# malhotra18.ppt - Chapter Eighteen Discriminant Analysis...

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Chapter Eighteen Discriminant Analysis
18-2 Chapter Outline 1) Overview 2) Basic Concept 3) Relation to Regression and ANOVA 4) Discriminant Analysis Model 5) Statistics Associated with Discriminant Analysis 6) Conducting Discriminant Analysis i. Formulation ii. Estimation iii. Determination of Significance iv. Interpretation v. Validation
18-3 Chapter Outline 7) Multiple Discriminant Analysis i. Formulation ii. Estimation iii. Determination of Significance iv. Interpretation v. Validation 8) Stepwise Discriminant Analysis 9) Internet and Computer Applications 10) Focus on Burke 11) Summary 12) Key Terms and Concepts
18-4 ANOVA, Regression, and Discriminant Analysis ANOVA REGRESSION DISCRIMINANT ANALYSIS Similarities Number of One One One dependent variables Number of independent Multiple Multiple Multiple variables Differences Nature of the dependent Metric Metric Categorical variables Nature of the independent Categorical Metric Metric variables Table 18.1
18-5 Discriminant Analysis Discriminant analysis is a technique for analyzing data when the criterion or dependent variable is categorical and the predictor or independent variables are interval in nature. The objectives of discriminant analysis are as follows: Development of discriminant functions , or linear combinations of the predictor or independent variables, which will best discriminate between the categories of the criterion or dependent variable (groups). Examination of whether significant differences exist among the groups, in terms of the predictor variables. Determination of which predictor variables contribute to most of the intergroup differences. Classification of cases to one of the groups based on the values of the predictor variables. Evaluation of the accuracy of classification.
18-6 When the criterion variable has two categories, the technique is known as two-group discriminant analysis. When three or more categories are involved, the technique is referred to as multiple discriminant analysis . The main distinction is that, in the two-group case, it is possible to derive only one discriminant function. In multiple discriminant analysis, more than one function may be computed. In general, with G groups and k predictors, it is possible to estimate up to the smaller of G - 1, or k , discriminant functions. The first function has the highest ratio of between- groups to within-groups sum of squares. The second function, uncorrelated with the first, has the second highest ratio, and so on. However, not all the functions may be statistically significant. Discriminant Analysis
18-7 Discriminant Analysis Model The discriminant analysis model involves linear combinations of the following form: D = b 0 + b 1 X 1 + b 2 X 2 + b 3 X 3 + . . . + b k X k where D = discriminant score b 's = discriminant coefficient or weight X 's = predictor or independent variable The coefficients, or weights ( b ), are estimated so that the groups differ as much as possible on the values of the discriminant function.

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