A bit of a silly question.
We have a model, which can be described as y = M(x) + some significant levels of noise.
We see that if we repeat the measurements of y N times, we can see a clear correlation between the measurements and M.
However we want to present the data in a different format, mainly answering the question "how many repeated measurements of the same object x are needed to get a good estimate of M(x)?"
Is there a statistical framework for that?