Fit data to a form other than a simple polynomial

I am wondering if it's possible to fit data to fit data to a form than like c1*x^n+c2*x^n-1+...+cn*x+c. Instead, I want to fit data to an equation like c1*x^-3 and so on. How could I do this?

Answer 1

[John D'Errico]

My polyfitn tool (on the file exchange) can do it of course. Or several tools from the curve fitting toolbox, the optimization toolbox, the stats tool box. You can do it trivially using backslash.

n = 100;
x = rand(n,1);
y = rand(n,1);

c = [ones(n,1),x,x.^-1]\y
c =
    0.49905
  -0.098795
  0.0043635