I need to find the variance of $\hat\beta_1 * \bar X_1 / \bar Y$ ,
where we have the regression equation Y= $\beta_0 + \beta_1* X_1 +…+ \beta_j* X_j$
I initially was thinking the answer is simply SE($\beta_1$) * $\bar X_1 / \bar Y$
However, I think the means are also random variables that have a variance. I also think that $\hat\beta_1$ and $\bar X_1 / \bar Y$ are not independent.