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Multivariate Analysis

Multivariate Analysis (Source: W.G Zikmund, B.J Babin, J.C Carr and M. Griffin, Business Research Methods, 8th Edition, U.S, South-Western Cengage Learning, 20. What is Multivariate Data Analysis?.

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Multivariate Analysis

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  1. Multivariate Analysis (Source: W.G Zikmund, B.J Babin, J.C Carr and M. Griffin, Business Research Methods, 8th Edition, U.S, South-Western Cengage Learning, 20

  2. What is Multivariate Data Analysis? • Research that involves three or more variables, or that is concerned with underlying dimensions among multiple variables, will involve multivariate statistical analysis. • Methods analyze multiple variables or even multiple sets of variables simultaneously. • Business problems involve multivariate data analysis: • most employee motivation research • customer psychographic profiles • research that seeks to identify viable market segments

  3. Which Multivariate Approach Is Appropriate?

  4. Classifying Multivariate Techniques • Dependence Techniques • Explain or predict one or more dependent variables. • Needed when hypotheses involve distinction between independent and dependent variables. • Types: • Multiple regression analysis • Multiple discriminant analysis • Multivariate analysis of variance

  5. Classifying Multivariate Techniques (cont’d) • Interdependence Techniques • Give meaning to a set of variables or seek to group things together. • Used when researchers examine questions that do not distinguish between independent and dependent variables. • Types: • Factor analysis • Cluster analysis • Multidimensional scaling

  6. Classifying Multivariate Techniques (cont’d) • Influence of Measurement Scales • The nature of the measurement scales will determine which multivariate technique is appropriate for the data. • Selection of a multivariate technique requires consideration of the types of measures used for both independent and dependent sets of variables. • Nominal and ordinal scales are nonmetric. • Interval and ratio scales are metric.

  7. Which Multivariate Dependence Technique Should I Use?

  8. Which Multivariate Interdependence Technique Should I Use?

  9. Interpreting Multiple Regression • Multiple Regression Analysis • An analysis of association in which the effects of two or more independent variables on a single, interval-scaled dependent variable are investigated simultaneously. • Dummy variable • The way a dichotomous (two group) independent variable is represented in regression analysis by assigning a 0 to one group and a 1 to the other.

  10. Multiple Regression Analysis • A Simple Example • Assume that a toy manufacturer wishes to explain store sales (dependent variable) using a sample of stores from Canada and Europe. • Several hypotheses are offered: • H1: Competitor’s sales are related negatively to sales. • H2: Sales are higher in communities with a sales office than when no sales office is present. • H3: Grammar school enrollment in a community is related positively to sales.

  11. Multiple Regression Analysis (cont’d) • Regression Coefficients in Multiple Regression • Partial correlation • The correlation between two variables after taking into account the fact that they are correlated with other variables too. • R2 in Multiple Regression • The coefficient of multiple determination in multiple regression indicates the percentage of variation in Y explained by all independent variables.

  12. Interpreting Multiple Regression Results

  13. ANOVA (n-way) and MANOVA • Multivariate Analysis of Variance (MANOVA) • A multivariate technique that predicts multiple continuous dependent variables with multiple categorical independent variables.

  14. ANOVA (n-way) and MANOVA (cont’d) Interpreting N-way (Univariate) ANOVA • Examine overall model F-test result. If significant, proceed. • Examine individual F-tests for individual variables. • For each significant categorical independent variable, interpret the effect by examining the group means. • For each significant, continuous covariate, interpret the parameter estimate (b). • For each significant interaction, interpret the means for each combination.

  15. Discriminant Analysis • A statistical technique for predicting the probability that an object will belong in one of two or more mutually exclusive categories (dependent variable), based on several independent variables. • To calculate discriminant scores, the linear function used is:

  16. 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.

  17. Multidimensional Scaling • Multidimensional Scaling • Measures objects in multidimensional space on the basis of respondents’ judgments of the similarity of objects.

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