Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.1 6/24/83; site brl-vgr.ARPA
Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!decvax!ucbvax!ucbcad!tektronix!hplabs!hao!seismo!brl-tgr!brl-vgr!gwyn
From: gwyn@brl-vgr.ARPA
Newsgroups: net.math,net.ai,net.research
Subject: Re: Best fitting curve - 3 points
Message-ID: <418@brl-vgr.ARPA>
Date: Thu, 28-Jun-84 11:24:45 EDT
Article-I.D.: brl-vgr.418
Posted: Thu Jun 28 11:24:45 1984
Date-Received: Sun, 1-Jul-84 07:25:35 EDT
References: <1970@sdccsu3.UUCP> <90@mouton.UUCP>, <470@hplabs.UUCP>
Organization: Ballistics Research Lab
Lines: 8

Usually the correct approach is to take the parameterized curve that
is expected by theory to pass through the data and do a weighted (by
inverse error squared) least squares fit (i.e. determine the values
of the parameters that minimizes the weighted sum of the squares of
the deviations of the known data points from the curve).  One method
that works well is the Marquardt gradient-expansion technique described
in Bevington's "Data Reduction and Error Analysis for the Physical
Sciences".  Of course this assumes that you HAVE a theory...