# Normality assumption in linear regression

As an assumption of linear regression, the normality of the distribution of the error is sometimes wrongly "extended" or interpreted as the need for normality of the y or x.

Is it possible to construct a scenario/dataset that where the X and Y are non-normal but the error term is and therefore the obtained linear regression estimates are valid?

• Trivial example: X has a Bernoulli distribution (ie, taking the values 0 or 1); Y = X + N(0, 0.1). Neither X nor Y is normally distributed on its own, but regressing Y on X still works. – Hong Ooi Feb 17 '14 at 8:45
• I guess you are thinking about the distribution of the residuals, not the distribution of the variables. – tashuhka Feb 17 '14 at 10:03
• I have an example worked out here: What if residuals are normally distributed but Y is not? – gung - Reinstate Monica Feb 17 '14 at 14:52
• – kjetil b halvorsen Dec 7 '19 at 13:25

library(psych)