Hint for physicists

Very often, the data to be fitted is a histogram of physical events. In that case, since each bin would follow a multinomial distribution, the error is equal to `√f`, where f is the expression you are trying to fit. Of course, since you don't know the parameter values yet, you don't actually know f, so you approximate by using the y data values. In the limit, these results are the same. In the case of a large number of bins, the variance can be approximated by `√y`. Hence, the correct weighting factor that will give properly normalized errors is w = 1/y, and the corresponding one standard deviation error, `σ = E1`.

`E2 = E1*sqrt(χ2/n)`, where `E1` is the standard error and `n` is the number of degrees of freedom, usually equal to the number of data points minus the number of parameters, `(N-M)`.

Chi-square and weights
Degrees of freedom