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#### Best fit line for an exponential line

Hi,
I am new to using GNUPLOT and am trying to find the best fit line (to
determine the slope) of a line that follows Power Law (is an
exponential line).  I realize I have to use a function f(x) = a*b**x.
But, I do not know what to do next. Any help in this matter would be
greatly appreciated.

Thanks,
Divya

 0
divyarao09
5/4/2004 4:53:35 PM
comp.graphics.apps.gnuplot 5008 articles. 0 followers.

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Divya Rao <divyarao09@yahoo.com> wrote:
> Hi,
>  I am new to using GNUPLOT and am trying to find the best fit line (to
> determine the slope) of a line that follows Power Law (is an
> exponential line).

First, a terminology issue: an exponential curve doesn't have a
"slope" to speak of.  More precisely, the slope is different at every
place, so it's not a property of the curve as such, but of each point
on the curve.

> I realize I have to use a function f(x) = a*b**x.

That's one way of expressing it. f(x)=a*exp(x/k) or
f(x)=exp(b1*(x-x0)) and any variations of those may be just as valid
choices.

> But, I do not know what to do next. Any help in this matter would be
> greatly appreciated.

Read through "help fit" and you should be on your way.

--
Hans-Bernhard Broeker (broeker@physik.rwth-aachen.de)
Even if all the snow were burnt, ashes would remain.

 0
Hans
5/4/2004 5:14:56 PM
On Tuesday 04 May 2004 12:53, Divya Rao (divyarao09@yahoo.com)  held forth
in comp.graphics.apps.gnuplot
(<69dbc103.0405040853.25260afb@posting.google.com>):

> Hi,
>  I am new to using GNUPLOT and am trying to find the best fit line (to
> determine the slope) of a line that follows Power Law (is an

The slope of an exponential is not a straight line. However, if you intend
to find a tangent to an exponential function, which you would calculate
*after* finding a best fit, that can be done.

> exponential line).  I realize I have to use a function f(x) = a*b**x.
> But, I do not know what to do next. Any help in this matter would be
> greatly appreciated.

Next step :

fit {xrange} {yrange} f(x) "<your filename>" {using ...} via a,b

For instance :

Say expdata.dat is your datafile and your data is plotted in the 5th column
vs the 1st one. And you want to restrict the fit to x \in [-1,1],

fit [-1:1] f(x) "expdata.dat" u 1:5 via a,b

HTH

gnuplot> help fit

should help further. Look particularly into defining initial values of
FIT_LIMIT, a and b (your fit function is going to be very sensitive to the
value of b).

 0
Madhusudan
5/5/2004 3:34:07 AM
 Reply:

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