3 independent variable regression.

I'm trying to fit a function with 3 independent variables and 1 dependent. I have all of the data and I've tried a few methods but nothing works.

I want a function set up so that the result would be F where F = f(x,y,z). Developing a model from a matrix of [ x, y, z, F] values. Any suggestions?

To clarify, I don't need to plot it (yet if ever).

[Julia Hoskins]

The code I used that ended up working was as follows:

%Fit Plot

fitobject = fit([X1,Y1],Z1,'poly11')

%Degree Polynomial ' poly11', poly'22' etc. each Number represents the degree of each variable

figure (3)

plot(fitobject,[X1,Y1],Z1)

hold on

grid on

title('title')

set(gca, 'ZLim',[0 6])

shading interp

hold off

[Karen Hejazi]

Hey,

i have the same problem too.I'm trying to fit a function with 3 independent variables and 1 dependent. I have all of the data. i mean the values of all 3 independent variables and 1 dependent are known

but i dont undrestand the solution you have written.

i mean where is F?

i hope you check it. i really appreciate it

[Karen Hejazi]

% Q, H and Theta are the three independent variables

Q = [0.5;0.6;0.8;0.9;0.99;1;1;1;1.2;1.2;1.2;1.2;1.5;1.5;1.6;1.8;2;2.3;2.5;2.5;2.8;3.2;3.5;4.5;5.5;6;6;7.1;8];

H = [5;5.3;1.35;2.1;1.05;3.16;3;5;3.57;1.75;3.2;1;3;3.17;1.1;3.45;1.8;2.55;2.55;1.8;2.1;3.6;4.05;1.5;5;5.8;2.97;1.7;1.73];

Theta = [28.5;31.2;25;21.6;20.3;25.2;30;28.9;21.8;22.8;28.7;18.8;20.2;22;20.6;21.5;21.9;22.8;20.4;21.1;19.2;26.4;24.5;17.2;22.9;22.3;25.8;22;19.2];

% Eff is the dependent variable

Eff = [64.8;60.9;70.8;75;71.6;67.7;71.4;67.3;69;67.5;71.5;68;74.8;70.7;73;75.5;73.6;76.5;73.2;70.2;74.5;70.8;70.5;72.6;71.2;73.2;74.4;70.9;72.9];

i want a function for Eff(Q,H,Theta)

Answer 1

[Ameer Hamza]

There are several ways to solve such problems in MATLAB. If you have the curve fitting toolbox, then you can use fit(): https://www.mathworks.com/help/releases/R2020a/curvefit/fit.html

Alternatively, you can also use functions from optimization toolbox

lsqcurvefit(): https://www.mathworks.com/help/releases/R2020a/optim/ug/lsqcurvefit.html

lsqnonlin(): https://www.mathworks.com/help/releases/R2020a/optim/ug/lsqnonlin.html

[Julia Hoskins]

I tried those, and the best I could fit was for a surface. 2 independent variables for equations like F = f(x,y).

[Ameer Hamza]

See this example using lsqcurvefit() for 3 independent variables

x = rand(10, 1);
y = rand(10, 1);
z = rand(10, 1);
F = 2*x+5*log(x+z)-3*sin(y); % example

fun = @(p,X) p(1)*X(:,1) + p(2)*log(X(:,1)+X(:,3)) - p(3)*sin(X(:,2));

X = [x y z];
sol = lsqcurvefit(fun, rand(1,3), X, F);

[Julia Hoskins]

Yeah, but my F values are an equally sized array and not a function, so the fitting doesn't work.