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