exponential regression functions with error in input values

Question

Benjamin Wilson 2023-11-22

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2050757-exponential-regression-functions-with-error-in-input-values

回答： Star Strider 2023-11-22

Hi, I am trying to fit a regression model that should look like something of the form y = e^(a-bx) for some positive constants a and b. I have been perviously using the linear least squares method after taking the log of both sides and then fitting a linear model and this works. However, due to some erros in my input data this will not work for the occasion where y = 0 for obvious reasons. The issue is I need to fit an exponential line that follows the points for example [4,100], [25,50], [100,0]. This line should remain postive although the point [100,0] is where the failure arises. Any help would be greatly appreciated!

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

Fabio Freschi 2023-11-22

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2050757-exponential-regression-functions-with-error-in-input-values#answer_1357947

编辑：Fabio Freschi 2023-11-22

在 MATLAB Online 中打开

you can use lsqnonlin or lsqcurvefit

clear variables, close all

% data

x = [4 25 100];

y = [100 50 0];

% fitting function

yfit = @(p,x) exp(p(1)-p(2)*x);

% nonlin problem

f = @(p) yfit(p,x)-y;

% initial guess

p0 = [1 1];

% use lsqnonlin

pfit1 = lsqnonlin(f,p0);

Local minimum possible. lsqnonlin stopped because the final change in the sum of squares relative to its initial value is less than the value of the function tolerance.

% use built-in lsqcurvefit

pfit2 = lsqcurvefit(yfit,p0,x,y);

Local minimum possible. lsqcurvefit stopped because the final change in the sum of squares relative to its initial value is less than the value of the function tolerance.

% plot

figure,hold on;

plot(x,y,'o')

xfit = linspace(min(x),max(x),100);

plot(xfit,yfit(pfit1,xfit))

plot(xfit,yfit(pfit2,xfit))

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。

Answer 2

Star Strider 2023-11-22

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2050757-exponential-regression-functions-with-error-in-input-values#answer_1357962

在 MATLAB Online 中打开

There are other options, however everyone hass fminsearch, so using it —

x = [4; 25; 100];

y = [100; 50; 0];

% objfcn = @(b,x) b(1) .* exp(b(2) - b(3).*x);

objfcn = @(b,x) exp(b(1) - b(2).*x);

[B,nres] = fminsearch(@(b)norm(y - objfcn(b,x)), rand(2,1))

B = 2×1

4.7478 0.0345

nres = 3.9186

xv = linspace(min(x), max(x), 50);

figure

plot(x, y, 'p')

hold on

plot(xv, objfcn(B,xv), '-r')

hold off

grid

The fitnlm function is more robust and provides statistics on the fit. Use the predict function to return the fitted curve and confidence region on the fit.

.