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William G. Zikmund, Barry J. Babin, Jon C. Carr, Mitch Griffin

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- 1. Business Research Methods William G. Zikmund Chapter 24 Multivariate Analysis
- 2. Multivariate Statistical Analysis • Statistical methods that allow the simultaneous investigation of more than two variables
- 3. All multivariate methods Are some of the variables dependent on others? Yes No Dependence methods Interdependence methods A Classification of Selected Multivariate Methods
- 4. Dependence Methods • A category of multivariate statistical techniques; dependence methods explain or predict a dependent variable(s) on the basis of two or more independent variables
- 5. Dependence Methods How many variables are dependent One dependent variable Several dependent variables Multiple independent and dependent variables
- 6. Dependence Methods How many variables are dependent One dependent variable NonmetricMetric Multiple discriminant analysis Multiple regression analysis
- 7. Dependence Methods How many variables are dependent NonmetricMetric Conjoint analysis Multivariate analysis of variance Several dependent variables
- 8. Dependence Methods How many variables are dependent Multiple independent and dependent variables Metric or nonmetric Canonical correlation analysis
- 9. Interdependence Methods • A category of multivariate statistical techniques; interdependence methods give meaning to a set of variables or seek to group things together
- 10. Interdependence methods Are inputs metric? Metric Nonmetric
- 11. Metric Metric multidimensional scaling Cluster analysis Factor analysis Interdependence methods Are inputs metric?
- 12. Nonmetric Nonmetric Interdependence methods Are inputs metric?
- 13. Multiple Regression • An extension of bivariate regression • Allows for the simultaneous investigation – two or more independent variables – a single interval-scaled dependent variable
- 14. Y= a +β1X1 +β2X2+β3X3...+βnXn Multiple Regression Equation
- 15. 2211 XXaY ββ ++= nn XX ββ +++ .....33 Multiple Regression Analysis
- 16. Coefficients of Partial Regression β1 Independent variables correlated with one another The % of the variance in the dependent variable that is explained by a single independent variable, holding other independent variables constant
- 17. Coefficient of Multiple Determination • R2 • The % of the variance in the dependent variable that is explained by the variation in the independent variables.
- 18. • Y = 102.18 + .387X1 + 115.2X2 + 6.73X3 • Coefficient of multiple determination (R2 ) .845 • F-value 14.6 Statistical Results of a Multiple Regression
- 19. ( ) ( ) ( )1/ / −− = knSSe kSSr F F-Test
- 20. Degrees of Freedom (d.f.) are Calculated as Follows: • d.f. for the numerator = k • for the denominator = n - k - 1
- 21. Degrees of Freedom • k = number of independent variables • n = number of observations or respondents
- 22. where k = number of independent variables n = number of observations )1/()( /)( −− = knSSe kSSr F F-test
- 23. Multiple Discriminant Analysis • A statistical technique for predicting the probability of objects belonging in two or more mutually exclusive categories (dependent variable) based on several independent variables
- 24. Zi = b1X1i + b2X2i + . . . + bnXni • where • Zi = ith applicant’s discriminant score • bn = discriminant coefficient for the nth variable • Xni = applicant’s value on the nth independent variable
- 25. iii XbXbZ 2211 += nin Xb++........ Discriminant Analysis
- 26. = applicant’s value on the jth independent variable = discriminant coefficient for the jth variable = ith applicant’s discriminant score jiX jb iZ Discriminant Analysis
- 27. Canonical Correlation • Two or more criterion variables (dependent variables) • Multiple predictor variables (independent variables) • An extension of multiple regression • Linear association between two sets of variables
- 28. Canonical Correlation • Z = a1X1 + a2X2 + . . . + anXn • W = b1Y1 + b2Y2 + . . . + bnYn
- 29. Factor Analysis • Summarize the information in a large number of variables • Into a smaller number of factors • Several factor-analytical techniques
- 30. Factor Analysis • A type of analysis used to discern the underlying dimensions or regularity in phenomena. Its general purpose is to summarize the information contained in a large number of variables into a smaller number of factors.
- 31. Height Weight Occupation Education Source of Income Size Social Status Factor Analysis Copyright © 2000 Harcourt, Inc. All rights reserved.
- 32. Cluster Analysis • A body of techniques with the purpose of classifying individuals or objects into a small number of mutually exclusive groups, ensuring that there will be as much likeness within groups and as much difference among groups as possible
- 33. Multidimensional Scaling • A statistical technique that measures objects in multidimensional space on the basis of respondents’ judgments of the similarity of objects
- 34. Multivariate Analysis of Variance (MANOVA) • A statistical technique that provides a simultaneous significance test of mean difference between groups for two or more dependent variables

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