# How to curve fit following summation equation in MATLAB with given experimental data.

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abxz on 12 Nov 2019
Edited: abxz on 15 Nov 2019 and
a,k,c,b, and g are constants to be determined.

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abxz on 12 Nov 2019
abxz on 12 Nov 2019
KALYAN ACHARJYA on 13 Nov 2019
For assignments or homework, we help only after looking at your efforts to solve the question.

Alex Sha on 13 Nov 2019
d(K/ (1+exp(c-b*t)))/dt=k*exp(c-b*t)*b/sqr(1+exp(c-b*t)),so your fitting function become: is the above correct? if yes, you may see the function is over-fit, that means the parameters will not be unique， one solution likes below:
Root of Mean Square Error (RMSE): 11257.9862380487
Sum of Squared Residual: 1647649303.76923
Correlation Coef. (R): 0.891727403408187
R-Square: 0.795177761989108
Determination Coef. (DC): 0.795103266693536
F-Statistic: 7.64708134900884
Parameter Best Estimate
-------------------- -------------
a 67082.9685482823
k 2.55264230357405E16
c 39.1820152654189
b 0.0511178327965598
g 1.74671169710137E-249 KALYAN ACHARJYA on 13 Nov 2019
@Alex
Why you are providing the two answers?
abxz on 13 Nov 2019
@ Alex Sha, Thanks a lot for your help.
will you please provide the code also.

Alex Sha on 12 Nov 2019
Hi, Yadav, in your function "a*d/dt(k/1+exp(c-b*t))", what is "d/dt"? does "k/1" equal to "k"? Please describe clearly.

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abxz on 12 Nov 2019
abxz on 13 Nov 2019
abxz on 13 Nov 2019
@ Alex Sha , Please send code . I need code so if i have to do similar kind of fitting , i can take the help from the code.
Thank you.

Alex Sha on 14 Nov 2019
Hi， Yadav, I actually use a software package other than Matlab, named 1stOpt, it is much easy for using without guessing initial start-values, since it adopts global optimization algorithm. The code looks like below:
Parameter a,k,c,b,g;
ConstStr f=a*(k*exp(c-b*t(i))*b)/(1+exp(c-b*t(i)))^2;
Variable t,z[OutPut],y;
StartProgram [Basic];
Sub MainModel
Dim as integer i, j, n
Dim as double temd1, temd2
for i = 0 to DataLength - 1
n = t(i)
temd1 = 0
for j = 0 to n
temd1 = temd1 + f
next
temd2 = 0
for j = 0 to n
temd2 = temd2 + g*y(j)
next
z(i) = temd1 + temd2
Next
End Sub
EndProgram;
Data;
t=[0,2,4,6,8,10,12,14,16,18,20,22,24];
z=[0,0,666.6,5333.33,10666.6,21333,42666.6,4666.6,42666.6,42666.6,42666.6,42666.6,85333.3];
y=[1.25*10^8,1.*10^8,1.25*10^8,2.2*10^10,1.3*10^11,1.4*10^11,1.25*10^11,4.7*10^10,7.9*10^10,9.5*10^10,9.4*10^10,8.8*10^10,9.4*10^10];
a much better result:
Root of Mean Square Error (RMSE): 9901.69220512954
Sum of Squared Residual: 1274565610.8266
Correlation Coef. (R): 0.918681151445272
R-Square: 0.84397505802081
Determination Coef. (DC): 0.841498837497943
F-Statistic: 9.7840155772957
Parameter Best Estimate
-------------------- -------------
a -277156.527610417
k -10698197.9029827
c 28.5533367811484
b 0.35649699061682
g 3.06293808255498E-8 KALYAN ACHARJYA on 14 Nov 2019
@Alex Is this package supports by Matlab? You are giving multiple answers for same question. you can add extentions answer in the comment section of respective answer.
Alex Sha on 14 Nov 2019
1stOpt is an independent software package I think, not the add-in or toolbox of Matlab.
abxz on 15 Nov 2019
@ Alex Sha , Thank you so much.