🚀 go-pugleaf

magdi@uxh.cso.uiuc.edu (Magdi N Azer) writes:

>diamong@gov.on.ca (Gerald Diamond) writes:

>>I am looking for a good reference (or references) for 
>>a least-squares type algorithm which treats both X and Y as 
>>having errors rather than the usual case of assuming all the
>>errors are in one variable.

>	Try the book "Data Reduction and Error Analysis for the Physical
>Sciences"  by Philip R Bevington.  It was printed in 1969, and just this
>year, one of his colleagues updated the book.  The 1992 version comes with
>a disk of the source code in Pascal.  Both versions have the Fortran code.
>I just used the book to write a nonlinear least sqaures program using the
>Levenberg-Marquardt algorithm.  Works great!

The 1969 Bevington copy only says that the usual ordinary linear squares can
be used if the errors in x are sufficiently small to ignore and does not offer
anything for the case where the x and y errors are comparable. Some
straight-forward articles for the case where both variables are subject to
errors are the following:

Mandel, John (1984) "Fitting Straight Lines When Both Variables are Subject to
Error", Journal of Quality Technology, v. 16(1):1.

Reilman, Miriam, Richard Gunst, and Mani Lakshminarayanan (1986) "Stochastic
Regression with Errors in Both Variables", Journal of Quality Technology,
v. 18(3): 162.

Feigelson, Eric and Gutti Babu (1992) "Linear Regression in Astronomy II",
Astrophysical Journal--will appear in Sept 20, 1992 (I have a preprint).

This subject has been the topic of heated debate for decades. The last
reference has a listing of the important papers in various disciplines in
its bibliography section. Code can be received by sending a request to
code@stat.psu.edu. Be aware that what algorithm you use depends on the
error structure of the (x,y) values and whether or not you want to find the
slope of the line or you want to predict a y given a x.

nick
strobel@dirac.phys.washington.edu