Re: How to fit like-elliptical funcion?

*To*: mathgroup at smc.vnet.net*Subject*: [mg51563] Re: How to fit like-elliptical funcion?*From*: koopman at sfu.ca (Ray Koopman)*Date*: Sat, 23 Oct 2004 00:21:44 -0400 (EDT)*References*: <cl9s12$7f1$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

kras at iwm.fhg.de (Andriy Krasowsky) wrote in message news:<cl9s12$7f1$1 at smc.vnet.net>... > does anyone knows how to fit an equation like > (x/P1)**a + (y/P2)**b = 1 > on data which are in the first quadrant? P1, P2, a, b are to fit. I assume you mean (x/P1)^a + (y/P2)^b = 1. Let {x,y} be a 2 by n matrix. For fixed a & b, let w = {x^a,y^b}; c = w.Transpose@w; t = Tr/@w . Then taking {P1^-a,P2^-b} == {p,q} = LinearSolve[c,t] gives a least-squares fit. The residual sum of squares is n - t.{p,q} . Minimize it as a function of a & b, then take {P1,P2} = {p^(-1/a),q^(-1/b)} . Note: to keep a & b positive, express them as E^alpha & E^beta and minimize with respect to alpha & beta.