Multicollinearity

In statistics, multicollinearity (also collinearity) is a phenomenon where one predictor variable in a multiple regression model can be linearly predicted from the others with a substantial degree of accuracy.
In statements of the assumptions underlying regression analyses, "no multicollinearity" usually refers to the absence of perfect multicollinearity, which is an exact (non-stochastic) linear relation among the predictors. In such a case, the design matrix X has less than full rank, and therefore the moment matrix X^\top X cannot be inverted. Under these circumstances, for a general linear model y = X \beta + u, the ordinary least squares estimator \hat{\beta}_{OLS} = (X^\top X)^{-1} X^\top y does not exist.
* Multicollinearity is a characteristic of the design matrix, not the underlying statistical model.
* Multicollinearity leads to parameters not being point identified. Set identification may be possible. For example, if two elements of x, say x_1, x_2 (with coefficients \beta_1, \beta_2
) are such that x_2 = \alpha x_1 then \beta_1 + \alpha \beta_2may be point identified but \beta_1, \beta_2
 can only be set identified with (\beta_1, \beta_2) \in \{ b_1, b_2 ~|~ b_1 + \alpha b_2 = c \} where c = \beta_1 + \alpha \beta_2, the point identified value.