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sbaruah
Germany
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 Posted - 03/01/2006 : 05:05:40 AM
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Hi,
If someone can help me out: I want to calculate by hand the confidence band for a linear fit of some data points; but nowhere I can find any hint. Any suggestions are appreciated..
Origin Version (Select Help-->About Origin): 7.5
Operating System: windows xp |
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easwar
USA
1964 Posts |
Posted - 03/01/2006 : 09:09:48 AM
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Hi,
First of all I wanted to make sure you are aware Origin can compute and draw the confidence band for you. The Linear Fit tool (menu:Tools->Linear Fit) has a check box for Confidence and Prediction bands on the Operations tab. Start with a graph of your data and bring up this tool.
If you are looking for the formula to check the computation by hand etc, you can get that information in the Origin help file, under the topic:
Analysis:Curve Fitting>Linear Fitting Using the Tools>
and then look under the Linear Fit Tools Controls and expand the Operations Tab link.
Easwar
OriginLab
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sbaruah
Germany
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Posted - 03/02/2006 : 06:05:25 AM
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Hi,
Thanks for the suggestion. I have looked into the way the confidence band is calculated, but found that this is not what I want. My problem is the following:
I have 3 data points (2,3), (3,4), (4,4) with error bars on y data as 0.5, 0.1 and 0.1 respectively. I want to fit the data linearly and want to find the value of y at x=1. This can be done with a linear fit. But how can I get the error on the y value of the point.
First I thought the confidence band will give me the error bar of y at x=1. But it seems that the confidence band is the same whether the error bars of the individual data points are smaller or bigger.
Any suggestions to lighten my head?
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Leo_Li
China
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Posted - 03/03/2006 : 01:25:12 AM
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Hi
Confidence bands are two lines such that they enclose the true best fit curve if you have more data points. For example, if you set confidence = 95, then you are 95% confident that the best fitted curve is surrounded by the confidence bands, leaving a 5% possibility the line is outisde.
In general, confidence bands change while error bars of the individual data points are smaller or bigger, unless all error bars are scaled by the same factor (since they are cancelled out in the calculation).
It is not a good idea to estimate error of an individual data point from the confidence band. Instead, you are suggested to use error propagation
y_err = sqrt( a_err^2 * x^2 + b_err^2 ),
in which, a_err and b_err are standard errors of slope and intercept, respectively. And x = 1; y_err is the standard error of y at x = 1.
This approach is reliable, since by finding value on fitted curve, y is simply calculated by
y = a * x + b
Please refer to http://en.wikipedia.org/wiki/Propagated_error for the formular of error propagation.
Leo
OriginLab Corp. |
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Leo_Li
China
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Posted - 03/03/2006 : 11:20:43 PM
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Hi sbaruah,
Sorry, the formula in above page needs another term, since the covariance between a and b is not negligible:
y_err = sqrt( a_err^2 * x^2 + b_err^2 + x * ab_cov^2),
and ab_cov is the covariance of a and b, which can be obtained in nonlinear curve fitting dialog (choose menu: action -> results, and click "Var-Cov Matrix" button).
Ref. http://www.itl.nist.gov/div898/handbook/mpc/section5/mpc55.htm
Leo
OriginLab Corp.
Edited by - Leo_Li on 03/03/2006 11:21:59 PM |
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sbaruah
Germany
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Posted - 03/06/2006 : 07:53:49 AM
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Hi Leo,
Thanks for you comments. I am now convinced that it would not be a appropriate to calculate the y_error from the confidence band. Thanks for your idea!
Regards
sbaruah |
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Confidence band for Linear Fit