Multiple Regression Analysis
MULTIPLE REGRESSION
After completing this chapter, you should be able to:
understand model building using multiple regression analysis
apply multiple regression analysis to business decision-making situations
analyze and interpret the computer output for a multiple regression model
test the significance of the independent variables in a multiple regression model
use variable transformations to model nonlinear relationships
recognize potential problems in multiple regression analysis and take the steps to correct the problems.
incorporate qualitative variables into the regression model by using dummy variables.
Multiple Regression Assumptions
The errors are normally distributed
The mean of the errors is zero
Errors have a constant variance
The model errors are independent
Model Specification
Decide what you want to do and select the dependent variable
Determine the potential independent variables for your model
Gather sample data (observations) for all variables
The Correlation Matrix
Correlation between the dependent variable and selected independent variables can be found using Excel:
Tools / Data Analysis… / Correlation
Can check for statistical significance of correlation with a t test
Example
A distributor of frozen desert pies wants to evaluate factors thought to influence demand
Dependent variable: Pie sales (units per week)
Independent variables: Price (in $)
Advertising ($100’s)
Data is collected for 15 weeks
Pie Sales Model
Sales = b0 + b1 (Price)
+ b2 (Advertising)
Interpretation of Estimated Coefficients
Slope (bi)
Estimates that the average value of y changes by bi units for each 1 unit increase in Xi holding all other variables constant
Example: if b1 = -20, then sales (y) is expected to decrease by an estimated 20 pies per
After completing this chapter, you should be able to:
understand model building using multiple regression analysis
apply multiple regression analysis to business decision-making situations
analyze and interpret the computer output for a multiple regression model
test the significance of the independent variables in a multiple regression model
use variable transformations to model nonlinear relationships
recognize potential problems in multiple regression analysis and take the steps to correct the problems.
incorporate qualitative variables into the regression model by using dummy variables.
Multiple Regression Assumptions
The errors are normally distributed
The mean of the errors is zero
Errors have a constant variance
The model errors are independent
Model Specification
Decide what you want to do and select the dependent variable
Determine the potential independent variables for your model
Gather sample data (observations) for all variables
The Correlation Matrix
Correlation between the dependent variable and selected independent variables can be found using Excel:
Tools / Data Analysis… / Correlation
Can check for statistical significance of correlation with a t test
Example
A distributor of frozen desert pies wants to evaluate factors thought to influence demand
Dependent variable: Pie sales (units per week)
Independent variables: Price (in $)
Advertising ($100’s)
Data is collected for 15 weeks
Pie Sales Model
Sales = b0 + b1 (Price)
+ b2 (Advertising)
Interpretation of Estimated Coefficients
Slope (bi)
Estimates that the average value of y changes by bi units for each 1 unit increase in Xi holding all other variables constant
Example: if b1 = -20, then sales (y) is expected to decrease by an estimated 20 pies per