# How to perform nonlinear regression accross multiple datasets

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Jack Nolan on 19 Feb 2021
Commented: Jack Nolan on 25 Feb 2021
Appolgies in advance as I am new to MATLAB.
I am trying to fit a model to mutiple data sets at once using non linear regression. I have found similiar examples but I am unable to modify them to suit my needs.
The model contains 3 unkown paramaters that must be tuned to satsifty (or give best model fit) accross 4 data sets at once.However, the model also contains 1 known paramater which is different for each of the 4 datasets.
Model to fit:
• ΔRon/Ron are the data set y values
• t is the data set x values
• A1, A2, γ are unkown paramaters (common to all data sets) which must be found
• tau is a kown paramaer whcih differs accross all data sets
I have attached an m-file with relevant data and information. If sombody could provide guidance or a commented solution I would be very grateful. Thanks.
Jack Nolan on 20 Feb 2021
@Alex Sha, can you recommend a free/more afordable software package please.
Alex Sha on 21 Feb 2021
Matlab should be OK, but need you to do more work.

Deepak Meena on 24 Feb 2021
Hi Jack,
The following post on MATLAB Answers discusses a similar case:
In that question , there were 2 unknown shared parameters and 1 parameter was different for all the dataset but was also unknown. In this question we have 3 unknown shared parameters and 1 known parameters whose value will be different for each dataset.So I modified that to illustrate that :
function sharedparams
t = (0:10)';
T = [t; t; t;t];
Y = 3 + [exp(-t/2); 2*exp(-t/2); 3*exp(-t/2);4*exp(-t/2)] + randn(44,1)/10;
dsid = [ones(11,1); 2*ones(11,1); 3*ones(11,1);4*ones(11,1)];
gscatter(T,Y,dsid)
X = [T dsid];
A3 = [-5;1;3;4];
b = nlinfit(X,Y,@subfun,ones(1,3))
line(t,b(1)+b(2)+b(3)*t+A3(1),'color','r');
line(t,b(1)+b(2)+b(3)*t+A3(2),'color','g');
line(t,b(1)+b(2)+b(3)*t+A3(3),'color','b');
line(t,b(1)+b(2)+b(3)*t+A3(4),'color','c');
function yfit = subfun(param,X)
T = X(:,1); % time
dsid = X(:,2); % dataset id
A0 = param(1);
A1 = param(2);
A2 = param(3);
A3 = [-5;1;3;4]; %known paramter
yfit = A0 + A1+ A2*T + A3(dsid);
Tom Lane on 25 Feb 2021
You have:
yfit = A1 * log(1 + T/tau(dsid)) + A2 * log(1 + (T/tau(dsid))*(1/gamma));
You should have:
yfit = A1 * log(1 + T./tau(dsid)) + A2 * log(1 + (T./tau(dsid))*(1/gamma));
You want element-by-element division, not vector division in the sense of a matrix operation.
Jack Nolan on 25 Feb 2021
Thanks alot @Tom Lane, it's working now

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