I'm fitting a model to some data, in this case I'm using LinearModelFit but I think it also applies to NonlinearModelFit as well. When I extract the fit parameters from the model, I can extract the Standard Error for each parameter. Is this the "standard deviation" of the parameter? Or is it a true "standard error" (i.e. standard deviation divided by the square root of the population size)? Or is it something else?

I want to propagate this extracted uncertainty through subsequent calculations. Specifically, I will use the Around function (i.e. Around[data,error]) to match up the parameters with their uncertainty. Do I have to perform some operation on the Standard Error I extract from the model before I can use it like this?

Thanks in advance!