I am trying to work out the errors of $m$ and $b$ in a linear least-square fit of a straight $y = m \cdot x + b$ to $N$ equally-spaced data points $Y_i$ on the interval $I = [-\Delta x \cdot N/2,\Delta x \cdot N/2]$, where $\Delta x$ is the distance between each data point. I do not assume an error for the $x$-position of that data-points and the error for $Y_i$ is $\sigma_Y$. I know that a linear dependence is a good model for my data-points due to the physical system from which the data was obtained.

My question now is how the fit-errors $\sigma_m$ and $\sigma_b$ of $m$ and $b$ will theoretically depend on the error $\sigma_Y$ and $N$, when correspondingly growing the interval $I$. This seems like a trivial problem and I would expect the their error to decrease as $N$ increases, but I can't work out the exact dependence. Perhaps someone can point me in the right direction, thanks in advance!


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.