How to minimize residual error (i.e., cost function) using least squares?

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TJ 2019-12-27

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/498146-how-to-minimize-residual-error-i-e-cost-function-using-least-squares

编辑： TJ 2020-1-4

I have a data set, 'x' and 'xhat', where 'x' is the experimental data and 'xhat' is calculated. The cost functions are b1, b2 and b3 - these are the values that need to be minimized to reduce the residual error. M is previously calculated elsewhere in the script.

% x is the experimental data
T = 100 + b1
K = b2 + b3 * M^2
xhat = T + (T * K * M^2) % xhat is supposed to be calculated
res=x-xhat % residual error 
min(b1,b2,b3)= sum(||res||).^2 % Least squares - Levenberg-Marquardt Algorithm

Having never worked with cftool before, can someone assist me in finding the values of the cost function?

Thanks in advance!

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Answer 1

Shubh Sahu 2019-12-31

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https://ww2.mathworks.cn/matlabcentral/answers/498146-how-to-minimize-residual-error-i-e-cost-function-using-least-squares#answer_408234

Load your dataset in workspace and then open cftool. Select data to fit in curve. Select the model type 'custom' and input the whole equation which you want to minimize. Please refer to these links for further help :

https://www.mathworks.com/help/curvefit/curvefitting-app.html

https://www.mathworks.com/help/curvefit/interactive-curve-and-surface-fitting-.html

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TJ 2020-1-4

编辑：TJ 2020-1-4

在 MATLAB Online 中打开

Shubh,

Thank you for the links. I was only able to implement a two variable custom equation - in my case, x = the equation behind

x = the equation behind '100' in T = 100 + b1
y = the value of M

However, I believe I'll need a three independent variable custom equation to calculate the residuals. How do I implement a three independent variable custom equation?

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