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how to fit a surface to 3d data points

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Alessandraro
Alessandraro 2019-4-17
评论： Star Strider 2019-6-12
Hi, I have a set of 3D data points (x,y,z) that I want to fit using the equation
A*x^2+B*y^2+C*x*y = [ z (1-z) ]^2
A, B, C being the parameters I have to estimate.
can anyone help me?

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Star Strider
Star Strider 2019-4-17
If your data points are each vectors, try this:
x = rand(1, 10); % Create Data
y = rand(1, 10); % Create Data
z = rand(1, 10); % Create Data
DM = [x(:).^2, y(:).^2, x(:).*y(:)]; % Design Matrix
P = DM \ (z(:).*(1-z(:))).^2; % Estimate Parameters
A = P(1);
B = P(2);
C = P(3)
Experiment to get the result you want.
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Alessandraro
Alessandraro 2019-6-12
编辑：Alessandraro 2019-6-12
Thank you. I am sorry, can I ask you why you calculate SStot
SStot = sum(([(z(:)-D(:))./(1-D(:)) (1-z(:))].^2 - mean(z(:))).^2);
calculating mean(z(:)) instead of mean([(z(:)-D(:))./(1-D(:)) (1-z(:))].^2)?
Thank you.
Star Strider
Star Strider 2019-6-12
Because that is how ‘SStot’ is calculated, at least as I interpret it in the context of yoiur model. See the Wikipedia article on: Coefficient of determination (link).

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