I have a set of experimental data, say x and y, where both x and y have experimental error following a normal distribution with different sigma. I want to fit the data y=f(x) to get some parameters that describe the physics. The final goal is to apply the regressed parameters in another numerical model to get one single result, say omega.
My question is how to determine the error of omega. I was thinking about using bootstrap to resample the experimental data, do the numerical computation and repeat many times to get the final result. But what to do with my experimental error? Is it also allowed to resample from the experimental error following a normal distribution. Then there will be two nested bootstrap, which makes things a little bit complicated... Does anyone know if there is any link or material that explain this type of problem?