# Curve fitting for power equation

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Jay on 4 Jun 2014
Answered: Star Strider on 4 Jun 2014
how to fit curve for an equation y=a*(x1)^b * (x2)^c; where a b and c are constants to find and we do know sets f y x1 and x2?

David Sanchez on 4 Jun 2014
Use the curve fitting tool
cftool % this will open the curve fitting tool interface
From the user interface, select you x, y, z, data and insert your Custom Equation (the default method is Interpolant, change it in the selection list) The rest is almost straight forward.

Star Strider on 4 Jun 2014
To fit your equation using fminsearch, this works:
% —————————— Define Function ——————————
PwrEqn = @(b,x) b(1) .* x(:,1).^b(2) .* x(:,2).^b(3);
% —————————— Create Data ——————————
b = [3 5 7]; % Parameters
x = rand(20,2); % Matrix of ‘x’ values
y = PwrEqn(b,x) + rand(20,1)*0.001; % Create ‘y’ using ‘PwrEqn’ and add noise
% —————————— Fit Data and Estimate Parameters ——————————
OLS = @(b) sum((y - PwrEqn(b,x)).^2);
b = fminsearch(OLS, [1 1 1]);
fprintf(1,'Estimated parameters:\n\ta = %.4f\n\tb = %.4f\n\tc = %.4f\n\n', b)
NOTE: Your x data have to be in one (Nx2) matrix (as [x1 x2]), and y as a (Nx1) vector.