Use the regress regression analysis in matlab to fit the surface (get the equation coefficients) and the residual graph

Today I have to use matlab to fit the surface. It takes at least three points to determine a face. With two points, there are multiple sides.

Use the regress regression analysis in matlab to fit the surface (get the equation coefficients) and the residual graph.

The matlab code is as follows:

% Sample data, freely compiled
a1 = 76 ;b1 = 72 ; 
a2 = 59 ;b2 = 113; 
a3 = 48 ;b3 = 63 ; 
a4 = 66 ;b4 = 158; 
a5 = 92 ;b5 = 166;
z0 = 20; 

 % Note that the column vector is required
x = [a1, a2, a3, a4]'; % [76;59;48;66]
y = [b1, b2, b3, b4]'; % [72;113;63;158]
z = [z0-0.1, z0, z0-0.2, z0+0.1]'; % [19.90;20;19.80;20.10]

 k = length(x);% returns the total number of samples
 X=[ones(k,1) x y];% where there are n data, fill in ones(n,1)
% X: [1,76,72;1,59,113;1,48,63;1,66,158]

 % Call regression function to find model parameters
[b, bint, r, rint, stats] = regress(z,X); 
 % Get the 95% confidence interval bint of parameter b,
 % Residual r and residual 95% confidence interval rint,
 % stats has a vector of three components, which are the coefficient of determination R-squared, F-value, and regression p-value.

 % Draw a picture of known points
figure(1)
scatter3(x, y, z, '*');
hold on

 % Regression result b: [19.5255;0.0024;0.0027], that is, z = 19.5255 + 0.0024*x + 0.0027*y
p00=b(1);
p10=b(2);
p01=b(3);


 % Make a regression surface, suppose we make a surface with a range of 150x100
m = 150; n =100;
data = ones(m,n);
for i = 1:m
    for j = 1:n
        data(i,j)= p00 + p10*i + p01*j;
    end
end
Z = data;
[X,Y]=meshgrid(1:1:n,1:1:m);     
 % Visualization   
surf(X,Y,Z);
 title('Fit the plane')
xlabel('x'); ylabel('y'); zlabel('z');
 legend('is a known point')

figure(2);
 rcoplot(r, rint);% Make residual plot
 title('Residual graph drawing');
 xlabel('data'); ylabel('residuals');

The regression analysis fitting surface is shown in the figure below:

The equation coefficients are in b:

The residual is shown in the figure below:

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