(I hope this question fits this site; if not, accept my apologies).
I ran a certain simulation, and got a time series y(t), t = 0, 1, ... 20. After trying some functions, I found that:
y(t) =~ 1 / (A t + B)
Where A and B are coefficients I calculated using linear regression, with R^2 > 0.99.
What is the standard way to report such results in a scientific paper? Specifically:
A. I have no theoretic explanation, why the output looks like this (I know it should be decreasing, and that it's bounded from below, but not much more). It was just a successful guess. Should I describe all other unsuccessful guesses that I tried?
B. Whenever I run the simulation, I get slightly different values of A and B. Should I just report a random run, or should I run the simulation many times and average the results? If so, how many times is enough?