MATLAB: Exponential curve fitting with custom equation

curve fittingexponentialStatistics and Machine Learning Toolbox

Hello.
I need to fit the following function to a set of data.
mymodel=@(a,x) (0.1744+0.1556*exp(-x/a));
xData=[ 1.0000
1.4142
2.2361
3.1623
4.1231
5.0990
6.0828
7.0711
8.0623
9.0554
10.0499
11.0454
12.0416
13.0384
14.0357
15.0333
16.0312
17.0294
18.0278
19.0263
20.0250
21.0238
22.0227
23.0217
24.0208];
yData=[ 0.3300
0.1896
0.1448
0.1216
0.1108
0.1128
0.1168
0.1064
0.1016
0.1040
0.1072
0.1012
0.1072
0.1068
0.1048
0.1084
0.1084
0.1104
0.1152
0.1112
0.1168
0.1164
0.1252
0.1136
0.1124];
ft=fit(xData,yData,mymodel)
figure(1)
plot(ft,xData,yData)
but I get poor fitting like this:
what is the problem?
Thank you in advance

Best Answer

Your model does not provide enough degree of freedom to fit all the points. Change the model to
mymodel=@(a,b,c,x) (b+c*exp(-x/a));
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