Re: Orthogonal Distance Regression available?

*To*: mathgroup at smc.vnet.net*Subject*: [mg109881] Re: Orthogonal Distance Regression available?*From*: Tomas Garza <tgarza10 at msn.com>*Date*: Fri, 21 May 2010 06:44:27 -0400 (EDT)

I don't know what you mean by "straightforward", but perhaps you'd care to look at a demonstration I submitted some time ago to the Wolfram Demonstrations Project: http://demonstrations.wolfram.com/OrdinaryRegressionAndOrthogonalRegressionInThePlane/ Tomas > Date: Wed, 19 May 2010 20:13:14 -0400 > From: biophys.hershey at me.com > Subject: [mg109839] Orthogonal Distance Regression available? > To: mathgroup at smc.vnet.net > > Is there any straightforward way to do Orthogonal Distance Regression (ODR) in Mathematica? If not, this would be a nice feature to have in Mathematica. > > Background: > > Regular nonlinear least square fitting minimizes in one dimension the distance between the data and some function. ODR does it in all dimensions simultaneously. This is desirable e.g. when the data have errors in more than one dimension, or if parametric equations are used. The basic approach is similar to nonlinear least squares, only that one additional step is done in each iteration on top of minimizing the distance between the function and the data. Each data point has a corresponding point on the fit function, and the distance between these two points is minimized by moving the corresponding point along the function. So, if nn is the number of fitting parameters in nonlinear least squares, and nd is the number of data points, then ODR has nn+nd fitting parameters if we are in 2D. > > Thanks, > Joerg >