Curve fitting for power equation

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?

Answer 1

[David Sanchez]

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.

Answer 2

[Star Strider]

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.