -1.000000
X2 1.000000
X3 -1.000000
Pooled Within Canonical Structure
CAN1
X1 -0.297982
X2 0.820717
X3 -0.686011
The SAS System 09:34 Monday, April 1, 2002 131
Canonical Discriminant Analysis
Total-Sample Standardized Canonical Coefficients
CAN1
X1 -.5296774441
X2 0.9590945769
X3 -.3406182305
Pooled Within-Class Standardized Canonical Coefficients
CAN1
X1 -.5231822320
X2 0.7822793210
X3 -.2945592974
Raw Canonical Coefficients
CAN1
X1 -.0395150038
X2 0.1265698218
X3 -.1792630797
Class Means on Canonical Variables
G CAN1
1 0.8064816283
2 -.9677779540
The SAS System 09:34 Monday, April 1, 2002 132
Stepwise Discriminant Analysis
16 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
G Frequency Weight Proportion
1 7 7.0000 0.437500
2 4 4.0000 0.250000
3 5 5.0000 0.312500
The SAS System 09:34 Monday, April 1, 2002 133
Stepwise Discriminant Analysis
Stepwise Selection: Step 1
Statistics for Entry, DF = 2, 13
Variable R**2 F Prob > F Tolerance
X1 0.0302 0.203 0.8192 1.0000
X2 0.0055 0.036 0.9648 1.0000
X3 0.2977 2.755 0.1005 1.0000
X4 0.2089 1.716 0.2181 1.0000
Variable X3 will be entered
The following variable(s) have been entered:
X3
Multivariate Statistics
Wilks' Lambda = 0.70228925 F( 2, 13) = 2.755 Prob > F = 0.1005
Pillai's Trace = 0.297711 F( 2, 13) = 2.755 Prob > F = 0.1005
Average Squared Canonical Correlation = 0.14885538
---------------------------------------------------------------------------------------------
Stepwise Selection: Step 2
Statistics for Removal, DF = 2, 13
Variable R**2 F Prob > F
X3 0.2977 2.755 0.1005
No variables can be removed
The SAS System 09:34 Monday, April 1, 2002 134
Stepwise Discriminant Analysis
Stepwise Selection: Step 2
Statistics for Entry, DF = 2, 12
Partial
Variable R**2 F Prob > F Tolerance
X1 0.0063 0.038 0.9626 0.9528
X2 0.2070 1.566 0.2487 0.6003
X4 0.4445 4.801 0.0294 0.9701
Variable X4 will be entered
The following variable(s) have been entered:
X3 X4
Multivariate Statistics
Wilks' Lambda = 0.39011223 F( 4, 24) = 3.606 Prob > F = 0.0194
Pillai's Trace = 0.610665 F( 4, 26) = 2.857 Prob > F = 0.0436
Average Squared Canonical Correlation = 0.30533230
---------------------------------------------------------------------------------------------
Stepwise Selection: Step 3
Statistics for Removal, DF = 2, 12
Partial
Variable R**2 F Prob > F
X3 0.5069 6.168 0.0144
X4 0.4445 4.801 0.0294
No variables can be removed
The SAS System 09:34 Monday, April 1, 2002 135
Stepwise Discriminant Analysis
Stepwise Selection: Step 3
Statistics for Entry, DF = 2, 11
Partial
Variable R**2 F Prob > F Tolerance
X1 0.1089 0.672 0.5303 0.8884
X2 0.2449 1.784 0.2133 0.1046
No variables can be entered
No further steps are possible
---------------------------------------------------------------------------------------------
Stepwise Selection: Summary
Variable Number Partial F Prob > Wilks' Prob <
Step Entered Removed In R**2 Statistic F Lambda Lambda
------------------------------------------------------------------------------------------
1 X3 1 0.2977 2.755 0.1005 0.70228925 0.1005
2 X4 2 0.4445 4.801 0.0294 0.39011223 0.0194
Average
Squared
Variable Number Canonical Prob >
Step Entered Removed In Correlation ASCC
--------------------------------------------------------------
1 X3 1 0.14885538 0.1005
2 X4 2 0.30533230 0.0436
