Curve fit equation calculation

Hi, i have a data set and i want to find the best equation can describe the data trend. Cftool need an equation to calculate the fit but i don't know which equation describe better my data; there is a tool or script that can ound the best equation.

Thanks

[Mathieu NOE]

hello

maybe you should share your data so we can find out which equation fits

[Isac Grossa]

This is the data, thanks.

[Mathieu NOE]

seems we could approximate this with a linear function plus some decayed exponential function

% curve fit
% initial segment slope crude estimate
ind = find(Time_2>30 & Time_2<225);
ini_slope = mean(diff(Log_storage_2(ind)))./ mean(diff(Time_2(ind)))

lin_curve = mean(Log_storage_2(1:4))+ini_slope*Time_2;

figure(1), 
subplot(2,1,1), plot(Time_2,Log_storage_2,'b',Time_2,lin_curve,'r')
legend('raw data','lin fit');
subplot(2,1,2), plot(Time_2,Log_storage_2-lin_curve,'b')
legend('raw data minus lin fit');

don't you have more data to see the longer term tendance ? - seems the curve goes down again (when lin fit removed)

[Isac Grossa]

Thanks for your help, but tere isn't a script, comand, app or tool that do it in automatically?

Attached data with more time.

[Mathieu NOE]

there is an interesting post about waht "automatic" curve fitting exist (according to each personnal definition)

Automatic Best Curve Fitting - MATLAB Answers - MATLAB Central (mathworks.com)

I don't have the Curve Fitting Tbx so I stick with basic methods , but maybe you have more ressources than I

otherwise , you can always fit a polynomial of sufficientlty high order to any data

load('workspace2.mat')

% polynomial fit method 
p = polyfit(Time_2,Log_storage_2,25);

% Evaluate the fitted polynomial p and plot:
f = polyval(p,Time_2);
figure(2),plot(Time_2,Log_storage_2,'b',Time_2,f,'r')
legend('data','poly fit')
        

[Alex Sha]

Hi, Isac, for time_1 series, one point is miss written? "36.5468 -2.72657737722164" should be "36.5468 -0.72657737722164", if so, refer to the result below:

y=A2+(A1-A2)/(1+exp((x-x0)/dx))+p1*exp(x*p2+p3/x)+p4*x;

Root of Mean Square Error (RMSE): 0.0199485805235078
Sum of Squared Residual: 0.0656610677089744
Correlation Coef. (R): 0.999763315428711
R-Square: 0.999526686877008

Parameter	Best Estimate
----------	-------------
a2	-0.94962007323826
a1	0.0535110752630396
x0	337.617289679719
dx	-39.219494340785
p1	-1.70924446590519
p2	0.0011217021565316
p3	-218.35619640782
p4	0.0059970024350561