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

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

Answer 1

[Star Strider]

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])

Answer 2

[Dan Mathotaarchchi]

thank you strider , for the answer however i need to generate the equation too, could you help me for that

[Star Strider]

My pleasure.

This will save the quadratic equation to the ‘Eqn’ variable:

Eqn = sprintf('y = %.2f*x^2%+.2f*x%+.2f', b)

and this will print the equation on the plot:

text(6.5, 260, sprintf('y = %.2f\\cdotx^2%+.2f\\cdotx%+.2f', b))

Change the numeric format descriptors to display the precision you want. See the documentation for sprintf for details.

[Dan Mathotaarchchi]

thank you for your solution method. now there is another thing.how do i code to Generate equation of second order polynomial with two variables? as an example, please be kind to check the image ,

dependent variable is Q . independent variables are T and P . many thanks

[Star Strider]

I would do the regression on each column (or row). This will require a loop, because polyfit (and polyval) only operate on vectors. You will get 5 equations, one for each value of inlet pressure, or 3 equations, one for each value of temperature, depending on what you are doing and the result you want.

[Dan Mathotaarchchi]

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]

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.