Instructor’s Manual
CHAPTER 18
Multivariate Data Analysis
LEARNING OBJECTIVES
1. To define multivariate data analysis.
3. To learn about cluster analysis and factor analysis.
5. To gain an appreciation of perceptual mapping.
KEY TERMS
Multivariate analysis
Multiple regression analysis
Coefficient of determination
Regression coefficients
Dummy variables
Discriminant coefficient
Classification matrix
Cluster analysis
K-means cluster analysis
Factor analysis
CHAPTER SCAN
This chapter examines several methods of multivariate data analysis. These techniques are
complex, requiring computers to do the mathematics. Multiple regression analysis is the
appropriate multivariate technique if the researcher’s goal is to examine to the relationship
between two or more metric predictor variables and on metric dependent variables. Discriminant
analysis is similar to multiple regression analysis, except the dependent variable is nominal or
McDaniel & Gates – Marketing Research, 9th Edition Instructor’s Manual
categorical in nature. Cluster Analysis is used to identify objects or people that are similar in
CHAPTER OUTLINE
1. Multivariate Analysis Procedures
2. Multivariate Software
3. Multiple Regression Analysis
I. Multiple Regression Analysis
A. Multiple Regression Analysis Defined
B. Applications of Multiple Regression Analysis
C. Purpose of Multiple Regression
4. Multiple Discriminant Analysis
I. Multiple Discriminant Analysis
5. Cluster Analysis
I. Cluster Analysis
6. Factor Analysis
I. Factor Analysis
7. Conjoint Analysis
I. Conjoint Analysis
A. Conjoint Analysis Defined
8. Summary
CHAPTER SUMMARY
1. MULTIVARIATE ANALYSIS PROCEDURES
McDaniel & Gates – Marketing Research, 9th Edition Instructor’s Manual
A. Multivariate Analysis Defined
1. General term for statistical procedures that simultaneously analyze multiple measurements on
each individual or object under study
B. Six Techniques for Multivariate Analysis
1. Multiple regression analysis
3. Cluster analysis
5. Perceptual mapping
6. Conjoint analysis
See Practicing Marketing Research: Statistician: The Hot Job of the Future (p 541)
With the dramatic proliferation of digital data over the last several years, professionals in the
fields of statistics and data analysis are becoming hot commodities. At top companies like
Questions
1. Where have you recently seen the use of statistics and data analysis where you might not have
expected it? How was it being used?
2. Top companies are finding that many talented analysts and statisticians actually have
backgrounds in other disciplines such as economics, mathematics, and computer sciences. How
do you think these disciplines relate to and inform the approach to data analysis?
See Exhibit 18.1 Brief Descriptions of Multivariate Analysis Procedures (p 542)
2. MULTIVARIATE SOFTWARE
1. Running the various types of analyses presented in this text requires appropriate software.
2. There is a wide variety of outstanding Window software available for multivariate analysis.
SPSS for Windows is one of the best and the most widely used by professional marketing
543)
1. What questions do you think you should be asking when choosing a multivariate analysis
technique?
2. Have you ever done a project in which the analytical technique chosen was not the best fit?
What difficulties did you encounter as a result?
3. MULTIPLE REGRESSION ANALYSIS
I. Multiple Regression Analysis
A. Multiple Regression Analysis Defined
1. Procedure for predicting the level or magnitude of a (metric) dependent variable based on the
levels of multiple independent variables
2. General Equation for Multiple Regression:
Y = a + b1X1 + b2X2 + b3X3 + . . . bnXn
where
Y = dependent or criterion variable
a = estimated constant
B. Applications of Multiple Regression Analysis
2. Estimating the relationship between various demographic or psychographic factors and
frequency of visiting fast food restaurants or other service businesses.
4. Quantifying the relationship between various classification variables, such as age and income,
and overall attitude toward a product or service.
5. Determining which variables are predictive of sales of a particular product or service.
McDaniel & Gates – Marketing Research, 9th Edition Instructor’s Manual
C. Purposes of Multiple Regression Analysis
2. Understanding the relationship between the independent variables and the dependent variable
D. Multiple Regression Analysis Measures
1. Coefficient of Determination, R2–measure of the percentage of the variation in the dependent
variable explained by variations in the independent variables
1) We determine the likelihood that each individual b value is the result of chance (H0: bn = 0)
E. Dummy Variables
1. Dummy Variables–nominally scaled independent variables
3. Nominally Scaled Independent Variables–can assume more than two values, a slightly
different approach is required.
a. Example: A question regarding racial group with three categories: African American,
F. Potential Use and Interpretation Problems
1. Collinearity – A key assumption when interpreting multiple regression results is that the
independent variables are not correlated (collinear) with each other.
c. Strategies for dealing with collinearity
1) If two variables are heavily correlated, one variable can be dropped
McDaniel & Gates – Marketing Research, 9th Edition Instructor’s Manual
2. Causation–Regression analysis can show that variables are correlated, but it cannot prove
causation.
3. Scaling of Coefficients
a. Magnitudes of regression coefficients can be compared directly only if they are scaled in the
4. Sample Size
a. The value of R2 is influenced by the number of predictor variables relative to sample size.
4. MULTIPLE DISCRIMINANT ANALYSIS
I. Multiple Discriminant Analysis
A. Multiple 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
2. Goals of Multiple Discriminant Analysis
a. To determine if there are statistically significant differences between the average discriminant
3. General Discriminant Analysis Equation
Z = b1X1 + b2X2 + . . . + bnXn
where
4. Discriminant Score–a score that is the basis for predicting to which group a particular object
or individual belongs; also called Z-score
5. Discriminant Coefficient–estimate of the discriminatory power of a particular independent
variable; also called discriminatory weight
B. Applications of Discriminant Analysis
1. Questions Answered by Discriminant Analysis
a. How are consumers who purchase various brands different from those who do not purchase
those brands?
b. How do consumers who show high purchase probabilities for a new product differ in
demographic and lifestyle characteristics from those with low purchase probabilities?
C. Example of Multiple Discriminant Analysis
United’s marketing director wants to predict whether or not the five importance ratings used in
the regression analysis predict whether or not an individual currently has a wireless telephone.
McDaniel & Gates – Marketing Research, 9th Edition Instructor’s Manual
telephone service. The model correctly predicted 73% of all respondents as wireless users or
nonusers.
See Exhibit 18.3 Classifications Matrix (pcstext.sta) (p 553)
See SPSS Jump Start for Multiple Discriminant Analysis (p 554-555)
5. CLUSTER ANALYSIS
I. Cluster Analysis
A. Cluster Analysis Defined–the term cluster analysis is used to refer to a group of techniques
used to identify objects or people that are similar in regard to certain variables or measurements.
1. Purpose–to classify objects or people into some number of mutually exclusive and exhaustive
B. Procedures for Clustering
1. Different Procedures–but all are similar in their general approach, which involves measuring
2. Scatter Plots– in the case of two clustering variables, the dots indicate the positions of
consumers with respect to the variables. The distance between any pair of dots is negatively
See Exhibit 18.4 Cluster Analysis Based on Two Variables (p 556)
3. Computer algorithms–the basic idea behind most of the algorithms is to start with some
arbitrary cluster boundaries and modify the boundaries until a point is reached where the average
C. Example of Cluster Analysis
Cluster analysis was performed using the K-means cluster analysis procedure. Cluster analysis
does not produce a “best” solution, so several were tried before a three-cluster solution was
chosen.
See Exhibit 18.5 Cluster Sizes and Average Ratings on Attribute Importance Variables (p
557)
McDaniel & Gates – Marketing Research, 9th Edition Instructor’s Manual
See Exhibit 18.6 Average Attribute Importance Ratings for Three Clusters (p 558)see From
The Frontline: How to Segment a Market Using Cluster Analysis (p 559-560)
2.Research objectives, past experience, knowledge of the market, qualitative research and
analysis of the available data may all be used to identify the best basis variable candidates.
4. Once your basis variables are determined, running a cluster analysis is very easy. Just input
6. FACTOR ANALYSIS
I. Factor Analysis
A. Factor Analysis Defined
1. Procedure for simplifying data by reducing a large set of variables to a smaller set of factors or
composite variables by identifying underlying dimensions of the data
a. Objective–to summarize the information contained in a large number of measures into a
See Exhibit 18.7 Importance Ratings of Luxury Automobile Features (p 561)
See Exhibit 18.8 Average Ratings of Two Factors (p 562)
B. Factor Scores
1. Factor–technical definition “a linear combination of variables”–weighted summary score of a
set of related variables.
2. Factor Analysis–each measure is first weighted according to how much it contributes to the
variation of each factor
3. Factor Score–calculated on each subject in the data set.
McDaniel & Gates – Marketing Research, 9th Edition Instructor’s Manual
4. Relative Sizes–of the scoring coefficients are used in determining relative importance of each
variable.
C. Factor Loadings
1. Correlation between each factor score and each of the original variables
2. Nature of the Factors Derived–determined by examining the factor loadings
See Exhibit 18.9 Factor Loadings for Two Factors (p 562)
D. Naming Factors
1. Identify Factors–the next step is to “name” the factors–name should communicate the
concept that the researcher feels the questions are measuring
E. Number of Factors to Retain
1. Final Results –one factor or up to as many factors as there are variables
2. Decision–determined by the percent of the variation explained by each factor
564)
F. Example of Factor Analysis
United is interested in identifying those attributes that go together to identify clusters of benefits
that are associated in the minds of target customers. This will allow United to design marketing
See Exhibit 18.11 Factor Loadings (Varimax raw) (pcstext.sta) Extraction: Principal
Components (p 524)
7. CONJOINT ANALYSIS
I. Conjoint Analysis
A. Conjoint Analysis Defined
1. Procedure used to quantify the value that consumers associate with different levels of
2. Conjoint Analysis
a. Is not a completely standardized procedure
b. Involves a series of steps covering a variety of procedures
B. Example of Conjoint Analysis
1. Golf Ball Manufacturer – Titleist, a major manufacturer of golf balls conducted a focus group
recently and determined from this group, past research studies, and personal experience that the
2. Approach
a. Traditional Approach
See Exhibit 18.12 Traditional Nonconjoint Rankings of Distance and Ball Life Attributes (p
566)
b. Considering Features Conjointly
1) Respondents are asked to evaluate features conjointly or in combination.
See Exhibit 18.13 Conjoint Rankings of Combinations of Distance and Ball Life for Golfer
1 (p 566)
See Exhibit 18.14 Conjoint Rankings of Combinations of Distance and Ball Life for Golfer
2 (p 566)
c. Estimating Utilities
1) The researcher calculates a set of values, referred to as utilities, for each attribute levels.
See Exhibit 18.15 Ranks (in parentheses) and Combined Metric Utilities for Golfer 1–
Distance and Ball Life (p 567)
See Exhibit 18.16 Conjoint Rankings of Combinations of Price and Ball Life for Golfer 1 (p
567)
See Exhibit 18.17 Ranks ( in parentheses) and Combined Metric Utilities for Golfer 1–Price
and Ball Life (p 567)
See Exhibit 18.18 Complete Set of Estimated Utilities for Golfer 1 (p 568)
d. Simulating Buyer Choice
1) Three steps discussed–collecting trade-off data, using the data to estimate buyer preference
structures, and predicting choice–are the basis of any conjoint analysis application
See Exhibit 18.19 Ball Profiles for Simulation (p 568)
See Exhibit 18.20 Estimated Total Utilities for the Two Sample Profiles (p 568)
C. Limitations of Conjoint Analysis
1. Conjoint analysis suffers from a certain degree of artificiality
3. The survey may provide more product information than respondents would get in a real
market situation
4. It is important to remember that the advertising and promotion of any new product or service
can lead to consumer perceptions that are very different from those created via descriptions used
in a survey
D. Data Mining
Data mining is a relatively new field that draws upon statistics (including all of the tools
E. Data Mining Process
The actual data mining process typically involves four classes of tasks i.e., clustering,
classification, modeling and application.
F. Results Validation
G. Privacy Concerns and Ethics
Most believe that data mining itself is ethically neutral. However, the ways in which data mining
H. Commercial Data Mining Software and Applications
There are an increasing number of highly integrated packages for data mining, including:
8. SUMMARY
QUESTIONS FOR REVIEW AND CRITICAL THINKING
1. Distinguish between multiple discriminant analysis and cluster analysis. Give several
examples of situations in which each might be used.
Multiple discriminant analysis analyzes the relationships between a set of metric independent
variables and a nominal or categorical dependent variable. It can test a hypothesized relationship
2. What purpose does multiple regression analysis serve? Give an example of how it might
be used in marketing research. How is the strength of multiple regression measures of
association determined?
Multiple regression analysis is used to examine the relationship between two or more metric
predictor variables and one metric dependent variable. It can also be used to generate predictions
3. What is a dummy variable? Give an example using a dummy variable.
4. Describe the potential problem of collinearity and multiple regression. How might a
researcher test for collinearity? If collinearity is a problem, what should the researcher do?
Collinearity refers to the condition when a significant correlation exists between two or more
independent variables. This condition reduces the statistical power of significance tests for the
5. A sales manager examined age data, education level, a personality measure that
indicated introvertedness / extrovertedness, and levels of sales attained by the company’s
120-person sales force. The technique used was multiple regression analysis. After
analyzing the data, the sales manager said, “It is apparent to me that the higher level of
education and the greater the degree of extrovertedness a salesperson has, the higher will
be an individual’s level of sales. In other words, a good education and being extroverted
cause a person to sell more.” Would you agree or disagree with the sales manager’s
conclusions? Why?
The manager should consider whether age and education are correlated (collinearity), as older
salespersons may have greater education and thus the “education effect” may really be an
“age/experience effect.” It is also plausible that the extroverted salespersons are also older, as
6. The factors produced and the result of the factor loadings from factor analysis are
mathematical constructs. It is the task of the researcher to make sense out of these factors.