The misconception that the normality assumption
applies to the response and/or predictor variables is
problematic in that there are certainly situations where
the response and/or predictors are not normally
distributed, but a normal distribution for the errors is
still plausible. As one example, dichotomous predictors
are often used in multiple regression; although such
predictors are clearly not normally distributed, the
errors of regression models using dichotomous
predictors may still be normally distributed, allowing
for trustworthy inferences. Furthermore, dichotomous
variables that are particularly strong predictors of a
response variable may induce a bimodality to the
marginal distribution of the response variable, even if
the errors are normally distributed. This is one situation
in which neither predictor nor response variable has a
normal distribution, despite the model errors being
normally distributed.