The following statement might surprise you, but it’s true.
To run a linear model, you don’t need an outcome variable Y that’s normally distributed. Instead, you need a dependent variable that is:
- Continuous
- Unbounded
- Measured on an interval or ratio scale
The normality assumption is about the errors in the model, which have the same distribution as Y|X. It’s absolutely possible to have a skewed distribution of Y and a normal distribution of errors because of the effect of X. (more…)