OK thanks Moshe I will think about your answer. Cheers Bill
On Tue, Sep 2, 2008 at 5:55 AM, Moshe Olshansky <[EMAIL PROTECTED]> wrote: > I do not see why you can not use regression even in this case. > > To make things more simple suppose that the exact model is: > > y = a + b*x, i.e. > y1 = a + b*x1 > ... > yn = a + b*xn > > But you can not observe y and x. Instead you observe > ui = xi + ei (i=1,...,n) and > vi = yi + di (i=1,...,n) > > Now you have > > vi = yi + di = a + b*xi + di = a + b*(ui - ei) + di > = a + b*ui + (di - b*ei) > > and under regular assumptions about ei's end di's we get a standard > regression problem (note that b is unknown to you but is constant). > > > --- On Tue, 2/9/08, William Simpson <[EMAIL PROTECTED]> wrote: > >> From: William Simpson <[EMAIL PROTECTED]> >> Subject: [R] intercept of 3D line? (Orthogonal regression) >> To: r-help@r-project.org >> Received: Tuesday, 2 September, 2008, 4:53 AM >> I posted before recently about fitting 3D data x, y, z where >> all have >> error attached. >> I want to predict z from x and y; something like >> z = b0 + b1*x + b2*y >> But multiple regression is not suitable because all of x, >> y, and z have errors. >> >> I have plotted a 3D scatterplot of some data using rgl. I >> see that the >> data form a cigar-shaped cloud. I think multiple regression >> is only >> suitable when the points fall on a plane (forgetting about >> the error >> in x and y). >> >> I now know the right way how to find the best fitting plane >> to x,y,z >> data using princomp. >> But a new problem is how to get the best fitting *line*. I >> actually >> know how to do that too using princomp. But there is a >> mathematical >> problem: there's no way to specify a line in 3D space >> in the form >> z=f(x,y) or in other words with an intercept and slopes. >> Instead, one way to deal with the problem is to use a >> parametric >> version of the line: you use an arbitrary starting point >> x0, y0, z0 >> and the direction vector of your line (I know how to get >> the direction >> vector). >> >> BUT how do I get the intercept??? At this point my lines >> just go >> through the origin. >> Do I just use $center from the princomp output modified in >> some way? >> >> Thanks for any help! >> >> Cheers >> Bill >> >> ______________________________________________ >> R-help@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. > ______________________________________________ R-help@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.