#### FlorenceCC

##### Member

I understand that the assumption that the sampling distribution of OLS estimators b0 and b1 is asymptotically normal is a key property. However I'm a bit stuck as to

__why__that is. I assume the magic CLT comes into play here, but I guess there are stil grey areas for me.

When we apply the CLT, we apply it not to the distribution of the sample, but the distribution of the sample mean as a random variable.

When we talk about i.i.d. samples of X and Y here, and the corresponding SRF, and b0/b1 estimators, we have a sampling distribution. But how does the sampling distribution of their sample mean/CLT becomes relevant. I guess what I am trying to express here is that we are interested in the sampling distribution, not the sampling distribution of the sample mean?

What am I missing? Hope my question makes sense, thanks!

Florence