If I have a vector y which follows a multivariate normal distribution with zero mean and unknown covariance matrix. I have the following simple linear regression: $y = \beta_0 + X\beta_1 + e$.
If I consider now that the vector y follows a multivariate normal distribution with non zero mean (and unknown) and unknown covariance matrix. So what can differ in the formula of the simple linear regression??
So by assuming that the mean vector of y is unknown, what can this affect the estimation of the regression coefficients?