MARKETING RESEARCH PART 19 docx

Ch 19 6Linear Relationships and Regression Analysis • Regression analysis is a predictive analysis technique in which one or more variables are used to predict the level of another by u

Regression Analysis

in Marketing Research

Ch 19 2

Understanding Prediction

• Prediction: statement of what is

believed will happen in the future

made on the basis of past experience

or prior observation

Understanding Prediction

Two Approaches

the past and projects it into the future

relationships among variables to make a prediction

Ch 19 4

Understanding Prediction

Goodness of Prediction

their “goodness” (accuracy)

based on examination of the

residuals (errors: comparisons of

predictions to actual values)

Analysis of Residuals

Ch 19 6

Linear Relationships and

Regression Analysis

• Regression analysis is a predictive

analysis technique in which one or

more variables are used to predict

the level of another by use of the

straight-line formula, y=a+bx

Bivariate Linear Regression

Analysis

• Bivariate regression analysis is a

type of regression in which only two variables are used in the regression, predictive model

variable (y), the other is termed the

Ch 19 8

Bivariate Linear Regression

Analysis

is used to predict another variable

of regression analysis

Bivariate Linear Regression

Analysis

regression straight-line equation)

• Dependent variable: that which is

predicted (y in the regression

straight-line equation)

• Least squares criterion: used in

regression analysis; guarantees that the “best” straight-line slope and

intercept will be calculated

Bivariate Linear Regression Analysis: Basic Procedure

slope must always be tested for

statistical significance

estimates that have some amount of error in them

• Standard error of the estimate: used

to calculate a range of the prediction made with a regression equation

Ch 19 12

Testing for Statistical Significance

of the Intercept and the Slope

whether the intercepts and slope are

significantly different from 0 (the null

hypothesis)

than the table t value, the null

hypothesis is not supported

Making a Prediction

Ch 19 14

Bivariate Linear Regression

Analysis: Basic Procedure

confidence intervals

Multiple Regression Analysis

same concepts as bivariate

regression analysis, but uses more

than one independent variable

• General conceptual model identifies independent and dependent variables and shows their basic relationships to one another

Ch 19 16

Multiple Regression Analysis:

A Conceptual Model

Multiple Regression Analysis

• Multiple regression means that you

have more than one independent

variable to predict a single dependent variable

Ch 19 18

Example of Multiple

Regression

Example of Multiple

Regression

intentions to purchase a Lexus

automobile

an attitude-toward-Lexus variable, a word-of-mouth variable, and an

income variable

Ch 19 20

Example of Multiple

Regression

means that we can predict a

consumer’s intention to buy a Lexus level if you know three variables:

Lexus, and

income grades

Example of Multiple

Regression

• Calculation of Lexus purchase intention using the multiple regression equation:

• Multiple regression is a powerful tool

because it tells us which factors predict the dependent variable, which way (the sign) each factor influences the

dependent variable, and even how much

Example of Multiple

Regression

– Independence assumption: the

independent variables must be statistically independent and uncorrelated with one another

– Variance inflation factor (VIF) can

be used to assess and eliminate multicollinearity

Ch 19 24

Multiple R

• Multiple R: also called the coefficient

of determination, is a measure of the strength of the overall linear

relationship in multiple regression

Multiple R

represents the amount of the

dependent variable is “explained,” or accounted for, by the combined

independent variables

Multiple R into a percentage: Multiple

R of 75 means that the regression

findings explain 75% of the

Ch 19 26

Multiple R

Multiple R

Ch 19 28

Multiple R

Making a Prediction

Ch 19 30

Example of Multiple Regression: Special Uses

with a nominal 0-versus-1 coding scheme

that indicate the relative importance

of alternative predictor variables

used to help a marketer apply market segmentation

Stepwise Multiple Regression

there are many independent

variables, and a researcher wants to narrow the set down to a smaller

number of statistically significant

variables

Ch 19 32

Stepwise Multiple Regression

is statistically significant and explains the most variance is entered into the multiple regression equation

independent variable is added in order of variance explained

variables are eliminated

Three Warnings Regarding Multiple Regression Analysis

cause-and-effect statement

applied outside the boundaries of

data used to develop the regression model

analysis is complex and requires

additional study

Ch 19 34

Regression Analysis

Regression Analysis