# Relationship Between Correlation and Multicollinearity [duplicate]

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

• Several relevant threads here e.g. stats.stackexchange.com/questions/1149/… – Nick Cox Dec 19 '13 at 17:48
• and this one is relevant too stats.stackexchange.com/q/70899/3277 – ttnphns Dec 19 '13 at 19:27
• – 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 7:07

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