I have a doubt about the distribution of the error in the standard linear regression framework.
$ Y = \beta X + e$
What is the hypotesis about? the error? the dependent variable Y? the regressors X?
if I say that the error is normally distributed since $e = Y-\beta X$ I am implying that:
$Y-\beta X$ is normal distributed so (Y,X) are jointly normal and the other way around.
if I say that $Y$ is normally distributed then I am implying that $\beta X + e$ is normal and so (X,e) are jointly normal.
So making the assumption of normality about Y or X ore e is the same thing. Am I right?