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fter 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 dif-
ferent stepwise regression methods.
■ (^) How to test for the various assumptions of the multiple linear regres-
sion model and correct the model when violations are found.
In this chapter we continue with our coverage of multiple linear regres-
sion analysis. The topics covered in this chapter are the problem of multicol-
linearity, 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 struc-
ture 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 inde-
pendent variables to be used in the final regression have been determined.
A good deal of intuition is helpful in assessing if the regression coef-
ficients make any sense. For example, one by one, select each independent
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