Is it in general acceptable by computer science community, if the run-time or space consumption of an algorithm is derived by experiment and not analytically?
For example let's say we have an algorithm for which it's running time is given by function $f(n)$, where $n$ is the size of the problem. There is no way to derive its asymptotic behaviour (respecting run time) analytically but only using numerical methods. In other words we have no analytical expression for $f(n)$ but we can probe it using specific values for $n$. Making some trials (trying a wide range of n) we see that run time follows for example very closely a line. Let's say that doing least square method we observe that $t= an+b$ is a good fit for the run time t of the problem (of size n). Good fit is a vague term, and I mean that residuals are within acceptable ranges.
So is it safe to say that the run time of this algorithm is $\Theta(n)$, at least in the range we made the trials? Moreover can we state that this algorithm is faster than another one whose asymptotic behavior is for example $O(n^2)$.
If the answer is negative, what other methods should I search for?