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3D - Surface Response Plot - Surface of best fit

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I'm having trouble plotting a curve/surface of best fit through data points. I have z - matrix of 9 data points, which correspend to different combinations of values from an x-vector of 3 and a y-vector of 3. I have managed to plot a surface plot which uses interpolation and fits a curve through the data. Instead of this, I would like to plot a curve of best fit through the data points using a low order polynomial instead.
Assistance would be greatly appreciated.
This is a plot of what I have so far.

Accepted Answer

Ameer Hamza
Ameer Hamza on 30 Oct 2020
Edited: Ameer Hamza on 30 Oct 2020
If you have a curve fitting toolbox, you can use fit(): https://www.mathworks.com/help/curvefit/fit.html function with fitype chosen from polyij as given here: https://www.mathworks.com/help/curvefit/list-of-library-models-for-curve-and-surface-fitting.html#btbcxlm. For example
x; % x-values 9x1
y; % y-values 9x1
z; % z-values 9x1
X = [x y];
Y = z;
fitted_model = fit(X, Y, 'poly22')
If you don't have the toolbox, you can still use mldivide (\) to do least square curve-fitting. For example, suppose you want to fit following model
Then you can do something like this
X = [ones(size(x)) x y x.^2 y.^2 x.*y];
Y = z;
a = X\Y;
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