Curve fitting for power equation

Question

Jay 2014-6-4

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https://ww2.mathworks.cn/matlabcentral/answers/132342-curve-fitting-for-power-equation

回答： Star Strider 2014-6-4

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?

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Answer 1

David Sanchez 2014-6-4

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https://ww2.mathworks.cn/matlabcentral/answers/132342-curve-fitting-for-power-equation#answer_139396

在 MATLAB Online 中打开

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.

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Answer 2

Star Strider 2014-6-4

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https://ww2.mathworks.cn/matlabcentral/answers/132342-curve-fitting-for-power-equation#answer_139423

在 MATLAB Online 中打开

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)