se of the regression

$\mbox{you've got data points }(x_i, y_i) \mbox{ that you've done a regression on to obtain }\\ \tilde{y}(x) = m x + b \\ \mbox{The standard error of the regression estimate is given by }\\ S = \sqrt{\dfrac 1 N \displaystyle{\sum_{i=1}^N}\left(\tilde{y}(x_i)-y_i\right)^2}$