Gnuplot fit does not match

Question

I try to fit my data file with a power law so I have:

f(x) = a*x**b //
fit f(x) 'data.txt' u 1:2 via a,b //
plot 'data,txt' u 1:2 with points, f(x)

My data are:

0.0001 2.283205 //
0.0002 3.007995 //
0.0003 3.535115 //
0.0004 3.960405 //
0.0005 4.331785 //
0.0006 4.655245 //
0.0007 4.954745 //
0.0008 5.224295 // 
0.0009 5.475875 //
0.001  5.709485 //

But in the end I just have the dots coming from my datas but I do not have the function.

enter image description here

Does someone know what happens and how I can get the plot for the function ?

Thank you in advance.

That doesn't sound plausible at all: https://www.wolframalpha.com/input/?i=plot+y%3D102.218*x%5E-919.215. Perhaps you need a better initial guess? — Mad Physicist, Dec 04 '19 at 17:52
Are you sure you have the right model for the data? Can a power law be concave down with positive `a`? — Mad Physicist, Dec 04 '19 at 17:54
@Xkcd Problem solved? Question answered? Any feedback would be polite and appreciated! — theozh, Jun 05 '23 at 21:59

score 1 · Answer 1 · answered Dec 04 '19 at 19:57

I don't see problems... if you start with some "reasonable" values for a and b.

Code:

### fitting
reset session


$Data <<EOD
0.0001 2.283205
0.0002 3.007995
0.0003 3.535115
0.0004 3.960405
0.0005 4.331785
0.0006 4.655245
0.0007 4.954745
0.0008 5.224295
0.0009 5.475875
0.001  5.709485
EOD

a=1
b=0.5

f(x) = a*x**b
set fit nolog results
fit f(x) $Data u 1:2 via a,b

plot $Data u 1:2 with points, f(x)
### end of code

Results:

Final set of parameters            Asymptotic Standard Error
=======================            ==========================
a               = 89.4411          +/- 0.1635       (0.1828%)
b               = 0.398318         +/- 0.0002467    (0.06193%)

Gnuplot fit does not match

1 Answers1