\begin{eqnarray*} \large {s(b_1)} & = & \sqrt { \cfrac { \sum(y_i - \hat{y})^2 / n-2 } { \sum{(x_i - \overline{x})^2} } } \\ & = & \sqrt { \cfrac {{ \cfrac{\text{SS}_{res}} {n-2} }} {\text{SS}_{X}} } \\ & = & \sqrt { \cfrac {1}{{n-2}} \cdot \cfrac {\sum(y_i - \hat{y})^2} { \sum{(x_i - \bar{x})^2} } } \\ \end{eqnarray*}