# Least Squares Method- Νon linear to Linear

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E on 9 Feb 2013
Hello! I need to approach some given points [X,Y]with the use of the method of the least squares.Also,for the approximation of these points we have the function f=ax/(b+x).My problem is that I can't bring the function to the standard form f=aX+b.Does anyone know what should I do? Thank you in advance!

Shashank Prasanna on 9 Feb 2013
You are talking about two different things here.
f=aX+b
is linear regression which can be solved by either \ or the regress function.
f=ax/(b+x)
as you noted is non-linear, you can use nlinfit in the statistics toolbox or set up your own optimization routine using fminsearch by setting up a least squares to solve it.
That said of course you can fit your data using the first linear model, but depending on your data this may not be the right model, but its this or that, its your choice of model for your data.
E on 9 Feb 2013
Τhank you! :)

Bill Whiten on 9 Feb 2013
You can write the equation as f=(a/b)x-(1/b)fx and use linear regression for the coefficients (a/b) and (1/b). Convert these to a and b as initial estimates for fminsearch or non linear least squares functions.
Greg Heath on 9 Feb 2013
Your equation makes no sense to me at all. How was it derived?