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 has less than full rank, and therefore the moment matrix 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.