exponential curve fitting with custom equation

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

Answer 1

[Ameer Hamza]

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));