The SAS System 1 ---------------------------------- GROUP=1 ----------------------------------- Correlation Analysis 2 'VAR' Variables: X2 X3 Covariance Matrix DF = 20 X2 X3 X2 0.0209155515 0.0257992199 X3 0.0257992199 0.1645475009 ---------------------------------- GROUP=2 ----------------------------------- Correlation Analysis 2 'VAR' Variables: X2 X3 Covariance Matrix DF = 24 X2 X3 X2 0.002313508 0.008729234 X3 0.008729234 1.045964830 The SAS System 2 General Linear Models Procedure Class Level Information Class Levels Values GROUP 2 1 2 Number of observations in data set = 46 Manova Test Criteria and Exact F Statistics for the Hypothesis of no Overall GROUP Effect H = Type III SS&CP Matrix for GROUP E = Error SS&CP Matrix S=1 M=0 N=20.5 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.53079156 19.0055 2 43 0.0001 Pillai's Trace 0.46920844 19.0055 2 43 0.0001 Hotelling-Lawley Trace 0.88397872 19.0055 2 43 0.0001 Roy's Greatest Root 0.88397872 19.0055 2 43 0.0001 The SAS System 3 Discriminant Analysis 46 Observations 45 DF Total 2 Variables 44 DF Within Classes 2 Classes 1 DF Between Classes Class Level Information Prior GROUP Frequency Weight Proportion Probability 1 21 21.0000 0.456522 0.500000 2 25 25.0000 0.543478 0.500000 Discriminant Analysis Pooled Covariance Matrix Information Covariance Natural Log of the Determinant Matrix Rank of the Covariance Matrix 2 -5.0089994 Discriminant Analysis Pairwise Generalized Squared Distances Between Groups 2 _ _ -1 _ _ D (i|j) = (X - X )' COV (X - X ) i j i j Generalized Squared Distance to GROUP From GROUP 1 2 1 0 3.40795 2 3.40795 0 The SAS System 4 Discriminant Analysis Linear Discriminant Function _ -1 _ -1 _ Constant = -.5 X' COV X Coefficient Vector = COV X j j j GROUP 1 2 CONSTANT -2.10813 -5.21921 X2 -11.28774 -1.08463 X3 2.40750 4.04725 The SAS System 5 Discriminant Analysis Classification Summary for Calibration Data: WORK.BANKRUPT 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 GROUP: 2 2 Pr(j|X) = exp(-.5 D (X)) / SUM exp(-.5 D (X)) j k k Number of Observations and Percent Classified into GROUP: From GROUP 1 2 Total 1 18 3 21 85.71 14.29 100.00 2 2 23 25 8.00 92.00 100.00 Total 20 26 46 Percent 43.48 56.52 100.00 Priors 0.5000 0.5000 Error Count Estimates for GROUP: 1 2 Total Rate 0.1429 0.0800 0.1114 Priors 0.5000 0.5000 The SAS System 6 Discriminant Analysis Classification Summary for Calibration Data: WORK.BANKRUPT Cross-validation Summary using Linear Discriminant Function Generalized Squared Distance Function: 2 _ -1 _ D (X) = (X-X )' COV (X-X ) j (X)j (X) (X)j Posterior Probability of Membership in each GROUP: 2 2 Pr(j|X) = exp(-.5 D (X)) / SUM exp(-.5 D (X)) j k k Number of Observations and Percent Classified into GROUP: From GROUP 1 2 Total 1 17 4 21 80.95 19.05 100.00 2 2 23 25 8.00 92.00 100.00 Total 19 27 46 Percent 41.30 58.70 100.00 Priors 0.5000 0.5000 Error Count Estimates for GROUP: 1 2 Total Rate 0.1905 0.0800 0.1352 Priors 0.5000 0.5000