# How to fit a custom equation?

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madhuri dubey el 9 de Jul. de 2018
Respondida: Alex Sha el 18 de Feb. de 2020
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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Star Strider el 9 de Jul. de 2018
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 el 11 de Jul. de 2018
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 el 11 de Jul. de 2018
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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### Más respuestas (2)

Image Analyst el 11 de Jul. de 2018
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.
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Alex Sha el 18 de Feb. de 2020
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
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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