I would like to fit a hyperbola to a set of data points. In the post at this link: How can I fit a set of data points to a hyperbola Claude Leibovici rearranges the equation I would like to use to give it a linear form suitable for least squares regression (or an initial estimate, at least).
He starts with: $$y=\frac{k}{b+x}+c$$ And then sets: $$t_i=\frac{1}{b+x_i}$$ To give: $$y=b t+b$$ I'm afraid I don't understand how this set of equations works - what happened to the rest of the parameters?
I would like to use the first equation in a linear form so that I can obtain a good initial estimate of $k$, $b$ and $c$.
Thanks.