Regression Analysis in Marketing Research

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Regression Analysis in Marketing Research. 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. Two approaches to prediction:

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Regression Analysis in Marketing Research

Understanding Prediction
• Prediction:statement of what is believed will happen in the future made on the basis of past experience or prior observation
Understanding PredictionTwo Approaches
• Two approaches to prediction:
• Extrapolation: detects a pattern in the past and projects it into the future
• Predictive model: uses relationships among variables to make a prediction
Understanding PredictionGoodness of Prediction
• All predictions should be judged as to their “goodness” (accuracy).
• The goodness of a prediction is based on examination of the residuals (errors: comparisons of predictions to actual values).
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.
• One variable is termed the dependent variable (y), the other is termed the independent variable (x).
• The independent variableis used to predict the dependent variable, and it is the x in the regression formula.
Bivariate Linear Regression Analysis
• With bivariate analysis, one variable is used to predict another variable.
• The straight-line equation is the basis of regression analysis.
Bivariate Linear Regression Analysis: Basic Procedure
• Independent variable:used to predict the independent variable (x in the 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
• The regression model, intercept, and slope must always be tested for statistical significance
• Regression analysis predictions are 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
• The t test is used to determine whether the intercepts and slope are significantly different from 0 (the null hypothesis).
• If the computed t value is greater than the table t value, the null hypothesis is not supported.
Bivariate Linear Regression Analysis: Basic Procedure
• Regression predictions are made with confidence intervals.
Multiple Regression Analysis
• Multiple regression analysis uses the 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.
Multiple Regression Analysis
• Multiple regressionmeans that you have more than one independent variable to predict a single dependent variable
Example of Multiple Regression
• We wish to predict customers’ intentions to purchase a Lexus automobile.
• We performed a survey that included an attitude-toward-Lexus variable, a word-of-mouth variable, and an income variable.
• Here is the result:
Example of Multiple Regression
• This multiple regression equation means that we can predict a consumer’s intention to buy a Lexus level if you know three variables:
• Attitude toward Lexus,
• Income level using a scale with 10 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 (the size of b) each factor influences it.
Example of Multiple Regression
• Basic assumptions:
• A regression plane is used instead of a line
• A coefficient of determination (multiple R) indicates how well the independent variables can predict the dependent variable in multiple regression
Example of Multiple Regression
• Basic assumptions:
• 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
Multiple R
• Multiple R:also calledthe coefficient of determination, is a measure of the strength of the overall linear relationship in multiple regression.
Multiple R
• Multiple R ranges from 0 to +1 and represents the amount of the dependent variable is “explained,” or accounted for, by the combined independent variables.
• Researchers mentally convert the Multiple R into a percentage: Multiple R of .75 means that the regression findings explain 75% of the dependent variable.
Example of Multiple Regression: Special Uses
• Special uses of multiple regression:
• Dummy independent variable: scales with a nominal 0-versus-1 coding scheme
• Standardized beta coefficient: betas that indicate the relative importance of alternative predictor variables
• Multiple regression is sometimes used to help a marketer apply market segmentation
Stepwise Multiple Regression
• Stepwise regression is useful when there are many independent variables, and a researcher wants to narrow the set down to a smaller number of statistically significant variables.
Stepwise Multiple Regression
• The one independent variable that is statistically significant and explains the most variance is entered into the multiple regression equation
• Then each statistically significant independent variable is added in order of variance explained
• All insignificant independent variables are eliminated
Three Warnings Regarding Multiple Regression Analysis
• Regression is a statistical tool, not a cause-and-effect statement.
• Regression analysis should not be applied outside the boundaries of data used to develop the regression model.
• Chapter 19 is simplified…regression analysis is complex and requires additional study.