Gnuplot: How can I fit a range of points (out of the entire data) to a function?

Question

I have a set of data obtained for the I-V characteristics of an LED.

0.005  -0.004
0.053  -0.003
0.101  -0.003
0.153  -0.002
0.201  -0.002
0.252  -0.002
0.303  -0.004
0.354  -0.004
0.403  -0.004
0.454  -0.003
0.503  -0.003
0.554  -0.003
0.603  -0.003
0.654  -0.003
0.702  -0.003
0.753  -0.002
0.802  -0.002
0.853  -0.002
0.902  -0.002
0.953  -0.001
1.002  -0.002
1.050  -0.001
1.104  -0.004
1.153  -0.004
1.204  -0.004
1.253  -0.004
1.304  -0.004
1.353  -0.003
1.404  -0.003
1.452  -0.003
1.503  -0.003
1.552  -0.002
1.603  -0.003
1.652  -0.002
1.703  -0.002
1.752  -0.002
1.803  -0.002
1.851  -0.001
1.903  -0.002
1.954  -0.004
2.005  -0.004
2.054  -0.004
2.102  -0.003
2.153  -0.003
2.202  -0.003
2.253  -0.003
2.301  -0.002
2.352  -0.001
2.398  0.001
2.442  0.008
2.475  0.024
2.501  0.050
2.519  0.081
2.533  0.118
2.544  0.156
2.552  0.199
2.560  0.240
2.567  0.284
2.573  0.327
2.578  0.373
2.583  0.417
2.587  0.462
2.591  0.509
2.595  0.554
2.599  0.601
2.602  0.647
2.606  0.694
2.609  0.740
2.611  0.789
2.615  0.835
2.617  0.883
2.620  0.929
2.622  0.978
2.625  1.025
2.627  1.073
2.630  1.120
2.632  1.169
2.635  1.215
2.637  1.264
2.639  1.311
2.641  1.358
2.643  1.407
2.645  1.454
2.648  1.503
2.649  1.550
2.652  1.599
2.653  1.646
2.655  1.696
2.657  1.743
2.658  1.792
2.660  1.839
2.662  1.889
2.664  1.936
2.666  1.985
2.667  2.033
2.668  2.082
2.670  2.129
2.672  2.179
2.674  2.226
2.675  2.276
2.676  2.324

How do I fit only a range of values out of this data to a linear function? I am able to achieve this by saving the required range of data as a separate file linear-07.txt and then fitting this set of values to the function f(x).

set term svg
set output 'blue.svg'
set term svg
set output 'blue.svg'

f(x) = a*x + b
fit f(x) 'linear-07.txt' via a,b

plot[][-1:3] '07-B.txt' pt 7, f(x)

However this seems to be exhausting. Is there an alternate method to this?

Also, How do I obtain the x-value (of the fit function) corresponding to f(x)=0?

Answer 1

Thanks to Thor, I figured out the solutions to my questions.

As he pointed out, the range of the function can be specified in the fit command. In the above data set, the linear region starts from x=2.63.

set term svg
set output 'blue.svg'
set term svg
set output 'blue.svg'

f(x) = a*x + b
fit[2.63:] f(x) '07-B.txt' via a,b

plot[][-1:3] '07-B.txt' pt 7, f(x)

Now, to obtain the $x$ corresponding to $f(x)=0$, since $f(x) = ax + b$, the required $x$ is given by $$x = -\dfrac{b}{a}$$

Hence, adding the line

print -b/a

gives the required value of x.