[R] how to fit a curve of form Y = X^Z

[Moshe Olshansky]

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 <alc at sanger.ac.uk> wrote:

> From: Avril Coghlan <alc at sanger.ac.uk>
> Subject: [R] how to fit a curve of form Y = X^Z
> To: "R mailing list" <r-help at 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
> 
> 
> 
> 
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