34
Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Embed Size (px)

Citation preview

Page 1: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Exploring Marketing Research

William G. Zikmund

Chapter 24

Multivariate Analysis

Page 2: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Multivariate Statistical Analysis

• Statistical methods that allow the simultaneous investigation of more than two variables

Page 3: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

All multivariatemethods

Are some of thevariables dependent

on others?

Yes No

Dependencemethods

Interdependencemethods

A Classification of Selected Multivariate Methods

Page 4: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

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

Page 5: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

DependenceMethods

How manyvariables aredependent

One dependentvariable

Severaldependentvariables

Multipleindependent

and dependentvariables

Page 6: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

DependenceMethods

How manyvariables aredependent

One dependentvariable

NonmetricMetric

Multiplediscriminant

analysis

Multipleregression

analysis

Page 7: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

DependenceMethods

How manyvariables aredependent

NonmetricMetric

Conjointanalysis

Multivariateanalysis of

variance

Severaldependentvariables

Page 8: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

DependenceMethods

How manyvariables aredependent

Multipleindependent

and dependentvariables

Metricor

nonmetric

Canonicalcorrelation

analysis

Page 9: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Interdependence Methods

• A category of multivariate statistical techniques; interdependence methods give meaning to a set of variables or seek to group things together

Page 10: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Interdependencemethods

Are inputs metric?

Metric Nonmetric

Page 11: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Metric

Metricmultidimensional

scaling

Clusteranalysis

Factoranalysis

Interdependencemethods

Are inputs metric?

Page 12: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Nonmetric

Nonmetric

Interdependencemethods

Are inputs metric?

Page 13: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Multiple Regression

• An extension of bivariate regression

• Allows for the simultaneous investigation– two or more independent variables– a single interval-scaled dependent variable

Page 14: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Y= aX1X2X3...nXn

Multiple Regression Equation

Page 15: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

2211 XXaY

nnXX .....33

Multiple Regression Analysis

Page 16: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

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

Page 17: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Coefficient of Multiple Determination

• R2

• The % of the variance in the dependent variable that is explained by the variation in the independent variables.

Page 18: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

• Y = 102.18 + .387X1 + 115.2X2 + 6.73X3

• Coefficient of multiple determination (R2) .845

• F-value 14.6

Statistical Results of a Multiple Regression

Page 19: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

1/

/

knSSe

kSSrF

F-Test

Page 20: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Degrees of Freedom (d.f.) are Calculated as Follows:

• d.f. for the numerator = k

• for the denominator = n - k - 1

Page 21: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Degrees of Freedom

• k = number of independent variables

• n = number of observations or respondents

Page 22: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

where

        k = number of independent variables

        n = number of observations

)1/()(/)(

knSSekSSr

F

F-test

Page 23: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

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

Page 24: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

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

Page 25: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

iii XbXbZ 2211 ninXb ........

Discriminant Analysis

Page 26: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

= applicant’s value on the jth independent variable

= discriminant coefficient for the jth variable

= ith applicant’s discriminant score

jiX

jb

iZ

Discriminant Analysis

Page 27: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

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

Page 28: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Canonical Correlation

• Z = a1X1 + a2X2 + . . . + anXn

• W = b1Y1 + b2Y2 + . . . + bnYn

Page 29: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Factor Analysis

• Summarize the information in a large number of variables

• Into a smaller number of factors

• Several factor-analytical techniques

Page 30: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

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.

Page 31: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Height

Weight

Occupation

Education

Source ofIncome

Size

Social Status

Factor Analysis

Copyright © 2000 Harcourt, Inc. All rights reserved.

Page 32: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

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

Page 33: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

Multidimensional Scaling

• A statistical technique that measures objects in multidimensional space on the basis of respondents’ judgments of the similarity of objects

Page 34: Exploring Marketing Research William G. Zikmund Chapter 24 Multivariate Analysis

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