怎么用matlab求解Logistic模型中的三个参数?

题目

怎么用matlab求解Logistic模型中的三个参数?
将Logistic模型的方程变为y=b/(1+a*exp(-kt)),已知t=[0,5,10,24,33,48,57,72,96,120,144,168,192,216];y=[0,0.028,0.103,0.336,0.450,0.597,0.716,0.778,0.835,0.849,0.816,0.839,0.811,0.816].怎么求出参数a,b,k的值,要具体的程序,

答案

建立m函数文件存为logistic1
function f=logistic1(b)
t=[0,5,10,24,33,48,57,72,96,120,144,168,192,216];y=[0,0.028,0.103,0.336,0.450,0.597,0.716,0.778,0.835,0.849,0.816,0.839,0.811,0.816];
f = y-b(1)./(1+b(2).*exp(-b(3).*t));
b0=[10,2,2];
>> b=leastsq('logistic1',b0)
b =
0.8221 13.9173 0.0818
或者cftool
General model:
f(x) = b/(1+a*exp(-k*x))
Coefficients (with 95% confidence bounds):
a = 13.92 (6.301,21.53)
b = 0.822 (0.7911,0.853)
k = 0.08184 (0.06479,0.0989)
Goodness of fit:
SSE:0.01404
R-square:0.9898
Adjusted R-square:0.9879
RMSE:0.03572