How to find coefficient and power of polynomial y=a*x^n

I have 2 vector and I need to approximate the scattered plot they make to a polynomial like mentioned above. I've been searching for a couple of days now but for no avail. Any help will be much appreciated.

Answer 1

[Star Strider]

Two options:

x = 1:20;
y = 3*x.^pi + randn(size(x));

blin = [ones(size(x(:))) log(x(:))] \ log(y(:))                     % Linear Approximation
blinc = [exp(blin(1)); blin(2)]
linreg = exp(blin(1)) * x.^blin(2);

figure
plot(x, y, 'p')
hold on
plot(x, linreg, '-r')
hold off
grid

b0 = [10; 10];
bnlin = fminsearch(@(b) norm(y(:) - b(1).*x(:).^b(2)), b0)          % Nonlinear Approximation
nlinreg = bnlin(1) .* x(:).^bnlin(2);

figure
plot(x, y, 'p')
hold on
plot(x, nlinreg, '-r')
hold off
grid

The nonlinear estimation is more accurate.

[kfir reuven]

Thank you very much. This is very helpful and works very well.

And of course, thank you for such a quick answer.

[Star Strider]

As always, my pleasure.