I am a bit confused about the normality assumption of the error term in linear regression models.
Several textbooks write that one of the Least Squares assumptions is that the (conditional) distribution of the error term is normal. Does this usually imply that the dependent variable is normally distributed itself?
This question came up while I was trying to understand generalized linear models. McCullagh and Nelder (1983, p.35) define Models for continuous data with constant variance in the following way:
As far as I understand, this should be the equivalent to the classical linear regression model, but within the framework of a glm. What I do not quite understand is the most left expression specifying that the dependent variable is normally distributed, but underneath they write "errors normally distributed and independent".
Do glms simply make stronger assumptions than would be necessary with an OLS framework? And does the dependent variable being normally distributed imply that the error terms are also normally distributed?
I would be very greatful for some enlightenment on this issue!