Exponential fit by customised equation

Question

Sushreesmita Mishra 2019-11-1

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https://ww2.mathworks.cn/matlabcentral/answers/488661-exponential-fit-by-customised-equation

评论： Sushreesmita Mishra 2019-11-1

When I am fiiting my experimental data clicking exponetial fit, then it fits well. But when I am writing the same equation in customised form its not fitting.

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Walter Roberson 2019-11-1

Is it a sum of exponential terms, or a single exponential?

Sushreesmita Mishra 2019-11-1

my values to fit

x = [0 120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800]

y = [1 0.861137 0.747681 0.664806 0.562721 0.485829 0.411907 0.356567 0.272409 0.199405 0.125686 0.100692 0.040232 0.019759 4.32E-05 2.7E-06]

In custom equation section of curve fitting tool the equation with form

a*exp(-b*x)

for y = f(x) returns a poor fit with negative R2 value which is illogical.

On the other hand, inbuilt exponential tool with same form returns a very good fit with R2 = 0.96

My question is that why this difference is seen with same form, i.e. "a*exp(-b*x)", and is the custom equation tool trustable for other forms?

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Answer 1

Alex Sha 2019-11-1

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https://ww2.mathworks.cn/matlabcentral/answers/488661-exponential-fit-by-customised-equation#answer_399298

Hi, Sushreesmita Mishra, the problem you met is normal. When chose build-in function for data fitting, since "build-in", so Matlab itself know which function user selected, then it can chose proper initial start-value acording to the type of function and the data, in the otherhand, for fitting function customised, Matlab doesn't know the type of the function, thus the initial start-values can not be given properly, it lead to the poor fit as your meeting. Same situation in other packages like OriginPro.