how can I fit nonlinear regression equations with a set of data

Hello everybody

I’m trying to find a nonlinear relationship between two input variables and one dependent variable (output). I do have a set of data that have three columns, the first two columns are the input variables and the third one is the output value. Any suggestion to figure out that? I have tried to use the regression and classification apps in the Matlab.

The attached file is a part of this data.

Thank you

Answer 1

[Star Strider]

There is no relationship. Every value in the third column is uniformly 1:

T = readtable('data1.xlsx','ReadVariableNames',0);
UT3 = unique(T{:,3})

producing:

UT3 =
     1

With ‘data2.xlsx’, you can fit anything you want to those data, depending on what they represent and the process that created them.

Two possibilities, both using linear regression:

T = readtable('data2.xlsx','ReadVariableNames',0);
xv = linspace(min(T{:,1}), max(T{:,1}), 20);
yv = linspace(min(T{:,2}), max(T{:,2}), 20);
[Xm,Ym] = ndgrid(xv, yv);

DM1 = [T{:,[1 2]}, ones(size(T{:,1}))];
B1 = DM1 \ T{:,3};
zv1 = [Xm(:), Ym(:), ones(size(Xm(:)))] * B1;
Zm1 = reshape(zv1, size(Xm));

DM2 = [T{:,1}, 1./T{:,2} ones(size(T{:,1}))];
B2 = DM2 \ T{:,3};
zv2 = [Xm(:), 1./Ym(:), ones(size(Xm(:)))] * B2;
Zm2 = reshape(zv2, size(Xm));

figure
stem3(T{:,1}, T{:,2}, T{:,3})
hold on
mesh(Xm, Ym, Zm1)
hold off
grid on
xlabel('X')
ylabel('Y')
zlabel('Z')

figure
stem3(T{:,1}, T{:,2}, T{:,3})
hold on
mesh(Xm, Ym, Zm2)
hold off
grid on
xlabel('X')
ylabel('Y')
zlabel('Z')

The best fit will be to estimate the relevant parameters of a mathematical model of the process that created them. Beyond that, you can fit anything to them.

Answer 2

[Mohanned Al Gharawi]

@ Star Strider

Sorry for that, I just updated the data set.

Thanks

Answer 3

[Mohanned Al Gharawi]

Thank you so much I appreciate your help.

[Star Strider]

As always, my pleasure!