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Copyright © 2002 South-Western/Thomson Learning

Multivariate Data Analysis

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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.

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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

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Multivariate SoftwareTo describe multiple regression analysis and multiple discriminant analysis.

SPSS STATISTICA

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.comGo to www.spss.com

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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 + b3X3 + . . . + bnXn

Y = dependent variable

a = estimated constant

b - bn = coefficients of predictor variables

X - Xn = predictor variables

Learning ObjectivesLearning ObjectivesTo 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

Learning ObjectivesLearning ObjectivesTo 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

Learning ObjectivesLearning ObjectivesTo describe multiple regression analysis and multiple discriminant analysis.

Multiple Regression Analysis Measures

Coefficient of Determination (R2)

• 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

Learning ObjectivesLearning ObjectivesTo 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

Learning ObjectivesLearning ObjectivesTo 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

Learning ObjectivesLearning ObjectivesTo 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

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Discriminant AnalysisTo 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.

Learning ObjectivesLearning ObjectivesTo 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

Learning ObjectivesLearning ObjectivesTo 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

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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 ObjectivesLearning ObjectivesFigure 17.1 Cluster Analysis Based on Two Variables

Cluster 1

Cluster 2 Cluster 3

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Frequency of Going to Fast Food Restaurants

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Learning ObjectivesLearning ObjectivesFigure 17.2 Average Attribute Ratings - 3 Clusters

Cluster 1

Cluster 2

Cluster 3

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Range Mobility Sound Place Preceiv Avgbil Telephone Install

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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.

Learning ObjectivesLearning 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

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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 ObjectivesLearning ObjectivesFigure 17.3 Sample Perceptual Map

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Slow Fast

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Restaurant A

Restaurant B

Restaurant C

Restaurant D

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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.

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• Multivariate Analysis

• Multivariate Software

• Multiple Regression Analysis

• Discriminant Analysis

• Cluster Analysis

• Factor Analysis

• Perceptual Mapping

• Conjoint Analysis

SUMMARY

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The End

Copyright © 2002 South-Western/Thomson Learning