求助最小二乘法拟合问题 。

数据xdata=[50 100 150 400 800];

ydata=[0.797595 0.754736 0.718371 0.555379 0.411674];

带拟合函数：y=(1-f)*exp(-b*x)+f*exp(-c*x).

当x大于200时，c可以或略不计，此时先拟合b,然后把b作为常数带人函数，用全部xdata拟合f和c.

我用curve fit工具箱custom equation拟合时出现Warning: A negative R-square is possible if the model does not contain a constant term and the fit is poor (worse than just fitting the mean). Try changing the model or using a different StartPoint.

请求高手帮助，怎么才能求出参数。

Answer 1

[xejabeh]

Matlab 当然是可以的

xdata=[50 100 150 400 800];
ydata=[0.797595 0.754736 0.718371 0.555379 0.411674];
[z,gof] = fit(xdata.',ydata.', @(b, c, f, x) (1-f)*exp(-b*x)+f*exp(-c*x), ...
             'StartPoint', [0.001, 0.001, rand], ...
             'Lower', [0, 0, 0], ...
             'Upper', [Inf, Inf, 1])
plot(xdata,ydata,'b-',xdata,z(xdata),'r-')
legend('data','fit')

z =

General model:

z(x) = (1-f)*exp(-b*x)+f*exp(-c*x)

Coefficients (with 95% confidence bounds):

b = 0.0008864 (0.0006362, 0.001137)

c = 0.04651 (-0.05451, 0.1475)

f = 0.1836 (0.1099, 0.2573)

gof =

sse: 4.4622e-04

rsquare: 0.9957

dfe: 2

adjrsquare: 0.9913

rmse: 0.0149

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