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Suppose I've a model such as

$Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \cdots + \beta_k X_k + \epsilon$.

Now, there's high correlation between $X_1$ & $X_2$ (say over 60% but below 75%). Does that means this model has multicollinearity problem? Is there any relationship between highly correlated variables & multicollinearity? If there's any short literature on this topic?


marked as duplicate by whuber Dec 19 '13 at 19:28

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.


The variance inflation factor (VIF) quantifies the severity of multicollinearity in an ordinary least squares regression analysis:

$$ VIF=\frac{1}{1-r^2} $$

Where r is the correlation between two independent variables such as $X1$ and $X2$ (Technically, $r^2$ is called the coefficient of determination, but it equals the squared correlation). We usually say there's collinearity if $VIF \geq 10$. In your case, $VIF=\frac{1}{1-0.75^2}=2.29$. So we can say there's no collinearity problem between $X1$ and $X2$. If you use R for modeling, the VIF can be easily checked by vif(fit).


Correlation is neither necessary nor sufficient for collinearity problems, although perfect correlation will cause problems. The best way to test for collinearity is with condition indices.

See my answer

  • 2
    $\begingroup$ Peter, when you can just link to another answer, the question almost certainly is a duplicate and ought to be closed as such. $\endgroup$ – whuber Dec 19 '13 at 19:29

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