IID for Parameter Regression

I want to regress some values $v_i$ according to a function $f(x)$.

I know that there is this relationship between $v_i$ and $f(x)$. For every $1 \le i \le n$, there exists a point $(a\cdot i, \space b\cdot v_i)$ near the curve $(x, \space f(x))$ where $a$ and $b$ are constants.

$f(x)$ is a positive, continuously decreasing, smooth function.
$\lim_{x\rightarrow \infty} f(x) = 0$

Is there a proper way to perform this regression and get the constants $a$ and $b$? I have a few ideas, but I am worried that the regression would be incorrect since the distribution of the votes may or may not be iid.

What is the generally correct way to do this regression?