How to generate Best fit second order polynomial equation from MATLAB for given data

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Dan Mathotaarchchi
Dan Mathotaarchchi 2017-5-30
评论： Star Strider 2017-6-1
Hi all can anybody tell me how to generate above equation for this x and y data using MATLAB ? x,y coordinates are 6,460 10,380 12,300 14,180

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Star Strider
Star Strider 2017-5-30
This works:
xy = [6 460; 10 380; 12 300; 14 180]; % Data
b = polyfit(xy(:,1), xy(:,2), 2); % Estimate Parameters For Quadratic Fit
y_fit = polyval(b, xy(:,1)); % Evaluate Fitted Curve
figure(1)
plot(xy(:,1), xy(:,2), 'pg')
hold on
plot(xy(:,1), y_fit, '-r')
hold off
grid
axis([5 15 ylim])

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Dan Mathotaarchchi
Dan Mathotaarchchi 2017-5-31
thank you strider , for the answer however i need to generate the equation too, could you help me for that
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Dan Mathotaarchchi
Dan Mathotaarchchi 2017-6-1
thank you star. but actually it should generate only one equation like this.
z=T^2(3*p^2+2.45*p+4.00)+ 3*p^2*T^2+1.45*pT+2.00T
actually i went through some sources but couldn't find good method to solve this .
Star Strider
Star Strider 2017-6-1
Here is one approach:
T = [500 650 800];
p = 100:100:500;
z = 10*[80 16 225 285 340; 75 150 210 265 310; 70 137.5 195 250 295];
% % % z=T^2(3*p^2+2.45*p+4.00)+ 3*p^2*T^2+1.45*pT+2.00T
zfcn = @(b,p,T) T.^2.*(b(1).*p.^2 + b(2).*p + b(3)) + b(4).*p.^2.*T.^2 + b(5).*T.*p + b(6).*T;
[pM,TM] = meshgrid(p,T);
b0 = ones(1,6);
Z = @(b) norm(z - zfcn(b,pM,TM)); % Residual Norm Cost Function
[B,resnrm] = fminsearch(Z, b0); % Estimate Parameters
figure(1)
stem3(pM, TM, z)
hold on
mesh(pM, TM, zfcn(B,pM,TM))
hold off
grid on
The fit is not good, however the code runs. I will leave it to you to experiment to get the result you want. There are probably other Optimization Toolbox functions that can give a better result.

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