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dominik.mierzwa
Poland
118 Posts |
 Posted - 09/26/2018 : 3:44:28 PM
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Origin Ver. and Service Release (Select Help-->About Origin): 2018b
Operating System: Windows 10
Hi,
I have 3 sets of data (x - time, y - response) and I'd like to approximate it with function:
y=a*exp(-k*x^n)+b*x
Initial values:
a=1, b=-1e-6, n=1e-3, b=1
Everything looks OK, I got code 100, Adj.R^2 is ~0,999 but the Reduced Chi-Square is extremely low (1e-5). As I read it should be similar to 1. I reviewed the literature and there are numerous papers in which authors stated that the lower reduced chi-square the better fit is. In my opinion, they think about the chi-square and not reduced chi-square.
I have tried:
- average the data and get mean +/- SD, then fit with instrumental weighting (reduced chi-square increased to 0,11)
- treat all 3 datasets as one (nothing change)
I'm not sure about the possibilities... Can you give me some info about the meaning of low reduced chi-square and the possible reason for such a problem?
Kind regards,
Dominik |
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yuki_wu
896 Posts |
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dominik.mierzwa
Poland
118 Posts |
Posted - 09/27/2018 : 03:48:57 AM
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Dear Yuki,
Thank you, I read this page carefully and that is why I'm asking about reduced chi^2.
I think that it would be more helpful if some exemplary file is provided.
https://www.dropbox.com/s/ruip4fklc9sndfa/ex_fit.opj?dl=0
I have a question about the fitting procedure of multiple curves, what is the practical difference between Global Fit and Concatenate?
Kind regards,
Dominik |
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yuki_wu
896 Posts |
Posted - 09/27/2018 : 05:44:40 AM
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Hi Dominik,
#1. I think that page has explained that:
quote:
If the error variance is over-estimated, the Reduced Chi-square value will be much less than 1. For under-estimated error variance, it will be much greater than 1. Note that it needs to select the correct variance in fitting procedure for Reduced Chi-square. For example, if the y data is multiplied by a scaling factor simply, the Reduced Chi-square will be scaled as well. Only if you also scale the error variance by a correct factor, the value of Reduced Chi-square will turn back into a normal value.
#2. You could find the answer on this page:
https://www.originlab.com/doc/Quick-Help/Multi-Dataset-Fitting
Regards,
Yuki
OriginLab
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dominik.mierzwa
Poland
118 Posts |
Posted - 09/27/2018 : 06:52:12 AM
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Thank you I got it. I thought that there is someone who faced the same problem and can give me some advice on how to set up the fitting procedure to make it more reliable.
Kind regards,
Dominik |
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Nonlinear curve fit - low reduced chi^2