exploring marketing research william g. zikmund chapter 24 multivariate analysis
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Exploring Marketing Research
William G. Zikmund
Chapter 24
Multivariate Analysis
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Multivariate Statistical Analysis
• Statistical methods that allow the simultaneous investigation of more than two variables
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All multivariatemethods
Are some of thevariables dependent
on others?
Yes No
Dependencemethods
Interdependencemethods
A Classification of Selected Multivariate Methods
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Dependence Methods
• A category of multivariate statistical techniques; dependence methods explain or predict a dependent variable(s) on the basis of two or more independent variables
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DependenceMethods
How manyvariables aredependent
One dependentvariable
Severaldependentvariables
Multipleindependent
and dependentvariables
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DependenceMethods
How manyvariables aredependent
One dependentvariable
NonmetricMetric
Multiplediscriminant
analysis
Multipleregression
analysis
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DependenceMethods
How manyvariables aredependent
NonmetricMetric
Conjointanalysis
Multivariateanalysis of
variance
Severaldependentvariables
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DependenceMethods
How manyvariables aredependent
Multipleindependent
and dependentvariables
Metricor
nonmetric
Canonicalcorrelation
analysis
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Interdependence Methods
• A category of multivariate statistical techniques; interdependence methods give meaning to a set of variables or seek to group things together
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Interdependencemethods
Are inputs metric?
Metric Nonmetric
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Metric
Metricmultidimensional
scaling
Clusteranalysis
Factoranalysis
Interdependencemethods
Are inputs metric?
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Nonmetric
Nonmetric
Interdependencemethods
Are inputs metric?
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Multiple Regression
• An extension of bivariate regression
• Allows for the simultaneous investigation– two or more independent variables– a single interval-scaled dependent variable
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Y= aX1X2X3...nXn
Multiple Regression Equation
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2211 XXaY
nnXX .....33
Multiple Regression Analysis
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Coefficients of Partial Regression
Independent variables correlated with one another
The % of the variance in the dependent variable that is explained by a single independent variable, holding other independent variables constant
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Coefficient of Multiple Determination
• R2
• The % of the variance in the dependent variable that is explained by the variation in the independent variables.
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• Y = 102.18 + .387X1 + 115.2X2 + 6.73X3
• Coefficient of multiple determination (R2) .845
• F-value 14.6
Statistical Results of a Multiple Regression
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1/
/
knSSe
kSSrF
F-Test
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Degrees of Freedom (d.f.) are Calculated as Follows:
• d.f. for the numerator = k
• for the denominator = n - k - 1
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Degrees of Freedom
• k = number of independent variables
• n = number of observations or respondents
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where
k = number of independent variables
n = number of observations
)1/()(/)(
knSSekSSr
F
F-test
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Multiple Discriminant Analysis
• A statistical technique for predicting the probability of objects belonging in two or more mutually exclusive categories (dependent variable) based on several independent variables
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Zi = b1X1i + b2X2i + . . . + bnXni
• where
• Zi = ith applicant’s discriminant score
• bn = discriminant coefficient for the nth variable
• Xni = applicant’s value on the nth independent variable
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iii XbXbZ 2211 ninXb ........
Discriminant Analysis
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= applicant’s value on the jth independent variable
= discriminant coefficient for the jth variable
= ith applicant’s discriminant score
jiX
jb
iZ
Discriminant Analysis
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Canonical Correlation
• Two or more criterion variables (dependent variables)
• Multiple predictor variables (independent variables)
• An extension of multiple regression
• Linear association between two sets of variables
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Canonical Correlation
• Z = a1X1 + a2X2 + . . . + anXn
• W = b1Y1 + b2Y2 + . . . + bnYn
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Factor Analysis
• Summarize the information in a large number of variables
• Into a smaller number of factors
• Several factor-analytical techniques
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Factor Analysis
• A type of analysis used to discern the underlying dimensions or regularity in phenomena. Its general purpose is to summarize the information contained in a large number of variables into a smaller number of factors.
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Height
Weight
Occupation
Education
Source ofIncome
Size
Social Status
Factor Analysis
Copyright © 2000 Harcourt, Inc. All rights reserved.
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Cluster Analysis
• A body of techniques with the purpose of classifying individuals or objects into a small number of mutually exclusive groups, ensuring that there will be as much likeness within groups and as much difference among groups as possible
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Multidimensional Scaling
• A statistical technique that measures objects in multidimensional space on the basis of respondents’ judgments of the similarity of objects
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Multivariate Analysis of Variance (MANOVA)
• A statistical technique that provides a simultaneous significance test of mean difference between groups for two or more dependent variables