# How to understand Chi-squared goodness-of-fit for linear regression?

I am trying to understand a claim from a paper*:

The slopes were calculated using least-squares linear regression to fit the level versus X functions. The goodness of fit of these linear functions was then determined.

...

C-levels decreased as a function of X in most cases. The rate of decrease was quantified by fitting a linear regression line to the level versus X functions.

Chi-square Goodness of Fit values of the C-level versus X functions ranged from ~0 to 1 with a median of 0.06. All Chi-square values were smaller than 1, indicating good fit.

They had 3 levels of X with 3 measurements per level, and both X and C are continuous variables. Edit: There were 11 such independent data-sets, each coming from different subjects.

I am having trouble understanding what they are saying. Is this a standard procedure? There seem to be different “chi-squared tests”, but none of the ones I’ve found so far seem to fit to this kind of data. I am mainly unsure about the claim that the fit is good if chi-square is below 1.

*NB: Neither me nor the authors of the papers are statisticians, so if the question is too simple, feel free to direct me to appropriate literature.

• Could you explain how the authors appear to have obtained multiple "Goodness of Fit" values in this situation? Your description makes it sound like there's a single dataset with nine observations; there should only be a single statistic and a single Chi-squares p-value for the regression. – whuber Feb 21 at 15:47
• Thanks, I missed that. There were 11 such independent data-sets, each coming from different subjects. The fits and the chi-squared were then calculated separately for each of the datasets. – Purple Rover Feb 21 at 15:57