This is something that is really causing me a lot of confusion.
Consider the functional form y = A + Bx.
As far as I understood, we could estimate the population parameters A and B with say a and b using least squares linear regression, and calculate the standard error of these respectively. For example, the standard error of the slope would be SQRT(Standard Error^2 / Sum of Squares XX). This is something that could be calculated exactly. This of course assumes that these estimates are normally distributed - but I thought that was the main assumption in linear regression?
My understanding is that by bootstrapping the confidence intervals, we don't need to assume anything about their distribution. But won't the outputs of the bootstrapped confidence intervals be normally distributed, anyways? If it isn't going to be normally distributed, does that violate the normality assumption?
So I guess my questions are:
- What is the purpose of bootstrapping?
- Is bootstrapping always recommended over the traditional calculation (provided you have the computing power / expertise)? I.e. you would only do the other method, if you don't have the time / skills to apply bootstrapping.
I know it's a really silly question, but the more I read around the subject the more confused that I get.