ch 24 multi variate

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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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

ch 24 multi variate

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