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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?

Nick Cox
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Beta
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  • Several relevant threads here e.g. http://stats.stackexchange.com/questions/1149/is-there-an-intuitive-explanation-why-multicollinearity-is-a-problem-in-linear-r – Nick Cox Dec 19 '13 at 17:48
  • and this one is relevant too http://stats.stackexchange.com/q/70899/3277 – ttnphns Dec 19 '13 at 19:27
  • Also http://stats.stackexchange.com/questions/38093/how-to-deal-with-high-correlation-among-predictors-in-multiple-regression – Peter Flom Dec 19 '13 at 19:42
  • Thank you everyone for your responses. I actually looked for my question in the forum before asking this one. But I didn't get it earlier. So, had to ask this question. Thank you again. – Beta Dec 20 '13 at 07:07

2 Answers2

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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).

David Z
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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

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