MATLAB: 3D – Surface Response Plot – Surface of best fit

Question

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.

Answer 1

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;