How to fit a custom equation?

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madhuri dubey
madhuri dubey 2018-7-9
回答： Alex Sha 2020-2-18
My equation is y=a(1-exp(-b(c+x)) x=[0,80,100,120,150] y=[2195,4265,4824,5143.5,5329] When I am solving it in matlab, I am not getting a proper fit in addition, sse=6.5196e+05 and r square=0.899. Although the r square value is acceptable, the sse is too high. Therefore kindly help to get minimum sse. Further I have tried in curve fitting tool but I got same thing.

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采纳的回答

Star Strider
Star Strider 2018-7-9
I get good results with this:
yf = @(b,x) b(1).*(1-exp(-b(2)*(b(3)+x)));
B0 = [5000; 0.01; 10];
[Bm,normresm] = fminsearch(@(b) norm(y - yf(b,x)), B0);
SSE = sum((y - yf(Bm,x)).^2)
Bm =
6677.76372320411
0.0084077646869843
47.1622210493944
normresm =
195.173589996072
SSE =
38092.7302319547
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madhuri dubey
madhuri dubey 2018-7-11
When I use polyfit to get initial estimates of ‘a’, ‘c’, and ‘d’ , I got [-0.0001, 0.0346, 2.1807]. Why there is difference in constant values for the same data.
Star Strider
Star Strider 2018-7-11
There isn’t. You’re ignoring the constant multiplication factor 1.0E+03. The full result:
p =
1.0e+03 *
-0.000088159928538 0.034559355475118 2.180742845451099

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更多回答（2 个）

Image Analyst
Image Analyst 2018-7-11
For what it's worth, I used fitnlm() (Fit a non-linear model) because that's the function I'm more familiar with. You can see it gives the same results as Star's method in the image below. I'm attaching the full demo to determine the coefficients and plot the figure.
Alex Sha
Alex Sha 2020-2-18
If don't care the type of fitting function, try the below function, much simple but with much better result:
y = b1+b2*x^1.5+b3*x^3;
Root of Mean Square Error (RMSE): 18.0563068929128
Sum of Squared Residual: 1630.15109305524
Correlation Coef. (R): 0.999873897456616
R-Square: 0.999747810815083
Adjusted R-Square: 0.999495621630167
Determination Coef. (DC): 0.999747810815083
Chi-Square: 0.165495427247465
F-Statistic: 3964.27710070773
Parameter Best Estimate
---------- -------------
b1 2195.84396843687
b2 3.66989234203779
b3 -0.00107101963512847

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