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.
