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I was reading about Linear Regression assumptions and I'm a little confused cause lots of websites and books mention different assumptions. What I found to be the most common assumptions mentioned are the LINE assumptions: Linearity in parameters, Independence of residuals, Normality of residuals and Equal variance.

I know that some of other assumptions is already included in the LINE assumptions, such as zero conditional mean, which is similar to Independence and Normality together (right?). However, I can't find any assumption in these four (LINE assumptions) related to MULTICOLLINEARITY. Is multicollinearity still an assumption for Linear Regression? How is multicollinearity related to LINE assumptions?

Yuxxxxxx
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  • I like Whuber's comments about multicollinearity [here](https://stats.stackexchange.com/a/16395/247274). – Dave Aug 24 '21 at 20:34
  • Zero conditional mean is *not* implied by the four LINE assumptions listed. I would drop "linearity in the parameters" and replace it with "correct functional specification of the conditional mean." This would imply zero conditional mean of errors, so that need not be stated as an assumption. The only need for "linearity of parameters" is to allow OLS, but NLS is trivial these days. Correct functional specification is clearly much more important. You can have model that is linear in the parameters, but is grossly misspecified. – BigBendRegion Aug 24 '21 at 22:50

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