# How to find the optimum intercept by fixing the gradient as a fit to experimental data?

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HaAgain on 15 Jan 2019
Edited: Torsten on 16 Jan 2019
I have a set of experimental data that share the relationship: y = A.x^n
I plot my data log y vs log x. The gradient is n and intercept is log(A) which I can obtain from the polyfit function.
I now want to fix the value of n and find the most optimum value of A by some kind of least squares algorithm with respect to the experimental data.
What is the best way to do this?
Thank you

Torsten on 15 Jan 2019
Edited: Torsten on 15 Jan 2019
Use polyfit to fit a polynomial of degree 0 against log(y) - n*log(x) and take exp() of the result.
This gives you optimal A for given n.
Solution is
A = exp( mean( log(y) - n*log(x) ) )
HaAgain on 15 Jan 2019
Yes! That makes a lot of sense based on analytical solution.
thank you
Torsten on 15 Jan 2019
Edited: Torsten on 16 Jan 2019
Or
A = sum(x.^n.*y)/sum(x.^(2*n))
for the original equation.