Research Methods, William G. Zikmund, Ch24

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Research Methods
William G. Zikmund

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Research Methods, William G. Zikmund, Ch24

  1. 1. BusinessResearch Methods William G. Zikmund Chapter 24Multivariate Analysis
  2. 2. Multivariate Statistical Analysis• Statistical methods that allow the simultaneous investigation of more than two variables
  3. 3. A Classification of Selected Multivariate Methods All multivariate methods Are some of the variables dependent on others? Yes NoDependence Interdependence methods 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 Multiple SeveralOne dependent independent dependent variable and dependent variables variables
  6. 6. Dependence Methods How many variables are dependent One dependent variable Metric Nonmetric Multiple Multipleregression discriminant analysis analysis
  7. 7. Dependence Methods How many variables are dependent Several dependent variables Metric NonmetricMultivariate Conjointanalysis of analysis variance
  8. 8. Dependence Methods Multiple How many independentvariables are and dependent 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. Interdependence methods Are inputs metric? Metric Metric Factor Cluster multidimensionalanalysis analysis scaling
  12. 12. Interdependence methodsAre inputs metric? Nonmetric Nonmetric
  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. Multiple Regression Equation Y= a +β1X1 +β2X2+β3X3...+βnXn
  15. 15. Multiple Regression AnalysisY = a + β1 X 1 + β 2 X 2 + β 3 X 3 + ..... + β n X n
  16. 16. Coefficients of Partial Regressionβ1Independent variables correlated with one anotherThe % 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. Statistical Results of a Multiple Regression• Y = 102.18 + .387X1 + 115.2X2 + 6.73X3• Coefficient of multiple determination (R2) .845• F-value 14.6
  19. 19. F-TestF= ( SSr ) / k ( SSe) / ( n − k − 1)
  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. F-test ( SSr ) / k F= ( SSe) /( n − k − 1)where k = number of independent variables n = number of observations
  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. Discriminant AnalysisZi = b1 X 1i + b2 X 2i + ........ + bn X ni
  26. 26. Discriminant AnalysisX ji = applicant’s value on the jth independent variablebj = discriminant coefficient for the jth variableZi = ith applicant’s discriminant score
  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.
  31. 31. Factor Analysis Height Size WeightOccupationEducation Social StatusSource of Income Copyright © 2000 Harcourt, Inc. All rights reserved.
  32. 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. 33. Multidimensional Scaling• A statistical technique that measures objects in multidimensional space on the basis of respondents’ judgments of the similarity of objects
  34. 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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