Error matrix significance for fit to data with no errorbars


When I fit a function to data that have no error-bars (TGraph instead of TGraphErrors), are the parameter uncertanties I obtain from the error-matrix meaningful? How is chi-squared calculated for such data?

Tim Daniels

ps I’m using Root 3.05

Hi Tim,

If you do not supply errors, all data point will have the same weight,
error = 1 . The parameter errors are calculated in the usual way
but they are scaled (multiplied) by the following factor :

chisq_reduced = sqrt( sum_i (y_i - y_fit_i)^2 / (degrees of freedom))

where degrees of freedom = number of data points - number of parameters

Reason is that the expectation value of that number is 1; so the
y errors are scaled so that that is fulfilled .

So the parameter errors are meaningful but of course the chisq