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7/28/2019 Ch 24 Multi Variate
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Business
Research Methods
William G. Zikmund
Chapter 24Multivariate 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 multivariate
methods
Are some of the
variables dependent
on others?
YesNo
Dependence
methods
Interdependence
methods
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 basisof two or more independent variables
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Dependence
Methods
How many
variables are
dependent
One dependent
variable
Several
dependent
variables
Multiple
independent
and dependentvariables
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Dependence
Methods
How many
variables are
dependent
One dependent
variable
NonmetricMetric
Multiple
discriminant
analysis
Multiple
regression
analysis
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Dependence
Methods
How many
variables are
dependent
NonmetricMetric
Conjoint
analysis
Multivariate
analysis of
variance
Several
dependent
variables
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Dependence
Methods
How many
variables are
dependent
Multiple
independent
and dependent
variables
Metric
or
nonmetric
Canonical
correlation
analysis
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Interdependence Methods
A category of multivariate statistical
techniques; interdependence methods give
meaning to a set of variables or seek togroup things together
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Interdependence
methods
Are inputs metric?
Metric Nonmetric
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Metric
Metric
multidimensional
scaling
Cluster
analysis
Factor
analysis
Interdependence
methods
Are inputs metric?
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Nonmetric
Nonmetric
Interdependence
methods
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= a +b1X1 +b2X2+b3X3...+bnXn
Multiple Regression Equation
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2211 XXaY bb ++
nnXX bb +++ .....33
Multiple Regression Analysis
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Coefficients
of Partial Regression
b1
Independent variables correlated with one
another
The % of the variance in the dependent
variable that is explained by a single
independent variable, holding otherindependent 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 inthe 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/
/
knSSekSSrF
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/()(
/)(
knSSe
kSSr
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 applicants discriminant score
bn = discriminant coefficient for the nth
variable
Xni =applicants value on the nth
independent variable
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iii XbXbZ 2211 +ninXb++ ........
Discriminant Analysis
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= applicants value on the jth independent
variable
= discriminant coefficient for the jth
variable
= ithapplicants discriminant score
jiX
jb
iZ
Discriminant Analysis
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Canonical Correlation
Two or more criterion variables (dependent
variables)
Multiple predictor variables (independentvariables)
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 tosummarize the information contained in a
large number of variables into a smaller
number of factors.
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Height
Weight
Occupation
Education
Source of
Income
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 ofobjects
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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 moredependent variables