Hyperbolic regression

[MedGen]

I'm currently trying to find a way to perform a hyperbolic regression on a set of data I have as various transformations (i.e. logarithmic and reciprocal) can't linearise it. Having look through the literature it would appear that it can be described by a hyperbola, which is all well and good, but I need to use it as a standard curve for later on.

 

The reason it is described by a hyperbola is because it is a the result of antibody binding and enzyme-substrate reactions which are themselves described by a hyperbola.

 

I have an article which describes a derivation and a description of the requisite Python script that spits out the relevant coefficients which can then be fed into their equation to describe the relationship of the dependent and independent. They say it is based on a least squares fit (????), I've tried to find something that describes that, but to no avail.

 

The problem is they don't actually link to the script itself which can be run in a Python shell, even though they say it is in the supplementary documents (it really isn't).

 

So this a bit of a computing and maths problem I've got. I can't write my own programme as I don't know how, and my maths is insufficient to be able to derive my own forumla for calculating the relevant coefficients to plug into their forumla.

 

Help!

[D H]

The linearization for [math]y=a/(x+b)[/math] is [math]z = \alpha x + \beta[/math], with [math]z= 1/y[/math], [math]\alpha = 1/a[/math], and [math]\beta = b/a[/math]. Use the standard linear regression techniques to solve for [math]\alpha[/math] and [math]\beta[/math] and then solve for a and b.

 

Note that this will give a least squares fit in 1/y, not y.