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)
.