.. _book_fig_chapter4_fig_chi2_eval:


Evaluating a model fit with chi-square
--------------------------------------
Figure 4.1.

The use of the :math:`\chi^2` statistic for evaluating the goodness of fit.
The data here are a series of observations of the luminosity of a star, with
known error bars. Our model assumes that the brightness of the star does not
vary; that is, all the scatter in the data is due to measurement error.
:math:`\chi^2_{\rm dof} \approx 1` indicates that the model fits the data
well (upper-left panel). :math:`\chi^2_{\rm dof}` much smaller than 1
(upper-right panel) is an indication that the errors are overestimated.
:math:`\chi^2_{\rm dof}` much larger than 1 is an indication either that the
errors are underestimated (lower-left panel) or that the model is not a good
description of the data (lower-right panel). In this last case, it is clear
from the data that the star's luminosity is varying with time: this situation
is be treated more fully in chapter 10.



.. image:: ../images/chapter4/fig_chi2_eval_1.png
    :scale: 100
    :align: center


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