Chapter Seventeen Copyright © 2004 John Wiley & Sons, Inc. Multivariate Data Analysis

Learning Objective John Wiley & Son, Inc 2 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. Learning Objectives

Learning Objective John Wiley & Son, Inc 3 To define multivariate analysis. Multivariate Analysis Statistical procedures that simultaneously analyze multiple measurements on each individual or object under study –Extensions of univariate and bivariate statistical procedures. –Techniques for Multivariate Analysis Multiple regression analysis Multiple discriminant analysis Cluster analysis Factor analysis Perceptual mapping Conjoint analysis

Learning Objective John Wiley & Son, Inc 4 Multivariate Software Go to SPSS –Technical support. product information, downloads, reviews –Examples of successful applications of multivariate analysis –Discussion of data mining and data warehousing applications

Learning Objective John Wiley & Son, Inc 5 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 + b1X1 + b2X2 + b3X bnXn where –Y = dependent variable –a = estimated constant –b - bn = coefficients of predictor variables –X - Xn = predictor variables

Learning Objective John Wiley & Son, Inc 6 To describe multiple regression analysis and multiple discriminant analysis. Multiple Regression 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 –Quantifying the relationship between various classification variables, such as age and income. –Determining which variables are predictive of sales of a product or service

Learning Objective John Wiley & Son, Inc 7 Multiple Regression Analysis 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. Regression Coefficients ( b values) –Values that indicate the effect of the individual independent variables on the dependent variable.

Learning Objective John Wiley & Son, Inc 8 Multiple Regression Analysis To describe multiple regression analysis and multiple discriminant analysis. Dummy Variables –Dichotomous Nominally Scaled Independent Variables Transformed into dummy variables by coding one value –Nominally Scaled Independent Variables gender, marital status, occupation, or race

Learning Objective John Wiley & Son, Inc 9 Multiple Regression Analysis 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.

Learning Objective John Wiley & Son, Inc 10 Multiple Regression Analysis To describe multiple regression analysis and multiple discriminant analysis. –Scaling of Coefficients Coefficients can be compared only if scaled in the same units or data has been standardized. –Sample Size Value of R 2 influenced by the number of predictor variables relative to sample size The number of observations should be equal to at least 10 to 15 times the number of predictor variables.

Learning Objective John Wiley & Son, Inc 11 Discriminant Analysis To describe multiple regression analysis and multiple discriminant analysis. Discriminant Analysis Defined –A procedure for predicting group membership for a (nominal or categorical) dependent variable on the basis of two or more independent variables.

Learning Objective John Wiley & Son, Inc 12 Discriminant Analysis To describe multiple regression analysis and multiple discriminant analysis. Goals of multiple discriminant analysis: –Determine statistically differences between the average discriminant score profiles of two or more groups –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.

Learning Objective John Wiley & Son, Inc 13 Discriminant Analysis To describe multiple regression analysis and multiple discriminant analysis. General discriminant analysis equation Z=b 1 X 1 + b 2 X 2 + ···· b n X n where Z = discriminant score b 1 - b n = discriminant weights X 1 -X n = independent variables –Discriminant score Referred to as the Z score –Discriminant coefficients Computed by means of the discriminant analysis program

Learning Objective John Wiley & Son, Inc 14 Discriminant Analysis 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.

Learning Objective John Wiley & Son, Inc 15 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.

Learning Objective John Wiley & Son, Inc 16 Exhibit 17.4 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

Learning Objective John Wiley & Son, Inc 17 Exhibit 17.6 Average Attribute Ratings - 3 Clusters Cluster 1 Cluster 2 Cluster RangeMobilitySoundPlacePreceivAvgbilTelephoneInstall Average rating Attribute

Learning Objective John Wiley & Son, Inc 18 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 –Factor—Linear combination of variables. –Factor Score—calculated on each subject in the data set

Learning Objective John Wiley & Son, Inc 19 To learn about factor analysis and cluster analysis. Factor 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.

Learning Objective John Wiley & Son, Inc 20 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

Learning Objective John Wiley & Son, Inc 21 Exhibit Sample Perceptual Map Good Poor SlowFast Value Service Restaurant A Restaurant B Restaurant C Restaurant D

Learning Objective John Wiley & Son, Inc 22 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. –Seeing promotions of a new product can create consumer perceptions that differ from those created by descriptions used in a survey

Learning Objective John Wiley & Son, Inc 23 Multivariate Analysis Multivariate Software Multiple Regression Analysis Multiple Discriminant analysis Cluster Analysis Factor Analysis Perceptual Mapping Conjoint Analysis SUMMARY

Learning Objective John Wiley & Son, Inc 24 The End Copyright © 2004 John Wiley & Son, Inc