Finding best fit function for a data set

Question

Abdullah Azzam 2023-2-9

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1909350-finding-best-fit-function-for-a-data-set

编辑： Arka 2023-2-9

Samples_Data.xlsx

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.

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KSSV 2023-2-9

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

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Answer 1

Sulaymon Eshkabilov 2023-2-9

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https://ww2.mathworks.cn/matlabcentral/answers/1909350-finding-best-fit-function-for-a-data-set#answer_1167235

在 MATLAB Online 中打开

Samples_Data.xlsx

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

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Answer 2

Arka 2023-2-9

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https://ww2.mathworks.cn/matlabcentral/answers/1909350-finding-best-fit-function-for-a-data-set#answer_1167395

编辑：Arka 2023-2-9

在 MATLAB Online 中打开

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)