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:

*

*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?

Myth: The error/deviation of the observations needs to be normally distributed.
No, it doesn't.
It is not just about the distribution of the errors of the observations, Instead what often matters is the distribution of the error of the estimates.
These estimates are computed as a weighted sum of the observations $$\hat\beta = M \cdot y$$ with $$M = (X^TX)^{-1}X^T$$
If we want to estimate the error or significance of the estimates $\hat\beta$, then it is sufficient if those estimates follow approximately a normal distribution. This can happen also when the sampled error of observations $y$ do not follow a normal distribution.
Due to the same principle of the central limit theorem, a statistic that is a weighted sum of variables or some sort of mean of variables will approach a normal distribution.
So even if the distribution of the error/deviation of the observations is not normally distributed, the error/deviation estimates might still be approximately normally distributed.
