The central limit theorem is exactly that √N(^βi−βi)∼N(0,σ2i) which implies what I said. The noise is not on the log scale because of the CLT.
Now, if you transform your coefficient into a log scale then all bets are off. But that is not happening throughout this post. And it’s not really what happens in reality either. I don’t know why anyone would do it.
The central limit theorem is exactly that √N(^βi−βi)∼N(0,σ2i) which implies what I said. The noise is not on the log scale because of the CLT.
Now, if you transform your coefficient into a log scale then all bets are off. But that is not happening throughout this post. And it’s not really what happens in reality either. I don’t know why anyone would do it.