Does linear regression require normal distribution?
Linear regression analysis, which includes t-test and ANOVA, does not assume normality for either predictors (IV) or an outcome (DV). Yes, you should check normality of errors AFTER modeling. In linear regression, errors are assumed to follow a normal distribution with a mean of zero.
Do predictors in regression have to be normally distributed?
The predictor variables are assumed to have NO random process. And therefore, there are no assumptions about the distribution of predictor variables. None. They don’t have to be normally distributed, continuous, or even symmetric.
Is the explanatory variable in linear regression normally distributed?
Some users think (erroneously) that the normal distribution assumption of linear regression applies to their data. They might plot their response variable as a histogram and examine whether it differs from a normal distribution. Others assume that the explanatory variable must be normally-distributed. Neither is required.
Do you have to use normality assumption in linear regression?
The answer is no: the estimation method used in linear regression, ordinary least squares (OLS) method, doesn’t not require the normality assumption. So, if you see that a variable is not distributed normally, don’t be upset and go ahead: it is absolutely useless trying to normalize everything.
Is the marginal distribution of dependent variables normal?
1) If the distribution of the residuals within each group is normal, and the groups have different means (i.e. in a linear regression there is a slope different from 0) then the marginal distribution of the dependent variable may very well be NOT normal at all.
Can a regression make an assumption about the distribution of the predictors?
(1) No regression, Poisson or otherwise, makes any assumption about the distribution of the predictors. (2) You should check how the residuals vary against the fitted values but they are only asymptotically normal. @Scortchi has covered the issues pretty well; though I wanted to make some additional comments
https://www.youtube.com/watch?v=AVxojKRPsWg