Solve Culomb's Law with Gnuplot: Plotting and Fitting for qQ and F*4*Pi*e0*r^2

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The discussion revolves around using Gnuplot to fit experimental data to Coulomb's Law, specifically isolating the product qQ as a function of force F. The user successfully plots the data but encounters an issue where the sum of squared residuals is zero, preventing the computation of uncertainties for the fitted parameters h and b. Despite the fit converging with h equal to 1 and b close to zero, the inability to compute errors suggests a potential problem with the data or fitting process. The user seeks guidance on resolving this issue to obtain uncertainty values for the fit parameters. The conversation highlights the challenges of data fitting in experimental physics using Gnuplot.
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Homework Statement


Okay here is the deal, I have made a experiment, and now I have some probs, getting the right stuff from gnuplot.

If I isolate qQ in Culombs Law I get:qQ = F*4*Pi*e0*r^2:
Here e0 is the permittivity of free space
r is a constent, the distence between the charges.
If I plot F*4*Pi*e0*r^2 as a function of qQ, the slope of the linear function schuld be one, right?.
I have the folowing data:

qQ F*4*Pi*e0*r^2 delta g(x)

3.94e-15 2.129e-15 2.2e-16
2.28e-15 7.413e-16 8.1e-17
1.17e-15 3.177e-17 3.2e-17
7.38e-16 -3.601e-16 4.8e-17
4.31e-16 -6.248e-16 7.1e-17
3.08e-16 -7.307e-16 8.0e-17
2.46e-16 -8.261e-16 8.9e-17
1.85e-16 -9.002e-16 9.6e-17
1.23e-16 -9.320e-16 9.9e-17


So I want to fit them to a linear function. I load this plot command:
#Nu definere vi funktionen f(x) som er den vi vil fitte efter:
g(x)=h*x+b


fit g(x) "data.txt" via h,b

set xlabel "qQ [C^2]"

set ylabel "(F*4*Pi*e0*r^2) [C^2]"

set title "Kraftens afhængihed af afstanden mellem 'punkt ladningerne.'"

plot g(x), "data.txt" w e

And then i get a fine plot, but also this in my fit log:
Wed May 09 16:19:02 2007


FIT: data read from "data.txt"
#datapoints = 9
residuals are weighted equally (unit weight)

function used for fitting: g(x)
fitted parameters initialized with current variable values



Iteration 0
WSSR : 9 delta(WSSR)/WSSR : 0
delta(WSSR) : 0 limit for stopping : 1e-005
lambda : 0.707107

initial set of free parameter values

h = 1
b = 1

After 4 iterations the fit converged.
final sum of squares of residuals : 5.99386e-031
abs. change during last iteration : -2.37224e-019


Hmmmm... Sum of squared residuals is zero. Can't compute errors.

Final set of parameters
=======================

h = 1
b = -1.20129e-015


I bellive the problem is here:
Hmmmm... Sum of squared residuals is zero. Can't compute errors.

I want gnuplot to give me uncertenties on the free values h and b, but it docent.
And got no clue on how to fix it.
So what is the problem, anyone?
 
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