Discriminant Rácios de Altman Output Created Comments Missing Value Handling

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1 Discriminant Rácios de Altman Output Created Comments Missing Value Handling Syntax Definition of Missing Cases Used User-defined missing values are treated as missing in the analysis phase. In the analysis phase, cases with no user- or system-missing values for any predictor variable are used. Cases with user-, system-missing, or out-ofrange values for the grouping variable are always excluded. DISCRIMINANT /GROUPS=(0 1) /VARIABLES=FMACT. RESULT.RET.ACT. EBITACT. CAP.PRORIOSPASS. V.P.S.ACTI /ANALYSIS ALL /PRIORS EQUAL /STATISTICS=MEAN STDDEV UNIVF BOXM COEFF TABLE /PLOT=MAP /CLASSIFY=NONMISSING POOLED. Resources Elapsed Time 0:00:00,11 Analysis Case Processing Summary Unweighted Cases N Percent Valid ,9 Excluded Missing or out-of-range group codes 0,0 At least one missing discriminating variable 3,1 Both missing or out-of-range group codes and at least one missing discriminating variable 0,0 Total 3,1 Total ,0 Para este modelo, verificam-se 2176 casos válidos, que correspondem a 99,9% da amostra, devido á existência de 3 casos de missing values. Analise discriminante racios Altman - VII Page 1

2 Group Statistics Mean Std. Deviation Valid N (listwise) Sem dívida FM/ACT., , ,000 Unweighted Weighted RESULT. RET./ACT. -, , ,000 EBIT/ACT., , ,000 2, , ,000 V. P. S./ACTI, , ,000 Com dívida FM/ACT. -, , ,000 RESULT. RET./ACT. -, , ,000 EBIT/ACT. -, , ,000, , ,000 V. P. S./ACTI, , ,000 Total FM/ACT., , ,000 RESULT. RET./ACT. -, , ,000 EBIT/ACT., , ,000 2, , ,000 V. P. S./ACTI, , ,000 Esta tabela resume a análise descritiva, que traduz as diferenças nas médias obtidas por cada uma situações nas variáveis, observando-se algumas diferenças entre o grupo com dividas e sem dividasna tabela do teste da igualdade das médias para cada uma das variáveis confirma-se o observado na tabela, ou seja, existem diferenças entre as duas situações, que são significativas para quatro das variáveis, sendo essas diferenças assinaladas a vermelho. Tests of Equality of Group Means Wilks' Lambda F df1 df2 Sig. FM/ACT.,968 71, ,000 RESULT. RET./ACT.,993 14, ,000 EBIT/ACT.,995 11, ,001 1,000, ,797 V. P. S./ACTI,995 9, ,002. Analise discriminante racios Altman - VII Page 2

3 Analysis 1 Box's Test of Equality of Covariance Matrices Log Determinants Rank Log Determinant Sem dívida 5 4,156 Com dívida 5-7,342 Pooled within-groups 5 4,328 The ranks and natural logarithms of determinants printed are those of the group covariance matrices. Test Results Box's M 1155,873 F Approx. 75,020 df1 15 df ,352 Sig.,000 Tests null hypothesis of equal population covariance matrices. O valor da prova é inferior a 5%, pelo que se rejeita a hipótese de igualdade das matrizes de variância-covariãncia para as duas situações em estudo Summary of Canonical Discriminant s Eigenvalues Canonical Eigenvalue % of Variance Cumulative % Correlation 1,043(a) 100,0 100,0,202 a First 1 canonical discriminant functions were used in the analysis. Wilks' Lambda Test of (s) Wilks' Lambda Chi-square df Sig. 1,959 90,539 5,000 Standardized Canonical Discriminant Coefficients FM/ACT.,816 RESULT. RET./ACT.,171 EBIT/ACT.,171 -,011 V. P. S./ACTI,474 1 Analise discriminante racios Altman - VII Page 3

4 Structure Matrix Coeficientes estruturais 1 FM/ACT.,880 RESULT. RET./ACT.,399 EBIT/ACT.,350 V. P. S./ACTI,327,027 Pooled within-groups correlations between discriminating variables and standardized canonical discriminant functions Variables ordered by absolute size of correlation within function. s at Group Centroids 1 Sem dívida,037 Com dívida -1,140 Unstandardized canonical discriminant functions evaluated at group means Classification Statistics Classification Processing Summary Processed 2179 Excluded Missing or out-of-range group codes 0 At least one missing discriminating variable 3 Used in Output 2176 Prior Probabilities for Groups Cases Used in Analysis Prior Specified Prior Effective Prior Unweighted Weighted Sem dívida, ,000 Com dívida, ,000 Total 1, ,000 Classification Coefficients (Funções lineares discriminantes de Fisher) Analise discriminante racios Altman - VII Page 4

5 Sem dívida Com dívida FM/ACT. -,249-2,356 RESULT. RET./ACT. -,102 -,220 EBIT/ACT. 2,981 2,296,001,001 V. P. S./ACTI 3,063 2,122 (Constant) -2,068-1,897 Fisher's linear discriminant functions Os coeficientes das funções lineares de Fisher apresentam maiores diferenças entre as duas situações para os rácios com maior poder discriminante identificados nas tabelas anteriores (coeficientes da Função discriminante e coeficientes estruturais). Classification Results(a) Predicted Group Membership Total Original Count Sem dívida Com dívida % Sem dívida 80,4 19,6 100,0 Com dívida 49,3 50,7 100,0 a 79,4% of original grouped cases correctly classified. Sem dívida Com dívida Discriminant Selecção Automática das Variáveis Significantes Unweighted Cases N Percent Valid ,9 Excluded Missing or out-of-range group codes 0,0 At least one missing discriminating variable 3,1 Both missing or out-of-range group codes and at least one missing discriminating variable 0,0 Total 3,1 Total ,0 Analise discriminante racios Altman - VII Page 5

6 Analysis Case Processing Summary Group Statistics Mean Std. Deviation Valid N (listwise) Sem dívida FM/ACT., RESULT. RET./ACT. -, EBIT/ACT., , V. P. S./ACTI, Com dívida FM/ACT. -, RESULT. RET./ACT. -, EBIT/ACT. -, , V. P. S./ACTI, Total FM/ACT., RESULT. RET./ACT. -, EBIT/ACT., , V. P. S./ACTI, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,000 Unweighted Weighted Tests of Equality of Group Means Wilks' Lambda F df1 df2 Sig. FM/ACT.,968 71, ,000 RESULT. RET./ACT.,993 14, ,000 EBIT/ACT.,995 11, ,001 1,000, ,797 V. P. S./ACTI,995 9, ,002 Analise discriminante racios Altman - VII Page 6

7 analysis 1 No teste de Box o valor de prova é inferior a 5% pelo que se rejeita a hipótese de igualdade das matrizes de variância - covariância para as duas situações em estudo, logo verifica-se o pressuposto da análise discriminante Box's Test of Equality of Covariance Matrices Log Determinants Rank Log Determinant Sem dívida 2-2,831 Com dívida 2-1,028 Pooled within-groups 2-2,629 The ranks and natural logarithms of determinants printed are those of the group covariance matrices. Test Results Box's M 314,606 F Approx. 103,752 df1 3 df ,37 4 Sig.,000 Tests null hypothesis of equal population covariance matrices. Stepwise Statistics Variables Entered/Removed(a,b,c,d) Wilks' Lambda Exact F Step Entered Removed 1 FM/ACT. 2 V. P. S./ACTI Statistic df1 df2 df3 Statistic df1 df2 Sig., ,000 71, ,000,000, ,000 44, ,000,000 At each step, the variable that minimizes the overall Wilks' Lambda is entered. a Maximum number of steps is 10. b Minimum partial F to enter is c Maximum partial F to remove is d F level, tolerance, or VIN insufficient for further computation. Analise discriminante racios Altman - VII Page 7

8 Variables in the Analysis Step Tolerance F to Remove Wilks' Lambda 1 Variables FM/ACT. 1,000 71,612 V. P. S./ACTI 2 Variables FM/ACT.,989 77,903,995 V. P. S./ACTI Variables Not in the Analysis,989 16,047,968 Step Tolerance Min. Tolerance F to Enter Wilks' Lambda 0 Variables FM/ACT. 1,000 1,000 71,612,968 RESULT. RET./ACT. 1,000 1,000 14,713,993 EBIT/ACT. 1,000 1,000 11,350,995 1,000 1,000,066 1,000 V. P. S./ACTI 1,000 1,000 9,902,995 1 Variables FM/ACT. RESULT. RET./ACT.,944,944 3,445,967 EBIT/ACT.,809,809,131,968,997,997,045,968 V. P. S./ACTI,989,989 16,047,961 2 Variables FM/ACT. RESULT. RET./ACT.,939,930 2,405,960 EBIT/ACT.,683,683 1,744,960,997,986,023,961 V. P. S./ACTI Wilks' Lambda Exact F Step Number of Variables Lambda df1 df2 df3 Statistic df1 df2 Sig. 1 1, , ,000, , , ,000,000 Analise discriminante racios Altman - VII Page 8

9 N a tabela dos valores próprios (Eigenvalues) a função discriminante constituida, corresponde a 100% da variância explicada em termos de diferenças entre grupos, observando-se uma correlação canónica entre a função discriminante e os grupos de 0,197. Summary of Canonical Discriminant s Eigenvalues Canonical Eigenvalue % of Variance Cumulative % Correlation 1,041(a) 100,0 100,0,197 a First 1 canonical discriminant functions were used in the analysis. O teste de Wilk permite concluir que a funçaõ discriminante é significativa (valor de prova de 0,0%), pelo que podemos concluir pela diferença entre as médias dos dois grupos (sem dívida e com dívida ) nesta função Wilks' Lambda Test of (s) Wilks' Lambda Chi-square df Sig. 1,961 86,414 2,000 Standardized Canonical Discriminant Coefficients FM/ACT.,948 V. P. S./ACTI 1,436 Variáveis seleccionadas como significantes para a função discriminante Structure Matrix FM/ACT.,901 V. P. S./ACTI,335 RESULT. RET./ACT.(a),245 EBIT/ACT. (a),240 (a),044 1 Pooled within-groups correlations between discriminating variables and standardized canonical discriminant functions Variables ordered by absolute size of correlation within function. a This variable not used in the analysis. Analise discriminante racios Altman - VII Page 9

10 s at Group Centroids 1 Sem dívida,036 Com dívida -1,113 Unstandardized canonical discriminant functions evaluated at group means Classification Statistics Classification Processing Summary Processed 2179 Excluded Missing or out-of-range group codes 0 At least one missing discriminating variable 1 Used in Output 2178 Prior Probabilities for Groups Cases Used in Analysis Prior Specified Prior Effective Prior Unweighted Weighted Sem dívida, ,000 Com dívida, ,000 Total 1, ,000 Classification Coefficients Sem dívida Com dívida FM/ACT.,434-1,956 V. P. S./ACTI 2,513 1,668 (Constant) -1,791-1,673 Fisher's linear discriminant functions Analise discriminante racios Altman - VII Page 10

11 Classification Results(a) Predicted Group Membership Total Original Count Sem dívida Com dívida % Sem dívida 79,1 20,9 100,0 Com dívida 50,7 49,3 100,0 a 78,1% of original grouped cases correctly classified. Sem dívida Com dívida Nos resultados da classificação verifica-se que 79,1% dos casos sem dívida foram classificados correctamente e 49,3% dos casos com dívida foram classificados correctamente, tendo portanto diminuído este valor,em relação á análise anterior. Analise discriminante racios Altman - VII Page 11