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Re: test a cloud of 2D points for linearity


From: Georg P. Israel
Subject: Re: test a cloud of 2D points for linearity
Date: Thu, 28 May 2009 15:21:58 +0200

Dear Joe,

thank you very much for the excellent pointers!

Best regards

Georg P. Israel


On Wed, 2009-05-27 at 16:37 +0000, address@hidden wrote:
> That's almost exactly what a principle component analysis will give you, 
> except the "best" line is based on the orthogonal distances you are 
> interested in rather than the vertical distances that are minimized in normal 
> linear regression.
> 
> The svd() function will give you the transformation matrices you need to 
> "rotate" your data set and calculate the distances (and then any statistics 
> of those that you want).
> 
> Sent via BlackBerry by AT&T
> 
> -----Original Message-----
> From: "Georg P. Israel" <address@hidden>
> 
> Date: Wed, 27 May 2009 18:02:41 
> To: Joe Craig<address@hidden>
> Subject: Re: test a cloud of 2D points for linearity
> 
> 
> Dear Joe,
> 
> thanks for the pointer.
> But I am still not sure if this is correct.
> The best fit line in 2D space is just an intermediate result.
> At the end, I need to look along this line and compute the root mean
> square orthogonal distance of the points from the cloud to the best
> fitting line.
> 
> And, this RMS error function has to be independent of the major angle of
> this cloud.
> Hence, the result has to be the same if I rotate the cloud by 90 degree
> or any other angle.
> But to my knowledge, the normal regression functions compute the
> vertical distance of the cloud point to the estimated line.
> 
> Anyhow,
> thanks for your suggestion
> 
> Georg
> 
> 
> 
> On Wed, 2009-05-27 at 11:37 -0400, Joe Craig wrote:
> > The topic you need to study is "Linear Regression."
> > 
> > On Wed, May 27, 2009 at 10:56 AM, Georg P. Israel
> > <address@hidden> wrote:
> >         Dear all,
> >         
> >         I am almost ashamed to ask this stupid question,
> >         but with all this wealth of function, i seem to not find the
> >         right
> >         stuff. Even thought, I know that it is there, probably just
> >         under my
> >         nose.
> >         
> >         here my problem:
> >         
> >         I have a number of points in a plain (2D points)
> >         This points can have an arbitrary distribution.
> >         I would like to have a function that will fit the line through
> >         this
> >         cloud of points.
> >         
> >         I expect that one point of this line is the mean of all points
> >         plus some
> >         direction vector.
> >         
> >         The next thing that I like to have now is the RMS of all the
> >         distances
> >         of the points along this line. This is basically a variance as
> >         seen
> >         along this line.
> >         
> >         Now, I can certainly start to clumsily develop this function,
> >         but I am
> >         sure that I am just overlooking the right function.
> >         
> >         Hence,
> >         please point my nose this this function ...
> >         
> >         Best regards
> >         
> >         Georg P. Israel
> >         
> >         
> >         
> >         _______________________________________________
> >         Help-octave mailing list
> >         address@hidden
> >         https://www-old.cae.wisc.edu/mailman/listinfo/help-octave
> > 
> > 
> > 
> > -- 
> > Joe
> > http://stockcentral.com
> > 
> > Join me in Salt Lake City, August 7-9, 2009 for
> > InvestEd 2009 (http://www.investor-education.org)
> 
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