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dchris
USA
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 Posted - 01/31/2008 : 02:14:06 AM
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Origin Version (Select Help-->About Origin): OriginPro 8 SR1
Operating System: Windows XP
Hello,
I'm wondering if it's possible to display individual chi values when doing non-linear curve fitting.
The idea is that the chi^2 is the sum of the individual chi_i's, squared, where i is an index number. More specifically,
chi_i = ((y_fit - y_data)/sigma_y
It's just the residual from the fit divided by the data point's instrumental uncertainty (I usually fit with the "Instrumental" setting in Origin).
What would really be nice is to be able to get these individual residuals that have been normalized and be able to plot them so that they can be visualized. Squaring of the chi_i's would also be nice, but isn't too critical. Thanks for your help. |
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larry_lan
China
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Posted - 02/01/2008 : 12:52:00 AM
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Hi David:
As you can see from the help, the chi-square minimization algorithm is defined as:
When you use the "Instrumental" weight, we have:
So the formula turns into:
Where sigma_i is the yErr column values. Traditionally, when the fit is done, we can evaluate the results by residual analysis, and the residuals can be normalized, or standardized by the error of the model:
Where r_i is the individual residual value and s is the square root of "mean residual variance" (Error Mean Square):
You can select to output such plots as follow:
As I know, the Chi-square test requires a sufficient sample size in order for the chi-square approximation to be valid. So I am not sure whether the individual Chi value makes sense, and we have no such output. Anyway, you can always manually do that by "Set Column Values". Make sure to output the Regular residuals:
And then compute the individual chi value you mentioned by:
Thanks
Larry
OriginLab Technical Services |
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Individual Chi Test Terms and Nonlinear Fitting