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giordandue
Italy
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 Posted - 05/07/2026 : 12:44:18 PM
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Origin Ver.2016 (64bit)Sr2 - b9.3.2.303
Operating System:WINDOWS 10 PRO
Dears,
With reference to (95%) confidence band associated to non linear regression analysis (two parameters), I have some problems in understanding which formulation OriginLab use for calculating the "Estimated standard error of y". I attach as an image, the specific reference documentation. Incidentally, I tried to use the formulation for residual standard error SE=[Summatory(Y-Y')^2/(n-2]^0.5, but if I search to reproduce in Excel, by multiplying for t.975, I derive different envelops. On the contrary, I am observing that simply to use [mean (+-)SE/2] fits very well OriginLab (i.e.in some way extending the approach of Schneider (1999) for the characteristic value as [mean (+-)StandardDeviation/2)].
Thank you very much for your opinion!  |
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NadeeshaSupport
USA
11 Posts |
Posted - 05/07/2026 : 3:20:59 PM
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Hello,
Could you please look at the 'Parameters' section on this page? https://docs.originlab.com/origin-help/nlfit-theory/ Pay close attention to equations (8) and (9) on this page.
Equation (9) is similar to your Excel calculation.
Equation (8) defines how Origin's variance-covariance matrix is calculated. Origin also accounts for how sensitive the fitted curve is to parameter uncertainty at different x-values.
In a given sample, usually there are more data points near the center of the dataset, so the fit is more reliable there and the CI band envelopes are narrower. Near the edges, small changes in the fitted parameters can shift the curve much more, so the CI band envelopes widen. You can see this in the image you shared.
Please let me know if this answers your question.
Thanks,
Nadeesha |
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giordandue
Italy
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Posted - 05/07/2026 : 4:43:28 PM
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Thank you very much Nadeesha
In effect until now I used direct equations, without using matrix formulation.I will try as you suggest... Anyway, what is still not clear to me is if the formulation I remarked for the residual should give a reasonable result while using Excel, or other similar equation could be employed, in eventual alternative to matrix.
I profit to attach the comparison Origin/Excel graph by using for 95% confidence. Note that I forced the passage through the origin axis, as required for the specific case. As i said, I used for 95% the value of SE/2..
Again thank you!
Giordan
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NadeeshaSupport
USA
11 Posts |
Posted - 05/07/2026 : 5:09:20 PM
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Hi Giordan,
Origin provides plotted values for the Confidence Bands and Prediction Bands.
Under the NLFit window, click Settings -> Fitted Curves, and enable Confidence Bands and Prediction Bands under the Fitted Curves Plot.
The worksheet FitNLCurve1 will display the values that were used to plot the two bands. You may cross-check to see if the values are similar to what was calculated in Excel.
If you are copying Origin values into Excel, make sure to copy with full precision of 14 decimal places. In an Origin worksheet, right click, select Properties, and change Set Decimal Places.
Let me know if you have any other questions.
Thanks,
Nadeesha |
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giordandue
Italy
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Posted - 05/07/2026 : 5:56:30 PM
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Hi Nadeesha, thanks..
As you can see from the graph comparison, I got good results in replaying the Origin Confidence band, and also I checked by overimposing the Origin values from the worksheet that you suggest.
Again, no problem by using/copying Origin values, but I am mainly interested to find the correct Excel formulation to be used independently, in theoretical absence of OriginLab. In effect sometime is useful in some technical discussion with people without OriginLab (of sure an extremely superior software), also to further prove the achieved result.
Regards
Giordan |
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NadeeshaSupport
USA
11 Posts |
Posted - 05/08/2026 : 08:52:24 AM
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Hi Giordan,
The [mean (+-)SE/2] cannot replace Origin's x-dependent error propagation approach. The agreement may work reasonably well for the data on hand, but we cannot assume that it will work in general for other datasets.
Thanks,
Nadeesha |
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giordandue
Italy
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Posted - 05/10/2026 : 10:05:11 AM
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Hi Nadeesha,
conceptually I agree with you. I will try to check the alternative simplified approach by some much larger database comparison. An additional question: some referenced literature (for example Orr et al., 2025) suggest for confidence bands the equation hereafter reported for linear fitting. Maybe, do you have some opinion/suggestion?
Best Regards
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NadeeshaSupport
USA
11 Posts |
Posted - 05/11/2026 : 11:10:24 AM
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Hi Giordan,
This approach may yield a better approximation, but it would still not replace what Origin is doing. Additionally, what may work for a linear fit may not necessarily work for nonlinear fit.
Thanks,
Nadeesha |
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Estimated standard error of y