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 ODR residual values and RSS
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RiverFalls

USA
26 Posts

Posted - 01/01/2022 :  8:48:15 PM  Show Profile  Edit Topic  Reply with Quote  View user's IP address  Delete Topic
OriginPro 2022 (64-bit) SR1 on Win10
-I've just recently tried out the ODR fitting method in OriginPro, and am trying to understand the values of the fitting results.

I made up a simple dataset of x, xerr, y, yerr values and fit it to a straight line equation in the NLSF, as well as using the 'Linear Fit with X error' option. Both routines produced the same fit results (parameters, parameter unc., RSS, etc.). However, when I try to make sense of the RSS value and the residual values, I cannot figure out how those values are being determined.
Here is the NLSF fit results:

When I look at the curve tab, I see:

Question 1): How are the "Residual of Sheet1..." values calculated? I cannot find a reference that explains these, and cannot figure them out based on the actual data values (columns C,E) and the values of the fit (columns A and B). For example, the very first row indicates that the 'y' residual should be: 2-0.04577 = 1.95423, yet column F has something completely different.
Question 2): The online information indicates that the RSS value is calculated the same as usual (for LM fits), but I cannot reproduce the value being reported by the ODR fit. I think this must be related to the first question.

Thank you for any help that anyone can provide.
Lowell

Castiel

329 Posts

Posted - 01/02/2022 :  10:35:04 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
quote:
Originally posted by RiverFalls

OriginPro 2022 (64-bit) SR1 on Win10
-I've just recently tried out the ODR fitting method in OriginPro, and am trying to understand the values of the fitting results.

I made up a simple dataset of x, xerr, y, yerr values and fit it to a straight line equation in the NLSF, as well as using the 'Linear Fit with X error' option. Both routines produced the same fit results (parameters, parameter unc., RSS, etc.). However, when I try to make sense of the RSS value and the residual values, I cannot figure out how those values are being determined.
Here is the NLSF fit results:

When I look at the curve tab, I see:

Question 1): How are the "Residual of Sheet1..." values calculated? I cannot find a reference that explains these, and cannot figure them out based on the actual data values (columns C,E) and the values of the fit (columns A and B). For example, the very first row indicates that the 'y' residual should be: 2-0.04577 = 1.95423, yet column F has something completely different.
Question 2): The online information indicates that the RSS value is calculated the same as usual (for LM fits), but I cannot reproduce the value being reported by the ODR fit. I think this must be related to the first question.

Thank you for any help that anyone can provide.
Lowell




Orthogonal Distance Regression (ODR) is a method that is used to calculate the error perpendicular to the line rather than vertically.

Google odrpack95 for details of the algorithm.


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