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 Post subject: How to calculate regression errors
PostPosted: Tue Feb 26, 2013 9:12 am 
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Joined: Tue Feb 26, 2013 9:00 am
Posts: 6
Apologies in advance as maths isn't my strong point, so please go easy with your replies!

I'm using the "lsfitlinearw" method (least squares linear fit with weighting) to calculate the slope and intercept for a series of X,Y points. I've now been asked to "calculate the standard error and relative standard error of the slope and intercept". How would I go about doing this? I've noticed the lsfitlinearw method returns a series of "fitting report" error values and wondered if any of these would be relevant?

The alglib documentation describes the error values as follows:-
- "RMS error on the X,Y"
- "Average error on the X,Y"
- "Average relative error on the non-zero Y"
- "Maximum error"

Thanks in advance
Andrew


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 Post subject: Re: How to calculate regression errors
PostPosted: Tue Feb 26, 2013 12:39 pm 
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Joined: Fri May 07, 2010 7:06 am
Posts: 880
You can use Rep.ErrPar - it stores vector of standard errors in parameters.


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 Post subject: Re: How to calculate regression errors
PostPosted: Tue Feb 26, 2013 1:38 pm 
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The "rep" output parameter contains properties like avgerror, avgrelerror, etc, but there isn't one called ErrPar. I'm using the C# alglib library if that makes a difference.


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 Post subject: Re: How to calculate regression errors
PostPosted: Tue Feb 26, 2013 1:46 pm 
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Joined: Tue Feb 26, 2013 9:00 am
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Apologies, I've just downloaded the latest version and can see it now.

So the ErrPar structure - is the first value the intercept standard error, and the second the slope std error?

Thanks again


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 Post subject: Re: How to calculate regression errors
PostPosted: Tue Feb 26, 2013 2:45 pm 
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It depends on how you generate your data :) First element of ErrPar corresponds to the first column of the FMatrix, second one corresponds to the second column. Which column is used for intercept is defined by you.


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 Post subject: Re: How to calculate regression errors
PostPosted: Tue Feb 26, 2013 3:23 pm 
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Joined: Tue Feb 26, 2013 9:00 am
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Ah, yes I see it now. I had written my own code to calculate the slope and intercept standard errors, but it was giving different results to those in rep.errpar. My code is using n-2 degrees of freedom, but changing it to n-1 d.f. gives the same results as alglib.

I confess to not really understanding "degrees of freedom". I based my original code on this article: http://www.chem.utoronto.ca/coursenotes/analsci/StatsTutorial/ErrRegr.html.
Is there a reason why this (and many other articles) generally seem to use n-2 d.f., while alglib uses n-1?


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 Post subject: Re: How to calculate regression errors
PostPosted: Tue Feb 26, 2013 6:14 pm 
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I've added this question to issues tracker and will investigate it later. Maybe it is minor error in the regression estimation code... maybe it is just another formula with some hidden meaning...

I recall that unbiased formula for variance uses degrees of freedom which are different from that of same formula for standard deviation. Maybe it is the reason...


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 Post subject: Re: How to calculate regression errors
PostPosted: Wed Feb 27, 2013 8:10 am 
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Thanks for your help on this.

Andrew


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