Finding best fit function for a data set

Hi All, I have a set of X,Y,Z Data and I am trying to find the best fit equation between the input variables (X,Y) and the output variable (Z). I have been manually trying different functions that and so far the best function I have came up with is (Z = Log(X*Y) with R2 of 0.59) I am not sure if there is an automated way to find even more best fitting equation for this data. I have attached the excel sheet that contain the data. Thanks in advance for your help.

[KSSV]

You may try this: https://in.mathworks.com/matlabcentral/fileexchange/34765-polyfitn

Answer 1

[Sulaymon Eshkabilov]

You can try cftool - curve fitting toolbox, or use fit(), e.g.:

D = readmatrix('Samples_Data.xlsx');
X = D(:,2);
Y = D(:,3);
Z = D(:,4);
FModel = fit([X,Y], Z, 'poly23');
plot(FModel, [X, Y], Z)

[FModel, Fit_quality]=fit([X,Y], Z, 'poly23')

     Linear model Poly23:
     FModel(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p21*x^2*y 
                    + p12*x*y^2 + p03*y^3
     Coefficients (with 95% confidence bounds):
       p00 =        2595  (-335.2, 5525)
       p10 =      -394.5  (-854.9, 65.83)
       p01 =      -4.988  (-15.39, 5.417)
       p20 =       14.19  (-2.286, 30.67)
       p11 =        1.61  (-0.3392, 3.559)
       p02 =     -0.0514  (-0.1291, 0.02633)
       p21 =     -0.0701  (-0.1506, 0.01037)
       p12 =    0.002326  (-0.001086, 0.005738)
       p03 =   1.234e-05  (-3.496e-05, 5.963e-05)

Fit_quality = struct with fields:
           sse: 592.8486
       rsquare: 0.8895
           dfe: 3
    adjrsquare: 0.5948
          rmse: 14.0576

Answer 2

[Arka]

Hello,

From what I understood, you have a 3 variable dataset, and you would like to automate the process of getting a line of best fit for the dataset.

You can use the ‘fit’ function and its supported polynomial solvers to automate the process of finding a polynomial best fit function for the dataset.

The code for the same is given below:

data = readmatrix('Samples_Data.xlsx');
x = data(:, 2);
y = data(:, 3);
z = data(:, 4);

solvers = ["poly11", "poly12", "poly13", "poly21", "poly22", "poly23", "poly31", "poly32", "poly33", "poly41"];
rSq = 0;
bestModel = 0;

for i=1:size(solvers, 2)
    [model, goodnessOfFit] = fit([x, y], z, solvers(i));
    if goodnessOfFit.rsquare > rSq
        rSq = goodnessOfFit.rsquare;
        bestModel = model;
    end
end
bestModel
plot(bestModel, [x, y], z)

The output gives us the best fit function (and the solver used for it):

The plot is given below:

You can refer to the documentation link for the ‘fit’ function below:

https://www.mathworks.com/help/curvefit/fit.html#bto2vuv-1-gof