Chapter Seventeen
Multivariate
Data Analysis
Copyright © 2004
John Wiley & Sons, Inc.
Learning Objectives
Learning Objective
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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Multivariate Analysis
Learning Objective
To define 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
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Multivariate Software
Learning Objective
• SPSS
– 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
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Multiple Regression
Analysis
Learning Objective
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
• where
–
–
–
–
Y = dependent variable
a = estimated constant
b - bn = coefficients of predictor variables
X - Xn = predictor variables
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Multiple Regression
Analysis
Learning Objective
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
– Quantifying the relationship between various classification
variables, such as age and income.
– Determining which variables are predictive of sales of a
product or service
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Multiple Regression
Analysis
Learning Objective
To 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.
• Regression Coefficients ( b values)
– Values that indicate the effect of the individual
independent variables on the dependent variable.
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Multiple Regression
Analysis
Learning Objective
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
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Multiple Regression
Analysis
Learning Objective
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.
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Multiple Regression
Analysis
Learning Objective
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 R2 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.
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Discriminant Analysis
Learning Objective
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.
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Discriminant Analysis
Learning Objective
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.
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Discriminant Analysis
Learning Objective
To describe multiple regression analysis
and multiple discriminant analysis.
• General discriminant analysis equation
Z=b1X1 + b2X2 + ···· bnXn
where
Z = discriminant score
b1- bn = discriminant weights
X1-Xn = independent variables
– Discriminant score
• Referred to as the Z score
– Discriminant coefficients
• Computed by means of the discriminant analysis program
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Discriminant Analysis
Learning Objective
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.
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Cluster Analysis
Learning Objective
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.
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Exhibit 17.4 Cluster Analysis Based on Two Variables
Learning Objective
Frequency of Eating Out
Cluster 2
Cluster 3
Z
X
Y
Cluster 1
W
Frequency of Going to Fast Food Restaurants
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Exhibit 17.6 Average Attribute Ratings - 3 Clusters
Learning Objective
10
Cluster 3
Average rating
9
8
7
Cluster 1
6
Cluster 2
5
4
Range
Mobility Sound
Place
Preceiv
Avgbil Telephone Install
Attribute
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Learning Objective
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
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Factor Analysis
Learning Objective
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.
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Learning Objective
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
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Exhibit 17.14 Sample Perceptual Map
Learning Objective
Good
Value
Restaurant B
Restaurant A
Restaurant C
Restaurant D
Poor
Slow
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Service
Fast
21
Learning Objective
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
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SUMMARY
•
•
•
•
•
•
•
•
Learning Objective
Multivariate Analysis
Multivariate Software
Multiple Regression Analysis
Multiple Discriminant analysis
Cluster Analysis
Factor Analysis
Perceptual Mapping
Conjoint Analysis
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Learning Objective
The End
Copyright © 2004 John Wiley & Son, Inc
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