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sbaruah
Germany
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 Posted - 03/08/2006 : 04:33:30 AM
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Hi,
Trying to understand: what will be the confidence band of a linear fit (with y-error as the weight) for 3 points like the following?
x | y | y-error
______|___________|__________
1.0 | 1.0 | 0.5
2.0 | 2.0 | 0.3
3.0 | 3.0 | 0.4
Is there any tricks I am missing as the confidence band reduces to a line?
Regards,
Sbaruah
Origin Version (Select Help-->About Origin): 7.5
Operating System: win xp
Edited by - sbaruah on 03/08/2006 06:24:02 AM
Edited by - sbaruah on 03/08/2006 06:27:46 AM |
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minimax
348 Posts |
Posted - 03/09/2006 : 01:02:04 AM
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Hi sbaruah,
It is a correct result that the confidence band reduces to a line in your case. It is simply casued by your data itself, in which all the x and y are equal. When your data consists of all equal x and y, the confidence band will reduce to a line no matter what the errors are.
With regard to the formula of confidence band, you could refer to Origin's help ->
Analysis:Curve Fitting ->
A Note on Linear Fitting Theory ->
Theory of Linear Regression...
Max
OriginLab GZoffice |
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sbaruah
Germany
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Posted - 03/09/2006 : 03:34:03 AM
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Hi,
Thanks for the comment. Can you please explain me the physical meaning why the band reduces to a line if the points are exactly in a line, no matter whatever their errors are..
Regards,
sbaruah |
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easwar
USA
1964 Posts |
Posted - 03/09/2006 : 10:28:54 AM
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Hi sbaruah,
First of all the confidence bands show the limit of all possible fit lines to the given data, within the chosen confidence limit (default 95%)
So if you look at the graph below (which has different data from yours), the green line is the conf bands, the red line is the fit, and the blue lines (drawn arbitrarily by hand) are possible fits to data that all fall within the confidence band.
Now, in the case of your data, as Max explained, ALL of your data points fall on a perfect straight line and there is no deviation from that straight line.
If you look at the Origin help file section:
Analysis: Curve Fitting>Anote on Linear Fitting Theory>Theory of Linear Regression, you will see the equation for minimizing Chi-sqr (SSR):
In this equation the error just appears as a weighting factor in the sum. If you look however at the numerator, in your case, since the data all fall on a perfect straight line, the sum will be zero, no matter what the error is. So in other words error bars on such "perfect" data have no effect and there is thus no "variation" of the fit line possible at all.
Because there is no variation of the fit line possible, there is no "curvature" to the confidence band - "all possible" fit lines in your case simply "collapse" into one single line represented by your data, and so the confidence bands are just one straight line.
Hope this explanation helps.
Easwar
OriginLab
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sbaruah
Germany
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Posted - 03/13/2006 : 04:29:04 AM
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Hi,
Thank you very much for your clear explannation. It will be helpful for me as well as others who are trying to understand the applicability of the confidence band for various physical data.
Thanks and regards,
S Baruah
Instt. for Physics
Univ. of Greifswald, Germany
Edited by - sbaruah on 03/13/2006 04:30:45 AM |
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what will be the Confidence band for this case?