What are the myths associated with linear regression, data transformations? I have been encountering many assumptions associated with linear regression (especially ordinary least squares regression) which are untrue or unnecessary. For example:

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*independent variables must have a Gaussian distribution

*outliers are the points either above or below the upper or lower whiskers correspondingly (employing Boxplot terminology)

*and that the sole purpose of transformations is to bring a distribution close to normal in order to suit the model.

I would like to know what are the myths that are generally taken for facts/assumptions about linear regression, especially concerning associated nonlinear transformations and distributional assumptions.  How did such myths come about?

There are three myths that bother me.

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*Predictor variables need to be normal.


*The pooled/marginal distribution of $Y$ has to be normal.


*Predictor variables should not be correlated, and if they are, some should be removed.
I believe that the first two come from misunderstanding the standard assumption about normality in an OLS linear regression, which assumes that the error terms, which are estimated by the residuals, are normal. It seems that people have misinterpreted this to mean that the pooled/marginal distribution of all $Y$ values has to be normal.
Indeed, as is mentioned in a comment, we still get a lot of what we like about OLS linear regression without having normal error terms, though we do not need a normal marginal distribution of $Y$ or normal features in order to have the OLS estimator coincide with maximum likelihood estimation.
For the myth about correlated predictors, I have two hypotheses.

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*People misinterpret the Gauss-Markov assumption about error term independence to mean that the predictors are independent.


*People think they can eliminate features to get strong performance with fewer variables, decreasing the overfitting.
I understand the idea of dropping predictors in order to have less overfitting risk without sacrificing much of the information in your feature space, but that seems not to work out. My post here gets into why and links to further reading.
