I don’t have the Curve Fitting Toolbox, so I’m using fminsearch here:
P = randi(9, 10, 1); % Create Data
W = randi(9, 10, 1); % Create Data
L = randi(9, 10, 1); % Create Data
Y = randi(9, 10, 1); % Create Data
PWL = [P(:) W(:) L(:)]; % Create Single Variable
% % MAPPING: b(1) = a, b(2) =b, b(3) = c, b(4) = d
Y_fit = @(b,PWL) PWL(:,1).^b(1) + PWL(:,2).^b(2) + PWL(:,3).^b(3) + b(4);
SSECF = @(b) sum((Y(:) - Y_fit(b,PWL)).^2); % Sum-Squared-Error Cost Function
B0 = [1; 1; 1; 1]; % Initial Parameter Estimates
[B, SSE] = fminsearch(SSECF, B0); % Estimate Parameters
figure(1)
subplot(3,1,1)
plot(P, Y,'xr', P, Y_fit(B,PWL),'bp')
grid
subplot(3,1,2)
plot(W, Y,'xr', W, Y_fit(B,PWL),'bp')
grid
subplot(3,1,3)
plot(L, Y,'xr', L, Y_fit(B,PWL),'bp')
grid
I added the plots, since it usually helps me determine how good the fit is. If you want to plot your data and the regression, you will have to experiment with the plots, since they can be a bit difficult when you have three independent variables. The plotting I did here works, but it may not be the best for your data.
