How to do weighted least square rgression?

Question

Pooneh Shah Malekpoor 2023-10-6

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2030189-how-to-do-weighted-least-square-rgression

评论： Torsten 2023-12-1

Hello

I want to fit an exponential curve to my data using MatLab. Could you please guide me how can I write a code to fit this through weighted least square reression? The weight matrix is as follows. I could not find any instruction or sample code to do so!

weight=[18.5204555170429; 24.8007492441765; 21.4204953742493; 12.0007299687922; 5.17482448096073;2.24987321147564]

x=[1.5;4.5;7.5;10.5;13.5;16.5]

y=[0.466132177250491;0.307694759285704;0.477550022494737;0.489169081512968;0.439027124884140;0.306938063199741]

Thanks

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Answer 1

Star Strider 2023-10-6

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https://ww2.mathworks.cn/matlabcentral/answers/2030189-how-to-do-weighted-least-square-rgression#answer_1328114

编辑：Star Strider 2023-10-6

在 MATLAB Online 中打开

One option is to use fitlm —

weight=[18.5204555170429; 24.8007492441765; 21.4204953742493; 12.0007299687922; 5.17482448096073;2.24987321147564];

x=[1.5;4.5;7.5;10.5;13.5;16.5];

y=[0.466132177250491;0.307694759285704;0.477550022494737;0.489169081512968;0.439027124884140;0.306938063199741];

mdl = fitlm(x,y, 'Weights',weight)

mdl =

Linear regression model: y ~ 1 + x1 Estimated Coefficients: Estimate SE tStat pValue _________ _________ ______ ________ (Intercept) 0.39951 0.07398 5.4003 0.005691 x1 0.0031898 0.0099772 0.3197 0.76519 Number of observations: 6, Error degrees of freedom: 4 Root Mean Squared Error: 0.353 R-squared: 0.0249, Adjusted R-Squared: -0.219 F-statistic vs. constant model: 0.102, p-value = 0.765

figure

plot(mdl)

grid

I assume that you want to do a linear regression, since you did not mention a nonllinear model of any sort.

.

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Star Strider 2023-10-6

编辑：Star Strider 2023-10-6

在 MATLAB Online 中打开

It would have been nice to know that at the outset.

weight=[18.5204555170429; 24.8007492441765; 21.4204953742493; 12.0007299687922; 5.17482448096073;2.24987321147564];

x=[1.5;4.5;7.5;10.5;13.5;16.5];

y=[0.466132177250491;0.307694759285704;0.477550022494737;0.489169081512968;0.439027124884140;0.306938063199741];

fcn = @(b,x) b(1) .* exp(x-b(2)) - b(3) .* exp(-(x-b(4))); % Nonlinear Exponential Model

mdl = fitnlm(x,y,fcn,[rand; 7; 12; rand], 'Weights',weight)

Warning: The Jacobian at the solution is ill-conditioned, and some model parameters may not be estimated well (they are not identifiable). Use caution in making predictions.

mdl =

Nonlinear regression model: y ~ F(b,x) Estimated Coefficients: Estimate SE tStat pValue _________ __________ __________ _________ b1 0.0020994 0.006279 0.33434 0.75492 b2 11.349 1.3173e-05 8.6156e+05 1.089e-23 b3 -1.0124 0.38895 -2.6029 0.059862 b4 0.76701 0.39382 1.9476 0.12329 Number of observations: 6, Error degrees of freedom: 4 Root Mean Squared Error: 1.63 R-Squared: -19.8, Adjusted R-Squared -25 F-statistic vs. zero model: 0.882, p-value = 0.482

xv = linspace(min(x), max(x))';

[yp,yci] = predict(mdl, xv);

figure

plot(x, y, 'p')

hold on

plot(xv, yp, '-r')

plot(xv, yci, '--r')

hold off

grid

I have no idea what sort of exponential model you want. This gives an approximation of one. Experiment with others, since you understand the process that created these data, and a mathematical model of that process would be the best option for ‘fcn’ here.

Shiba shankar 2023-12-1

how to know then,any steps to know

Torsten 2023-12-1

The explanations given here might help:

https://quantifyinghealth.com/weighted-regression/

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How to do weighted least square rgression?

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