9: Examining Relationships in Quantitative Research

ESSENTIALSESSENTIALS OF MARKETING RESEARCHOF MARKETING RESEARCHHair/Wolfinbarger/Ortinau/BushHair/Wolfinbarger/Ortinau/Bush

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Relationships between Variables

Is there a relationship between the two variables we are interested in?

How strong is the relationship?How can that relationship be best

described?

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Describing Relationships Between Variables

Presence Direction

Strengthof association

Type

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Covariation and Variable Relationships

Covariation is amount of change in one variable that is consistently related to the change in another variable

A scatter diagram graphically plots the relative position of two variables using a horizontal and a vertical axis to represent the variable values

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Exhibit 13.1 Scatter Diagram Illustrates No Relationship

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Exhibit 13.2 Positive Relationship between X and Y

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Exhibit 13.3 Negative Relationship between X and Y

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Exhibit 16.4 Curvilinear Relationship between X and Y

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Correlation Analysis

Pearson Correlation Coefficient–statistical measure of the strength of a linear relationship between two metric variablesVaries between – 1.00 and +1.00The higher the correlation coefficient–the

stronger the level of associationCorrelation coefficient can be either positive

or negative

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Exhibit 13.5 Strength of Correlation Coefficients

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Exhibit 13.6 SPSS Pearson Correlation Example

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What is Regression Analysis?

A method for arriving at more detailed answers (predictions) than can be provided by the correlation coefficient

AssumptionsVariables are measured on interval or ratio

scalesVariables come fro a normal populationError terms are normally and independently

distributed

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Exhibit 13.9 Straight Line Relationship in Regression

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y = a + bX + ei

y = the dependent variablea = the interceptb = the slope X = the independent variable used to predict yei = the error for the prediction

Formula for a Straight Line

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Exhibit 13.10 Fitting the Regression Line Using the “Least Squares” Procedure

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Ordinary Least Squares (OLS)

OLS is a statistical procedure

that estimates regression equation

coefficients which produce

the lowest sum of squared differences

between the actual and predicted

values of the dependent variable

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Exhibit 13.11 SPSS Results for Bivariate Regression

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SPSS Results say...

Percieved reasonableness of prices is positively related to overall customer satisfaction

Th relationship is positiveBut weak! Prices and satisfaction is associated,

but there are other factors as well!!

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Multiple Regression Analysis

Multiple regression analysis is a statistical technique which analyzes the linear relationship between a dependent

variable and multiple independent variables by estimating coefficients for

the equation for a straight line

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Assess the statistical significance of the overall regression model using the F statistic and its associated probability

Evaluate the obtained r2 to see how large it is

Examine the individual regression coefficient and their t-test statistic to see which are statistically significant

Look at the beta coefficient to assess relative influence

Evaluating a Regression Analysis