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Hans5
Czech Republic
4 Posts |
 Posted - 05/23/2011 : 5:11:42 PM
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Hi,
I have a set of data with error bars and I'd like to fit it with linear function. But it seems like Origin fits just those five points, without their error bars. The confidence band (green) is much narrower than error bars and standard errors of constants a and b are too low I think.
So here's my question - how to make linear fit which respects the uncertainties of X and Y? Thanks for any piece of advice. |
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greg
USA
1378 Posts |
Posted - 05/24/2011 : 12:33:32 PM
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The sort answer is : This is very linear data even without error bars.
I am not sure what version you are using, but in every version I can recall we automatically include weighting if there are error bars in the plot. If you start from a worksheet, you have to select both Y and Y Err columns when you start the fit or add the error after starting if you have the fit dialog open.
In either case, the error bars serve only to give more or less weight to the individual points and in your case, the errors are so large, they have little effect on the fit, which is so good that even at 99.8% confidence, the band is still smaller than the errors.
I captured your data using our new Digitizer (8.5.1) and got this result:
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Hans5
Czech Republic
4 Posts |
Posted - 05/24/2011 : 1:23:08 PM
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I'm using version 8 (SR0).
My problem is I need to know the uncertainties of a and b. I see that the linear function is ok. But if Y values are e.g. 120 +/- 50, I'd estimate the intercept to be about 110 +/- 50, not 110 +/- 5.
When I use the same data without error bars, I get the same results with the same uncertainties. So those error bars can be used only for weighting the individual points, or is there any possibility to obtain those "larger" uncertainties?
Thanks. |
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Hans5
Czech Republic
4 Posts |
Posted - 05/24/2011 : 5:05:59 PM
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| I'm trying to say that 95% confidence band of the linear function should be approximately as wide as the error bars, I think. |
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larry_lan
China
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Posted - 05/24/2011 : 10:36:41 PM
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quote:
My problem is I need to know the uncertainties of a and b.
You should go to the report worksheet and see 'Standard Error' for the uncertainties of a and b.
quote:
But if Y values are e.g. 120 +/- 50, I'd estimate the intercept to be about 110 +/- 50, not 110 +/- 5.
How can you get this conclusion?
quote:
When I use the same data without error bars, I get the same results with the same uncertainties.
See the image above, either fitted result and sd are different.
quote:
I'm trying to say that 95% confidence band of the linear function should be approximately as wide as the error bars, I think.
Again, how can you get this conclusion? Confidence bands show the limits of all possible fitted lines for the given data. In other words, say, 95% confidence band means there is 95% possibility that the best-fit line lies within the confidence bands. Generally speaking, the better the fit, the narrower the band.
As Greg mentioned above, a large error bar mean less weights the point contribute to the fitted curve. It doesn't means the confidence band as wide as the error bar.
Please read our Help document to see how Origin compute parameter values, standard error, and confidence band.
Thanks
Larry
OriginLab
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Standard Error of Linear Fitting