Collinearity means that some independent predictor variables (xi) are mutually correlated with each other, resulting in ill-conditioned data. Correlated or
ill-conditioned predictor variables usually lead to unreliable bi regression coefficients. Sometimes, the predictor variables (xi) are so strongly correlated that a (X0X)1 matrix cannot be computed, because there is no unique solution. If xi variables are not correlated, their position (first or last) in the regression equation does not matter. However, real world data are usually not
perfect and often are correlated to some degree. We have seen that adding or
removing xis can change the entire regression equation, even to the extent that different xi predictors that are significant in one model are not in another. This is because, when two or more predictors, xi and xj, are correlated, the contribution of each will be greater the sooner it goes into the model.