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# Business Research Methods, 9th ed.Chapter 24

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

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• ### Business Research Methods, 9th ed.Chapter 24

1. 1. Business Research Methods William G. Zikmund Chapter 24 Multivariate Analysis
2. 2. Multivariate Statistical Analysis • Statistical methods that allow the simultaneous investigation of more than two variables
3. 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. 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. 5. Dependence Methods How many variables are dependent One dependent variable Several dependent variables Multiple independent and dependent variables
6. 6. Dependence Methods How many variables are dependent One dependent variable NonmetricMetric Multiple discriminant analysis Multiple regression analysis
7. 7. Dependence Methods How many variables are dependent NonmetricMetric Conjoint analysis Multivariate analysis of variance Several dependent variables
8. 8. Dependence Methods How many variables are dependent Multiple independent and dependent variables Metric or nonmetric Canonical correlation analysis
9. 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. 10. Interdependence methods Are inputs metric? Metric Nonmetric
11. 11. Metric Metric multidimensional scaling Cluster analysis Factor analysis Interdependence methods Are inputs metric?
12. 12. Nonmetric Nonmetric Interdependence methods Are inputs metric?
13. 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. 14. Y= a +β1X1 +β2X2+β3X3...+βnXn Multiple Regression Equation
15. 15. 2211 XXaY ββ ++= nn XX ββ +++ .....33 Multiple Regression Analysis
16. 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. 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. 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. 19. ( ) ( ) ( )1/ / −− = knSSe kSSr F F-Test
20. 20. Degrees of Freedom (d.f.) are Calculated as Follows: • d.f. for the numerator = k • for the denominator = n - k - 1
21. 21. Degrees of Freedom • k = number of independent variables • n = number of observations or respondents
22. 22. where k = number of independent variables n = number of observations )1/()( /)( −− = knSSe kSSr F F-test
23. 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. 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. 25. iii XbXbZ 2211 += nin Xb++........ Discriminant Analysis
26. 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. 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. 28. Canonical Correlation • Z = a1X1 + a2X2 + . . . + anXn • W = b1Y1 + b2Y2 + . . . + bnYn
29. 29. Factor Analysis • Summarize the information in a large number of variables • Into a smaller number of factors • Several factor-analytical techniques
30. 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.