brm multi var

8/12/2019 BRM Multi Var

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March 21, 2014

1

Business Research Methods

Multivariate Analysis & Use of StatisticalPackages


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March 21, 2014

2

Topic Outline Introduction

Nature & Techniques of Multivariate Analysis

Analysis of Dependence

Multiple Regression Regression Model

Dummy Variable Treatments

Discriminant Analysis

Factor Analysis Cluster analysis

Applications of SPSS

Topic & Structure of the lesson


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March 21, 2014

3

Learning Outcomes

On completion of this chapter you should beable to understand:

how to classify and select multivariate techniques

multiple regression applications

how multivariate analysis of variance assesses the relationship

between two or more metric dependent variables and independent

classificatory variables

how principal components analysis extracts uncorrelated factorsfrom an initial set of variables and exploratory factor analysis

reduces the number of variables to discover the underlying

constructs


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Classifying Multivariate Techniques20-4

InterdependencyDependency


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Multivariate Techniques20-5


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Multiple Regression Analysis

Conceptualization A Path Model of a

Regression Analysis

i iY k b x b x b x e

1 1 2 2 3 3

Path Diagram of A Linear Regression

Analysis

YY

X1

X2

x3

error

Have a clear notion of what you can andcannot do with regression analysis


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Multiple Regression

Multiple Independent Variables (IVs):X1,X2,X3Xk Independent Variables can be correlated with one

another and with dependent variable to varying degrees Exploring relationship between IVs and DV: Xs vs. Y;

Regressing Xs onto Y

Dependent variable(Y)

User decision to use the

information

Independent Variables (Xs)

-Information Accuracy

-Information Relevancy

-Ease of use


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Goals of Multiple Regression

Investigation of many-to-one relationships where independentvariables are imperfectly related to the dependent variable

To ascertain the overall degree of relationship treating thevariables as a set (Multiple R)

To determine the usefulness of particular IVs as predictors andto compare the usefulness of different IVs

To determine if adding a particular IV to an existing set of IVsmeaningfully improves prediction

To assess the interaction of particular pairs of IVs (or, less often,

higher order interactions) To use a previously established set of regression coefficients to

predict DV scores for members of a new sample


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Generalized Regression Equation20-12


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Multiple Regression: Practical Consideration

1)Degrees of Relationship

How good is the regression equation?

Example: Can one predict user decision of usinginformation given computer system capabilities andservice accessibility?

2) Importance of IVs

Which IV is more important in the regression equationand which IVs are not.

Example: Is experience helpful in predicting theoutcome of doctors information seeking activities ORgender, age, hours work also influence the outcome?


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3)Adding IVs

Can we improve our prediction? If yes, which IV to addin?

Example: Is prediction of information seeking behaviorsof doctors enhanced by adding library usage variable tothe four variables included in the model (experience,age, gender & hours work)?

4) Changing IVs

Researchers may include nonlinear relationships in theanalysis by redefining IVs( e.g. Curvelinearrelationship)


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5)Comparing Set of Independent Variables

Given 2 set of predictors, which set can predict better theDV.

Example: Is prediction of the use of information sourcesin a company based on individual characteristics (age,gender, experience) or based on organizationalresources (staff, budget for attending annualconferences)


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6) Predicting DV scores for Members of a New Sample

Predict DV based on available IV data

Regression equation is developed from a portion of asample and then applied to other portion of thesample.

If solution generalizes, the regression equation predictsDV scores better than chance for the new cases, aswell.


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Test for Multiple Regression

Ho: All regression coefficients are zero (B1= B2 =Bk=0)H1: Not all of the coefficients are zero

To test the regression relation between DV and Ivs

F statistic

)1()1(

*2

2

kNR

k

R

F

s

s

F*>F(k, N-k-1), Reject Ho; significant relationship between DV

and IVs.


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Multiple Regression Example


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Model

R2

Adj R2

VariablesIncluded Unstandardize

d

Coefficients

Standardized

Coefficients

StandardError

1 .45 .445 Constant

X3

33.33

1.67 0.85 0.33

2 .73 .722 Constant

X3

X5

23.76

1.48

2.75

0.66

0.85

0.28

0.62

3 .75 .732 Constant

X3

X5

X1

22.84

1.32

2.40

3.66

0.55

0.95

0.14

0.25

0.58

2.75

4 .77 .71 Constant

X3

X5X1

X4

18.96

1.15

1.894.22

1.80

0.33

0.850.11

0.05

0.28

0.723.15

2.77

Interpret R & R2 for all the Models.

Interpret R2 and Adjusted R2 for Model 1.

Among all the models which one would you choose finally to adopt for determining the price of the automobile spare part. Give

reason(s)

For the Model you would chose, indicate the relative importance of the independent variables.

Ex. A student collected 25 data points in order to carry out a regression estimation for the Price of the Automobile Spare Part based

on the several independent variable which were designated as X1, X2, X3, X4 and X5. He performed stepwise regression. The results

were as follows:


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Ex. Consider the issue of Gender discrimination in the salary earning of women in Manufacturing Industry. In examining this issue, a

random sample of 15 workers is drawn from a pool of employed laborer and the workers monthly salary is determined, along with their

age and gender. A gender can only be male or female. Let 1 denote male and 0 denote female. The following output was obtained:

Model R R Square Adjusted R Square Std. Error of the Estimate

Sig.

1 .943 .890 .872 96.79158 .000

Model Summary

Model Unstandardized Coefficients Standardized

Coefficients

t

Sig.

Beta Std. Error Beta

1 Constant 732.061 235.584 3.107 .009

Age 11.122 7.208 .158 1.543 .149

Gender 458.684 53.458 .877 8.580 .000

Coefficients

Determine

I)The two estimating equations for male and female

II)Interpret the table

III)By what amount does the equation suggest males and females are paid higher than the female.


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Selection Methods20-21

Forward

Backward

Stepwise


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Researcher often wishes to classify people or objectsin to two or more groups. One might need to classifypersons as eitherbuyers or non-buyers, good orbad credit risks, or to classify superior,average or poor products in some market.

The objective is to establish a procedure to find the

predictors that best classify subjects.

Discriminant Analysis is frequently used in marketsegmentation research.

20-22


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Similarities and Differences between ANOVA,Regression, and Discriminant Analysis

23

ANOVA REGRESSION DISCRIMINANT ANALYSIS

SimilaritiesNumber of One One Onedependent

variablesNumber ofindependent Multiple Multiple Multiplevariables

DifferencesNature of the

dependent Metric Metric CategoricalvariablesNature of theindependent Categorical Metric Metricvariables


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When the criterion variable has two categories, thetechnique is known as two-group discriminant analysis.

When three or more categories are involved, the technique

is referred to as multiple discriminant analysis.

The main distinction is that, in the two-group case, it ispossible to derive only one discriminant function. Inmultiple discriminant analysis, more than one function maybe computed. In general, with Ggroups and kpredictors, itis possible to estimate up to the smaller of G - 1, or k,discriminant functions.

25


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Predicted Success

Actual Group

Number

of Cases 0 1

Unsuccessful

Successful

0

1

15

15

13

86.70%

320.00%

2

13.30%

1280.00%

Note: Percent of grouped cases correctly classified: 83.33%

Unstandardized Standardized

X1

X1

X1

Constant

.36084

2.61192

.53028

12.89685

.65927

.57958

.97505

20-27

A.

B.


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Interdependency Techniques20-28

Factor Analysis

Cluster Analysis


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Factor Matrices

A

_____Unrotated Factors_____

B

__Rotated Factors__

Variable I II h2 I II

A

B

C

D

E

F

Eigenvalue

Percent of variance

Cumulative percent

0.70

0.60

0.60

0.50

0.60

0.60

2.18

36.3

36.3

-.40

-.50

-.35

0.50

0.50

0.60

1.39

23.2

59.5

0.65

0.61

0.48

0.50

0.61

0.72

0.79

0.75

0.68

0.06

0.13

0.07

0.15

0.03

0.10

0.70

0.77

0.85

20-30


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Orthogonal Factor Rotations


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Correlation Coefficients, Metro U MBA Study

Variable Course V1 V2 V3 V10

V1

V2

V3

V4V5

V6

V7

V8

V9

V10

Financial Accounting

Managerial Accounting

Finance

MarketingHuman Behavior

Organization Design

Production

Probability

Statistical Inference

Quantitative Analysis

1.00

0.56

0.17

-.14-.19

-.21

-.44

0.30

-.05

-.01

0.56

1.00

-.22

0.05-.26

-.00

-.11

0.06

0.06

0.06

.017

-.22

1.00

-.48-.05

-.56

-.04

0.07

-.32

0.42

-.01

0.06

0.42

-.10-.23

-.05

-.08

-.10

0.06

1.00


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Factor Matrix, Metro U MBA Study

Variable Course Factor 1 Factor 2 Factor 3 Communality

V1

V2

V3

V4V5

V6

V7

V8

V9

V10

Eigenvalue

Percent of variance

Cumulative percent



Finance


Organization Design

Production

Probability



0.41

0.01

0.89

-.600.02

-.43

-.11

0.25

-.43

0.25

1.83

18.30

18.30

0.71

0.53

-.17

0.21-.24

-.09

-.58

0.25

0.43

0.04

1.52

15.20

33.50

0.23

-.16

0.37

0.30-.22

-.36

-.03

-.31

0.50

0.35

0.95

9.50

43.00

0.73

0.31

0.95

0.490.11

0.32

0.35

0.22

0.62

0.19


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Varimax Rotated Factor Matrix

Variable Course Factor 1 Factor 2 Factor 3

V1

V2

V3

V4V5

V6

V7

V8

V9

V10



Finance


Organization Design

Production

Probability



0.84

0.53

-.01

-.11-.13

-.08

-.54

0.41

0.07

-.02

0.16

-.10

0.90

-.24-.14

-.56

-.11

-.02

0.02

0.42

-.06

0.14

-.37

0.65-.27

-.02

-.22

-.24

0.79

0.09


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Cluster Analysis

Select sample to cluster

Define variables

Compute similarities

Select mutually exclusive clusters

Compare and validate cluster


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Cluster Analysis


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Cluster Membership

________Number of Clusters ________

Film Country Genre Case 5 4 3 2

Cyrano de Bergerac

Il y a des Jours

Nikita

Les Noces de Papier

Leningrad Cowboys . . .

Storia de Ragazzi . . .

Conte de Printemps

Tatie Danielle

Crimes and Misdem . . .

Driving Miss Daisy

La Voce della Luna

Che Hora E

Attache-Moi

White Hunter Black . . .

Music Box

Dead Poets Society

La Fille aux All . . .

Alexandrie, Encore . . .

Dreams

France

France

France

Canada

Finland

Italy

France

France

USA

USA

Italy

Italy

Spain

USA

USA

USA

Finland

Egypt

Japan

DramaCom

DramaCom

DramaCom

DramaCom

Comedy

Comedy

Comedy

Comedy

DramaCom

DramaCom

DramaCom

DramaCom

DramaCom

PsyDrama

PsyDrama

PsyDrama

PsyDrama

DramaCom

DramaCom

1

4

5

6

19

13

2

3

7

9

12

14

15

10

8

11

18

16

17

1

1

1

1

2

2

2

2

3

3

3

3

3

4

4

4

4

5

5

1

1

1

1

2

2

2

2

3

3

3

3

3

4

4

4

4

3

3

1

1

1

1

2

2

2

2

3

3

3

3

3

3

3

3

3

3

3

1

1

1

1

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2


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Dendogram

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