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So what is that parameter. When I make a non-linear fit, the program gives me a value χ2/doF. What is it?

I know some statistics and I know those χ2 distributions are used for non-parametric contrasts, like how good a fit is to a data, knowing that λ⇝χ2n−1 (that's supposed to mean the pearson parameter behaves like that distribution). I suspect it's totally related to that, telling me how good the fit is actually making the contrast, I don't know though, how to relate that value, as I'm not giving aconfidence level, so I guess it's a general number something independent of that so you decide if it's good or not, what is it exactly? Why is it divided by the degrees of freedom?

Thanks

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    $\begingroup$ Because there are many ways to "make a nonlinear fit," please provide some details of what you are doing, including what program you are using. (Doesn't the program's documentation explain its output?) $\endgroup$
    – whuber
    Mar 21, 2013 at 17:47
  • $\begingroup$ @whuber I'm using SciDavies. And I'm fitting to an arbritary function (not linear) to a set of points. I searched the documentation and didn't find anything. The algorithm it says it's using is Levenberg-Marquardt $\endgroup$ Mar 21, 2013 at 18:47

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It is the reduced Chi-Square statistic, used for testing how 'useful' a model is for the data. You divide the chi-square statistic by the degrees of freedom to get a scaled measure of variance (it equals sum of squares divided by degrees of freedom). The ratio of two reduced Chi-Square statistics is the F statistic (used for testing variance between the two).

See this wikipedia article for information on interpreting the resulting value: http://en.wikipedia.org/wiki/Goodness_of_fit

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  • $\begingroup$ But what is that value. I know it must provide some information about that chi-square distribution. What I want to know is what is that value. $\endgroup$ Mar 21, 2013 at 18:46
  • $\begingroup$ In your case it is a test statistic for how 'useful' the model is. This wiki article should answer your questions: en.wikipedia.org/wiki/Goodness_of_fit $\endgroup$
    – TLJ
    Mar 21, 2013 at 19:27
  • $\begingroup$ I edited my answer to include the additional info. Please mark as answered if it helped you! $\endgroup$
    – TLJ
    Mar 21, 2013 at 19:51
  • $\begingroup$ I already did... thanks for the info, I finally understood what that was, I had never seen that called as Chi-Square, but RSS. $\endgroup$ Mar 21, 2013 at 19:53

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