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Slev1n
Germany
4 Posts |
 Posted - 03/10/2016 : 05:13:40 AM
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Origin Ver. and Service Release (Select Help-->About Origin): 8.6
Operating System: win7
Hey guys,
My intention:
I am using originLab but I am a bit confused about the Standard error calculated by origin for my linear fit. My intention is to include the standard error into my error calculation for the !x-axis! value.
My situation:
I have 11 points, each created by the average of 50 measurement values. The R²=0,99998 and the standard error of the y-axis interception and slope are small. The standard deviation of the 11 average values is more or less constant and small, too.
I am making a calibration and later I only measure my y-axis value and want to tell the user the correct corresponding x-axis value.
The problem:
complete error = error due to fit + error due to the averaged values
--> I dont know how to compute the error due to fit.
1, Is there a way to calculate the standard deviation of the slope and y-axis interception out of the standard error to calculate the error due to fit?
2, The origin help articel ("linear regressions results" formula (9) and (10)) showing a corrected and uncorrected form of SXX and SXY is different to the formulas shown here: http://www.originlab.de/doc/Origin-Help/LR-Algorithm
Hope you guys can answer my 2 questions.
kind regards
Slev1n
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Edited by - Slev1n on 03/10/2016 07:07:31 AM |
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SeanMao
China
288 Posts |
Posted - 03/11/2016 : 12:35:36 AM
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Hi,
I am not fully sure that I understand your question correctly, so you have 1 X column and 11 Y column, you will fit the averaged 11 Y columns with respect to 1 X column while including the deviations from averaging 11 Ys?
For this case, I would suggest you use the multi-data fitting mode-- Concatenate Fit in NLFit dialog which will combines replicate data into a single dataset and then fit. This will account for the your so-called "error due to the averaged values" without doing it pre-hand by yourself.
A brief introduction can be seen here:
http://originlab.com/index.aspx?go=Products/Origin/DataAnalysis/CurveFitting/NonlinearFitting#3
A detailed reference can be found here:
http://originlab.com/doc/Origin-Help/Fit-ReplicaData
Regards!
Sean
OriginLab Tech. |
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Slev1n
Germany
4 Posts |
Posted - 03/16/2016 : 08:13:41 AM
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I have measured the amplitude (y-axis) for different concentrations (x-axis). For every concentrations I took 50 values to build an average amplitude value for the corresponding concentration value. At the end, I have 11 averaged amplitudes values for 11 different concentrations showing a very good linear relation. The linear fit has an R² value of 0,99998.
Now I wanted to do some error calculations but I dont know how to use the parameter "standard error". The standard error is given for the y-axis intersection and slope and I want to use this parameter to calculate the standard deviations of these two fit parameters.
kind regards Slev1n |
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SeanMao
China
288 Posts |
Posted - 03/21/2016 : 02:36:36 AM
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Hi,
In fitting, the "Standard Error" in report sheet is the "Standard Deviation" you are looking for.
Regards!
Sean
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Slev1n
Germany
4 Posts |
Posted - 03/21/2016 : 04:18:29 AM
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So if I understand you correctly, the "standard error" shown in the parameter box is already the "standard deviation"?
Well, maybe you should note this somewhere :). Although Wikipedia states this, too, I found the explanation in the "help" puzzling.
However, thank you very much for your help!
Kind regards
Slev1n |
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SeanMao
China
288 Posts |
Posted - 03/21/2016 : 04:50:17 AM
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Hi,
I will bring up your suggestion for discussion.
Thanks!
Regards!
Sean |
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Using Standard error of linear fit