So I have some data for program running time, that follows a power law relation aN^b. I log-log plotted the data and saw that it became a straight line, so I calculated the slope of this line to get b, and then calculated a using one of my data points.
I also did a version where I used FindFit in Mathemathica, to find a best fit for the log10 version of the data in y = kx + m form.
If I test these two functions and compare to my data, the Mathemathica generated version is more accurate for lower N values(input-size). The function I calculated is less accurate for lower N's, but more accurate for higher N's.
It makes sense to me to use the one I calculated, because it's more important that the equation is correct for large N values in this case.
Now my question is: Is it better mathemathically to use the mathemathica equation that is more accurate for most of my data, or the equation I calculated that is more correct for high N values? I was thinking maybe it's better to use the mathemathica one and the error should be calculated using statistics?
Edit: data on a log-log plot
For my calculation of the slope i used the 2 farthest data points and calculated the slope of this straight line:
Then I calculated the constant a in aN^b using the data point where N = 65536 and T = 4630.283.
My calculated equation: 
The Mathemathica generated equation:
