In reply to Rick Wicklin.

IF the inclusion of the intercept term in the model is valid / makes "business" sense and one is evaluating that specific model where colinearity within the underlying data may impact the application of that model, then I would consider what it means for there to be collinearity within the design matrix that includes an intercept as opposed to collinearity within a corresponding design matrix / data set that does not include the intercept term. In this case, the inclusion of the intercept term in the collinearity analysis may assist in the diagnosis of collinearity between the "explanatory" variables in the model and the evaluation of the data quality issues w.r.t. the statistical model being developed and evaluated. However, the numerical computations on the design matrix that are required to estimate the model parameters and which are also used to evaluate the degree of collinearity and thus the stability of the model, should be used with caution and as a guide to possibly modifying the model. You certainly CAN drop the intercept term but the question is which model is better suited to solving the decision problem and thus the question is: SHOULD you drop the intercept term? Evaluation of the impact of including and excluding the intercept term during the Collinearity Diagnosis as well as the evaluation of the impact on the statistical model are joined at the hip