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# Building and Testing a Multiple Linear Regression Model

After reading this chapter you will understand:

• What is meant by multicollinearity in a multiple linear regression model.
• How to detect multicollinearity and mitigate the problem caused by it.
• The model building process in the sense of ascertaining the independent variables that best explain the variable of interest.
• How stepwise regression analysis is used in model building and the different stepwise regression methods.
• How to test for the various assumptions of the multiple linear regression model and correct the model when violations are found.

In this chapter we continue with our coverage of multiple linear regression analysis. The topics covered in this chapter are the problem of multicollinearity, model building techniques using stepwise regression analysis, and testing the assumptions of the models that were described in Chapter 3.

## THE PROBLEM OF MULTICOLLINEARITY

When discussing the suitability of a model, an important issue is the structure or interaction of the independent variables. The statistical term used for the problem that arises from the high correlations among the independent variables used in a multiple regression model is multicollinearity or, simply, collinearity. Tests for the presence of multicollinearity must be performed after the model's significance has been determined and all significant independent variables to be used in the final regression have been determined.

A good deal of intuition ...

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