🚀 go-pugleaf

A chemist has asked me to solve a problem: she has data and a model
which is to be fit by 'least squares'.  It looks like non-linear
regression, except that:

    1. the model has two equations
    2. both are non-linear
    3. there are parameters common to the two equations.

I would like to know:

    1. is there a 'standard' method for solving this problem?
    2. is there literature in stat or chemistry which I could read?

Clearly, I can form the sum of squared errors for each equation and
add them together.  I have lots of methods for minimizing the result.
However, this seems to ignore the question of the weighting of the two
equations.

I solved this kind of problem several years ago by writing FORTRAN +
IMSL.  Now that it has come up again, I wish I had some backup
literature that at least suggests the 'standard' solution method.  I
don't like reinventing the wheel.

Since the current data matrix is small, 4 by 2, I'm going to use
non-linear optimization in Quattro Pro this time.  It produces nice
graphs.  But, if I stick with QP, I'll also have to calculate the
standard errors of the parameter estimates.  Right now, I'm not
looking forward to this.

Thanks for the help,
-- 
Jeff Bangert			jeff@kuhub.cc.ukans.edu
Computer Center			jeff@ukanvax.bitnet
University of Kansas
Lawrence, KS 66045
(913)864-0466