What does gnuplot do if I have a data.txt file like this:
#x y dx dy
1 2 0.2 0.1
3 5 0.1 0.3
Where the dx and dy are the errors directly related to x and y (x +- dx, y +- dy). And I do this:
plot data.txt using (1/$1):($2*5):3:4 with xyerrorbars
Will gnuplot do this for x and y
(1/x) +- dx
5y +- dy
or that
1/(x +- dx)
5(y +- dy)
or that
1/x +- 1/dx
or that, the Gaussian error propagation, which would be the right one, gotten from the sqrt(sum(derivative times the error)^2)
1/x -+ dx/x^2
And how to fit in this case?
Gnuplot will certainly do the first option (1/x) +- dx
. As for the fitting, you'll have to be a little more specific ...