I see two possibilities: 1) Taking logarithm yields log(Y) = log(X)*Z and this is the regular linear regression with intercept = 0, and in this case Z = Sum(log(Xi)*log(Yi))/Sum(log(Xi)^2). This is very simple but not necessarily what you want (but this solution can be used as a starting point for the next one).
2) Let f(Z) = Sum((Yi-Xi^Z)^2) and use nonlinear optimization (see ?nls, ?nlm, ?optim, etc.). Note that you can compute the first two derivatives analytically. --- On Wed, 18/6/08, Avril Coghlan <[EMAIL PROTECTED]> wrote: > From: Avril Coghlan <[EMAIL PROTECTED]> > Subject: [R] how to fit a curve of form Y = X^Z > To: "R mailing list" <r-help@r-project.org> > Received: Wednesday, 18 June, 2008, 12:16 AM > Hello, > > I have a question about R, and will be very grateful for > any help. > I have two variables X and Y, and think that Y is related > to X by a function of the form : Y = X^Z, where Z is < > 1. > However, I'm not sure how to find the best-fit equation > to > fit my data to a curve of this form using R. Have you any > ideas? > > regards > Avril Coghlan > Wellcome Trust Sanger Institute, > Cambridge, UK > > > > > -- > The Wellcome Trust Sanger Institute is operated by Genome > Research > Limited, a charity registered in England with number > 1021457 and a > company registered in England with number 2742969, whose > registered > office is 215 Euston Road, London, NW1 2BE. > > ______________________________________________ > 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.
