Probability and Statistics for Finance

Chapter 21. Designing and Building a Multivariate Linear Regression Model

In this chapter we continue with our coverage of multivariate linear regression analysis. The three topics covered in this chapter are the problem of multicollinearity, incorporating dummy variables into a regression model, and model building techniques using stepwise regression analysis.

THE PROBLEM OF MULTICOLLINEARITY

When discussing the suitability of a model, an important issue is the structure or interaction of the independent variables. This is referred to as multicollinearity. 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. Investigation for the presence of multicollinearity involves the correlation between the independent variables and the dependent variable.

A good deal of intuition is helpful in assessing if the regression coefficients make any sense. For example, one by one, select each independent variable and let all other independent variables be equal to zero. Now, estimate a regression merely with this particular independent variable and see if the regression coefficient of this variable seems unreasonable because if its sign is counterintuitive or its value appears too small or large, one may want to consider removing that independent variable from the regression. The reason may very well be attributable to multicollinearity. Technically, ...