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?


"Also, how did such myths come about?"

One common assumption in regression is homoscedasticity (and a myth is that this is also necessary). Transformations are used to bring the data closer to this assumption.
The violation of the assumption doesn't make the fitting method bad, least squares regression is the best unbiased linear estimator (in terms of lowest variance of the estimates) no matter what the underlying distribution is.
But, the violation of the assumptions may cause wrong inferences when we express the observed effects in terms of significance/p-values.
There is a difference between the assumptions that are necessary for least squares regression to work, and the assumptions that are necessary for the significance and hypothesis tests based on least squares regression to work.
