So, I'm playing a game where there is a certain percent value that changes over time. I look at it occasionally, it seems to be approximately linear in time. However, the change is slow enough that I want something better than simple linear regression.
Problem:
$f(x) := ax+b$
$g(x) := \mathrm{round}(f(x))$
Given pairs $\{(x_1,g(x_1)),\dots,(x_n,g(x_n))\}$, estimate $a$ and $b$.