Many sources state that a condition index >30 constitutes a multicollinearity problem. When I've tried to implement this check in practice, I've realized that the condition index (and VIFs) change depending on whether or not the intercept is included in the model. Is the standard approach to include the intercept? Does it matter if there is collinearity between the intercept and the predictors?

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    $\begingroup$ You should probably include the intercept. If collinearity is a problem, that must also include variables that is close to a constant, that is, collinear with the intercept $\endgroup$ – kjetil b halvorsen Sep 17 '17 at 17:32

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