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

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

Answer 1

[Torsten]

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]

Yes! That makes a lot of sense based on analytical solution.

thank you

[Torsten]

Or

A = sum(x.^n.*y)/sum(x.^(2*n))

for the original equation.