The problem of multicollinearity

Abstract

It will be recalled that one of the factors that affects the standard error of a partial regression coefficient is the degree to which that independent variable is correlated with the other independent variables in the regression equation. Other things being equal, an independent variable that is very highly correlated with one or more other independent variables will have a relatively large standard error. This implies that the partial regression coefficient is unstable and will vary greatly from one sample to the next. This is the situation known as multicollinearity. Multicollinearity exists whenever an independent variable is highly correlated with one or more of the other independent variables in a multiple regression equation. Multicollinearity is a problem because it undermines the statistical significance of an independent variable. Other things being equal, the larger the standard error of a regression coefficient, the less likely it is that this coefficient will be statistically significant.