Reduced chi-squared
= Reduced chi-squared
{title2=$\chi^2_\nu=\chi^2/\nu$}
The <reduced chi-squared> divides a weighted squared-residual statistic by its <degrees of freedom>. For an identifiable Gaussian linear model with $N$ independent observations, known correct errors and $p$ fitted coefficients, $\nu=N-p$ and its expectation is one. An observed value close to one is compatible with the model but does not prove it. Unknown <systematic errors>, dependent residuals or fitted <noise> scales change this interpretation.