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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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