Standard error of OLS estimates with error in measured values

This is not strictly Igor pro related, but I thought other researchers can help.

For ordinary least squares, say you have the model Y=XB+e, where B is the vector of parameters to be estimated. In this case the standard error is sqrt(diag(σ2(X′X)^−1)), where σ2=∑(Y−Xβ^)2/(n−2).

What happens to this standard error when there is a variance in the measured values of Y, say dY ?