1. Learning Objectives Copyright © 2002 South-Western/Thomson Learning Multivariate Data Analysis CHAPTER seventeen

2. Learning Objectives 1. To define multivariate data analysis. 2. To describe multiple regression analysis and multiple discriminant analysis. 3. To learn about factor analysis and cluster analysis. 4.To gain an appreciation of perceptual mapping. 5.To develop an understanding of conjoint analysis.

3. Learning Objectives Statistical procedures that simultaneously analyze multiple measurements on each individual or object under study Extensions of univariate and bivariate statistical procedures. To define multivariate analysis. Multivariate Analysis

4. Learning Objectives Multivariate Software To describe multiple regression analysis and multiple discriminant analysis. SPSSSTATISTICA  Both offer: Technical support. product information, downloads, reviews Examples of successful applications of multivariate analysis Discussion of data mining and data warehousing applications Go to www.spss.com

5. Learning Objectives Multiple Regression Analysis To describe multiple regression analysis and multiple discriminant analysis. Multiple Regression Analysis Defined To predict the level or magnitude of a dependent variable based on the levels of more than one independent variable The general equation: Y = a + b 1 X 1 + b 2 X 2 + b 3 X 3 +... + b n X n Y = dependent variable a = estimated constant b - b n = coefficients of predictor variables X - X n = predictor variables

6. Learning Objectives To describe multiple regression analysis and multiple discriminant analysis. Possible Applications of Multiple Regression Estimating the effects various marketing mix variables have on sales or share. Estimating the relationship between various demographic or psychological factors. Determine the relative influence of individual satisfaction elements on overall satisfaction. Multiple Regression Analysis

7. Learning Objectives To describe multiple regression analysis and multiple discriminant analysis. Quantifying the relationship between various classification variables, such as age and income. Determining which variables are predictive of sales of a product or service. Multiple Regression Analysis

8. Learning Objectives To describe multiple regression analysis and multiple discriminant analysis. Multiple Regression Analysis Measures Coefficient of Determination (R 2 ) Assumes values from 0 to 1 Provides a measure of the percentage of the variation in the dependent variable that is explained by variation in the independent variables. Multiple Regression Analysis

9. Learning Objectives To describe multiple regression analysis and multiple discriminant analysis. Regression Coefficients ( b values) Values that indicate the effect of the individual independent variables on the dependent variable. Dummy Variables Nominally scaled independent variables such as gender, marital status, occupation, or race Multiple Regression Analysis

10. Learning Objectives To describe multiple regression analysis and multiple discriminant analysis. Potential Problems in Using and Interpreting Multiple Regression Analysis Collinearity The correlation of independent variables with each other. Can bias b estimates Causation Regression cannot prove causation. Multiple Regression Analysis

11. Learning Objectives To describe multiple regression analysis and multiple discriminant analysis. Scaling of Coefficients Coefficients can be compared only if scaled in the same units. Sample Size The number of observations should be equal to at least 10 to 15 times the number of predictor variables. Multiple Regression Analysis

12. Learning Objectives Discriminant Analysis To describe multiple regression analysis and multiple discriminant analysis. Discriminant Analysis Defined A procedure for predicting group membership on the basis of two or more independent variables. Goals of multiple discriminant analysis: Determine statistically differences between the average discriminant score profiles.

13. Learning Objectives To describe multiple regression analysis and multiple discriminant analysis. Establish a model for classifying individuals or objects into groups on the basis of their values on the independent variables Determine how much of the difference in the average score profiles is accounted for by each independent variable. Discriminant score The basis for predicting which group an object belongs. Discriminant Analysis

14. Learning Objectives To describe multiple regression analysis and multiple discriminant analysis. Possible Applications of Discriminant Analysis How are consumers different? How do consumers with high purchase probabilities for a new product differ from low purchase probabilities? How do consumers that frequently go to one fast food restaurant differ from those who do not. Discriminant Analysis

15. Learning Objectives Cluster Analysis To learn about factor analysis and cluster analysis. Cluster Analysis Defined Classifying objects or people into some number of mutually exclusive and exhaustive groups on the basis of two or more classification variables.

16. Learning Objectives Figure 17.1 Cluster Analysis Based on Two Variables Cluster 1 Cluster 2Cluster 3 Frequency of Eating Out Frequency of Going to Fast Food Restaurants W X Z Y

17. Learning Objectives Figure 17.2 Average Attribute Ratings - 3 Clusters Cluster 1 Cluster 2 Cluster 3 4 5 6 7 8 9 10 RangeMobilitySoundPlacePreceivAvgbilTelephoneInstall Average rating Attribute

18. Learning Objectives Factor Analysis To learn about factor analysis and cluster analysis. Factor Analysis Defined Data simplification through reducing a set of variables to a smaller set of factors by identifying dimensions underlying the data. Factor Scores Produces composite variables when applied to a number of variables. A factor is a weighted summary score of a set of related variables.

19. Learning Objectives To learn about factor analysis and cluster analysis. Factor Loadings The correlation between each factor score and each of the original variables. Naming Factors Combine intuition and knowledge of the variables with an inspection of the variables that have high loadings on each factor. How Many Factors? Look at the percent of variation. Factor Analysis

20. Learning Objectives Perceptual Mapping To learn about factor analysis and cluster analysis. Perceptual Mapping Defined Visual representations of consumer perceptions of products, brands, companies, or other objects. Producing Perceptual Maps Approaches include: factor analysis multidimensional scaling discriminant analysis correspondence analysis

21. Learning Objectives Figure 17.3 Sample Perceptual Map Good Poor SlowFast Value Service Restaurant A Restaurant B Restaurant C Restaurant D

22. Learning Objectives Conjoint Analysis To develop an understanding of conjoint analysis. Overview of Conjoint Analysis To quantify the value that people associate with different levels of product/service attributes. Limitations Suffers from artificiality: Respondents may be more deliberate than in a real situation. Respondents may have additional information.

23. Learning Objectives Multivariate Analysis Multivariate Software Multiple Regression Analysis Discriminant Analysis Cluster Analysis Factor Analysis Perceptual Mapping Conjoint Analysis SUMMARY

24. Learning Objectives The End Copyright © 2002 South-Western/Thomson Learning