Hi there, I am trying to measure orthogonal/perpendicular distances from regression lines (i.e. the shortest distance from a given point to my regression line). As it sounds rather easy (basically just an orthogonal/perpendicular residual) I hoped that there was some function in R that can do that. All efforts so far remained unsuccessful, however. Does anybody know? Thnx and cheers, Philipp -- View this message in context: http://www.nabble.com/orthogonal-perpendicular-distance-from-regression-line-tp22123179p22123179.html Sent from the R help mailing list archive at Nabble.com.
roger koenker
2009-Feb-20 19:17 UTC
[R] orthogonal/perpendicular distance from regression line
For the bivariate case:
g <- function(b,x,y)
(abs(y - b[1] - b[2] * x))/sqrt(1 + crossprod(b))
url: www.econ.uiuc.edu/~roger Roger Koenker
email rkoenker at uiuc.edu Department of Economics
vox: 217-333-4558 University of Illinois
fax: 217-244-6678 Champaign, IL 61820
On Feb 20, 2009, at 11:12 AM, GAF wrote:
>
> Hi there,
> I am trying to measure orthogonal/perpendicular distances from
> regression
> lines (i.e. the shortest distance from a given point to my
> regression line).
> As it sounds rather easy (basically just an orthogonal/perpendicular
> residual) I hoped that there was some function in R that can do
> that. All
> efforts so far remained unsuccessful, however.
> Does anybody know?
> Thnx and cheers,
> Philipp
> --
> View this message in context:
http://www.nabble.com/orthogonal-perpendicular-distance-from-regression-line-tp22123179p22123179.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
Jeff Newmiller
2009-Feb-21 02:05 UTC
[R] orthogonal/perpendicular distance from regression line
On Fri, 20 Feb 2009, GAF wrote:> > Hi there, > I am trying to measure orthogonal/perpendicular distances from regression > lines (i.e. the shortest distance from a given point to my regression line). > As it sounds rather easy (basically just an orthogonal/perpendicular > residual) I hoped that there was some function in R that can do that. All > efforts so far remained unsuccessful, however. > Does anybody know?You could do this with [1], but if you are hoping to learn something statistical by doing this you should probably reconsider, because the regression line residuals are minimized along the dependent variable axis, and if the coordinate system is rotated (that is, you look at deviation from the regression line to the points along a different direction) then the residuals on that regression line will no longer be minimized. [1] http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html --------------------------------------------------------------------------- Jeff Newmiller The ..... ..... Go Live... DCN:<jdnewmil at dcn.davis.ca.us> Basics: ##.#. ##.#. Live Go... Live: OO#.. Dead: OO#.. Playing Research Engineer (Solar/Batteries O.O#. #.O#. with /Software/Embedded Controllers) .OO#. .OO#. rocks...2k
Mark Difford
2009-Feb-21 09:06 UTC
[R] orthogonal/perpendicular distance from regression line
Hi Jeff,>> You could do this with [1], but if you are hoping to learn something >> statistical by doing this you should probably reconsider, because the >> regression line residuals are minimized along the dependent variable >> axis,It should be said that there are valid forms of linear regression where this is not true and it is the orthogonal residuals that are wanted. Perhaps the main case is where there are errors in x and y: indeed, this is how the "lines" (i.e. principal components) are fitted in principal component analysis. Regards, Mark. Jeff Newmiller wrote:> > On Fri, 20 Feb 2009, GAF wrote: > >> >> Hi there, >> I am trying to measure orthogonal/perpendicular distances from regression >> lines (i.e. the shortest distance from a given point to my regression >> line). >> As it sounds rather easy (basically just an orthogonal/perpendicular >> residual) I hoped that there was some function in R that can do that. All >> efforts so far remained unsuccessful, however. >> Does anybody know? > > You could do this with [1], but if you are hoping to learn something > statistical by doing this you should probably reconsider, because the > regression line residuals are minimized along the dependent variable axis, > and if the coordinate system is rotated (that is, you look at > deviation from the regression line to the points along a different > direction) then the residuals on that regression line will no longer be > minimized. > > [1] http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html > > --------------------------------------------------------------------------- > Jeff Newmiller The ..... ..... Go > Live... > DCN:<jdnewmil at dcn.davis.ca.us> Basics: ##.#. ##.#. Live > Go... > Live: OO#.. Dead: OO#.. Playing > Research Engineer (Solar/Batteries O.O#. #.O#. with > /Software/Embedded Controllers) .OO#. .OO#. > rocks...2k > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > >-- View this message in context: http://www.nabble.com/orthogonal-perpendicular-distance-from-regression-line-tp22123179p22134025.html Sent from the R help mailing list archive at Nabble.com.