Starting with an example:
Having the points $P_1(1,29),P_2(2,50),P_3(4,88)$. Then there are $4$ possible ways to choose points to find the "best" line (using ordinary least-squares). The $4$ possibilities are:
Choosing $P_1$ and $P_2$ only, we will get intercept $=8$
Choosing $P_1$ and $P_3$ only, we will get intercept $= \frac{28}{3} = 9. \overline{333}$
Choosing $P_2$ and $P_3$ only, we will get intercept $= 12$
Choosing $P_1$, $P_2$ and $P_3$, we will get intercept $=10$
Now calculating the Sample Standard Deviation of these intercepts, using the formula
$$s=\sqrt{\frac{\sum_{k=1}^n (x_k-\overline{x})}{n-1}},$$
we get $s=\frac{5}{3}=1.\overline{666}$ [which is the required value to be calculated].
In general, having $n \ge 3$ points, means having $\binom{n}{2}+\binom{n}{3}+\dots+\binom{n}{n}$ possible combinations (intercepts). It maybe difficult/lengthy, for example when $n=5$, we have $26$ intercepts!
So the question is:
Is there an easy way, tabular or otherwise, to calculate the Sample Standard Deviation with the intercepts (all possible ones) being our samples?