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Multivariate Analysis

(Source: W.G Zikmund, B.J Babin, J.C Carr and M. Griffin, Business Research Methods, 8th Edition, U.S, South-Western Cengage Learning, 20

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What is Multivariate Data Analysis? Research that involves three or more variables, or that is

concerned with underlying dimensions among multiple variables, will involve multivariate statistical analysis. Methods analyze multiple variables or even

multiple sets of variables simultaneously. Business problems involve multivariate data

analysis: most employee motivation research customer psychographic profiles research that seeks to identify viable market

segments

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Which Multivariate Approach Is Appropriate?

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Classifying Multivariate Techniques Dependence Techniques

Explain or predict one or more dependent variables.

Needed when hypotheses involve distinction between independent and dependent variables.

Types: Multiple regression analysis Multiple discriminant analysis Multivariate analysis of variance

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Classifying Multivariate Techniques (cont’d) Interdependence Techniques

Give meaning to a set of variables or seek to group things together.

Used when researchers examine questions that do not distinguish between independent and dependent variables.

Types: Factor analysis Cluster analysis Multidimensional scaling

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Classifying Multivariate Techniques (cont’d) Influence of Measurement Scales

The nature of the measurement scales will determine which multivariate technique is appropriate for the data.

Selection of a multivariate technique requires consideration of the types of measures used for both independent and dependent sets of variables.

Nominal and ordinal scales are nonmetric. Interval and ratio scales are metric.

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Which Multivariate Dependence Technique Should I Use?

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Which Multivariate Interdependence Technique Should I Use?

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Interpreting Multiple Regression Multiple Regression Analysis

An analysis of association in which the effects of two or more independent variables on a single, interval-scaled dependent variable are investigated simultaneously.

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Dummy variable The way a dichotomous (two group) independent

variable is represented in regression analysis by assigning a 0 to one group and a 1 to the other.

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Multiple Regression Analysis A Simple Example

Assume that a toy manufacturer wishes to explain store sales (dependent variable) using a sample of stores from Canada and Europe.

Several hypotheses are offered:

H1: Competitor’s sales are related negatively to sales.

H2: Sales are higher in communities with a sales office than when no sales office is present.

H3: Grammar school enrollment in a community is related positively to sales.

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Multiple Regression Analysis (cont’d) Regression Coefficients in Multiple

Regression Partial correlation

The correlation between two variables after taking into account the fact that they are correlated with other variables too.

R2 in Multiple Regression The coefficient of multiple determination in

multiple regression indicates the percentage of variation in Y explained by all independent variables.

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Interpreting Multiple Regression Results

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ANOVA (n-way) and MANOVA Multivariate Analysis of Variance (MANOVA)

A multivariate technique that predicts multiple continuous dependent variables with multiple categorical independent variables.

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ANOVA (n-way) and MANOVA (cont’d)Interpreting N-way (Univariate) ANOVA

1. Examine overall model F-test result. If significant, proceed.

2. Examine individual F-tests for individual variables.

3. For each significant categorical independent variable, interpret the effect by examining the group means.

4. For each significant, continuous covariate, interpret the parameter estimate (b).

5. For each significant interaction, interpret the means for each combination.

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Discriminant Analysis A statistical technique for predicting the probability that

an object will belong in one of two or more mutually exclusive categories (dependent variable), based on several independent variables. To calculate discriminant scores, the linear

function used is:

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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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Multidimensional Scaling

Multidimensional Scaling Measures objects in multidimensional space on

the basis of respondents’ judgments of the similarity of objects.