Multicollinearity - Level II Quantitative Methods

Multicollinearity occurs when two or more independent variables (or combinations of independent variables) are highly (but not perfectly) correlated with each other. 

Consequences of Multicollinearity

• A high degree of multicollinearity can make it difficult to detect significant relationships.

• Multicollinearity does not affect the consistency of the estimates of the regression coefficients but estimates become extremely imprecise and unreliable.

• It does not affect F-statistic.

• The multicollinearity problem does not result in biased coefficient estimates; however, standard errors of regression coefficients can increase, causing insignificant t-tests and wide confidence intervals i.e. Type-II error increases.

Detecting Multicollinearity

• High pair-wise correlations among independent variables do not necessarily indicate presence of multicollinearity while a low pair-wise correlation among independent variables is not evidence that multicollinearity does not exist. Correlation between independent variables is useful as an indicator of multicollinearity only in case of two independent variables.

• The classic symptom of multicollinearity is a high R² and significant F-statistic even though the T statistics on the estimated slope coefficients are not significant

Correcting Multicollinearity

The problem of multicollinearity can be corrected by excluding one or more of the regression variables