I have two variables $X$ and $Y$.
Consider that there is one sample with 1000 observations, we can get the standard error of coefficient by this equation: $se(\hat\beta) = \sqrt{\sigma^2(X^TX)^{-1}}$.
Then consider that we have 100 samples, each sample has 1000 observations. By running 100 regressions, we can get 100 $\hat\beta$. Then, we can compute the standard error of the mean: $SEM=\sum(\hat\beta-\bar{\beta})^2/100$.
So what is the relationship between the two standard errors?