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If I have a dependent variable Y and two independent variables X1 and X2 , that are highly correlated.

Y ~ beta1*X1 + beta2*X2

What issues can multicollinearity cause in an OLS regression, apart from unstable beta1 and beta2 estimates ?

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marked as duplicate by gung - Reinstate Monica, Glen_b, Peter Flom - Reinstate Monica May 6 '14 at 9:48

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.

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    $\begingroup$ What would it mean for the $R^2$ to be "higher than it should be"? $\endgroup$ – gung - Reinstate Monica May 6 '14 at 2:27
  • $\begingroup$ removed that part of the question. It was an ambiguous statement. $\endgroup$ – silencer May 6 '14 at 2:39
  • $\begingroup$ @PatrickCoulombe: I thought about it too, but that one seems to pertain specifically to parameter estimates, and this one specifically not to them. $\endgroup$ – Nick Stauner May 6 '14 at 3:05
  • $\begingroup$ If you have high multi-collinearity, your beta1 and beta2 are essentially meaningless, you cannot trust their statistically significance nor magnitude. Your R-squared is inflated, so it is largely meaningless. There is no useful information that the regression provides, what other issues could there be? $\endgroup$ – Akavall May 6 '14 at 4:00