Regression Analysis — Multicollinearity

Collinearity is the correlation between two independent variables, and multicollinearity is the correlation between three or more independent variables. The terms, however, are often used interchangeably.

Multicollinearity reduces the predictive power of an independent variable by the extent to which it is associated with other independent variables. As the correlation increases, the proportion of the variance explained by each independent variable decreases, while their shared contribution increases.

An extreme example of multicollinearity would be duplicate variables, for instance advertising spend in dollars and in ‘000 dollars. These two variables are essentially identical, and one should be removed.

On the other hand, if one of the variables is GRP and the other is spend in dollars, in that case the analyst should pick the one that has the greater predictive power. (In theory, that ought to be GRP, if the dependent variable is advertising awareness or sales).

Finally, consider Brand Equity research. Of the large number of attributes that relate to brand equity, many are correlated. For instance, value for money, low price, attractive promotions, and house brands.

The approach in this case is to club variables together to form factors, or composite variables. The dependent variable is then regressed with the factors; the regression coefficients reveal the importance of each factor, and the factor loading reveals the importance of each attribute or independent variable.

To sum up, sometimes factor analysis and other means of combining variables into summated scales, can effectively address multicollinearity. In other instances, one or more of the variables may be redundant.