How to do custom equation (non linear) regression?

Question

yehuda kristo 2023-4-12

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1945899-how-to-do-custom-equation-non-linear-regression

评论： Image Analyst 2023-4-12

I need to find some constant from data that usually is shown in log-log scale, the equation related to the data would be y=(a*x^b)/(26.1-x). How do I find the a and b constants?

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Star Strider 2023-4-12

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1945899-how-to-do-custom-equation-non-linear-regression#answer_1214624

在 MATLAB Online 中打开

experiment_data.xlsx

There are several nonlinear parameter estimation function to choose from.

This uses fitnlm —

yfcn = @(a,b,x) (a*x.^b)./(26.1-x);

T1 = readtable('experiment_data.xlsx');

x = T1.x;

y = T1.y;

B0 = rand(2,1);

mdl = fitnlm(x,y,@(b,x)yfcn(b(1),b(2),x), B0)

mdl =

Nonlinear regression model: y ~ yfcn(b1,b2,x) Estimated Coefficients: Estimate SE tStat pValue ________ _______ _______ _______ b1 0.059055 0.28207 0.20936 0.83475 b2 -1.6212 1.5325 -1.0578 0.29362 Number of observations: 75, Error degrees of freedom: 73 Root Mean Squared Error: 0.00156 R-Squared: -0.0655, Adjusted R-Squared -0.0801 F-statistic vs. zero model: 1.29, p-value = 0.282

xsrt = sort(x);

[ypred,yci] = predict(mdl,xsrt);

figure

plot(x, y, '.', 'DisplayName','Data')

grid

hold on

plot(xsrt, ypred, '-r', 'DisplayName','Function Fit')

plot(xsrt, yci, '--r', 'DisplayName','±95% Confidence Intervals')

hold off

legend('Location','best')

The model is a statistically poor fit to the data and does not describe the data well.

.