Let's say we have a simple linear regression model, that is, $y = X\beta + r$ where $y$ is a vector of size n x 1, $X$ a matrix of size n x p, $\beta$ the regression coefficient vector of size p x 1 and $r$ is a residual error of size n x 1.
Most of papers I read consider that $y$ follows a multivariate normal distribution. My question is whether $y$ can follow a distribution different from normal, for example elliptical, etc. Is it necessary that in linear regression, for $y$ to be assumed Gaussian?
I discussed with a researcher and he told me that linear regression models are only suitable (or efficient) for Gaussian assumption. Is this true?