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Multicollinearity
Linear dependency situation in a regression model
Multicollinearity
In statistics, multicollinearity or collinearity is a situation where the predictors in a regression model are linearly dependent. Perfect multicollinearity refers to a situation where the predictive variables have an exact linear relationship. When there is perfect collinearity, the design matrix X {\displaystyle X} has less than full rank, and therefore the moment matrix X T X {\displaystyle X^{\mathsf {T}}X} cannot be inverted. In this situation, the parameter estimates of the regression are not well-defined, as the system of equations has infinitely many solutions. Imperfect multicollinearity refers to a situation where the predictive variables have a nearly exact linear relationship. The Gauss–Markov theorem assumes absence of perfect multicollinearity. The adverse effect of highly correlated variables is...
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