Multicollinearity: Causes, Effects And

If there is no linear relationship between the regressors, they are said to be orthogonal. Multicollinearity is a case of multiple regression in which the predictor variables are themselves highly correlated. If the goal is to understand how the various X variables impact Y, then multicollinearity is a big problem. Multicollinearity is a matter of degree, not a matter of presence or absence. In presence of multicollinearity the ordinary least squares estimators are imprecisely estimated. There are several methods available in literature for detection of multicollinearity. By observing correlation matrix, variance influence factor (VIF), eigenvalues of the correlation matrix, one can detect the presence of multicollinearity. The degree of the multicollinearity becomes more severe as X X′ approaches zero. Complete elimination of multicollinearity is not possible but the degree of multicollinearity can be reduced by adopting ridge regression, principal components regression, etc.