The OLS formation $Y = \beta X$ and its derivation all have dependent variable $Y$ as a $n$ by $1$ vector, each entry of $Y$ is a scalar observation. But what if each observation is a vector of size $m$, not a single scalar value? Are there any statistical model to help model that?
I guess a lazy way is to let $Y = [ Y_1, Y_2, .. Y_m ]$ and we run regression separately $Y_1 = \beta_1 X$， $Y_2 = \beta_2 X$, etc. But I feel like this model misses the correlation between $Y_1$ and $Y_2$
