Standard deviation of the residuals (s)
The standard deviation of the residuals, s, is roughly the typical size of a prediction error from the regression line, in the units of y.
The value answers a practical question: when you predict with this line, how far off are you usually? It is , so you square the residuals, average them using because the line costs you two estimated coefficients, then take the square root, which returns you to the units of the response variable. For example, five residuals of 2, -1, 0, 1, and -2 give and , so predictions typically miss by about 1.83 units of . Software prints it as s, and a smaller for the same response values means a tighter fit, the same tightness a residual plot shows visually.
Where this comes up
More regression and correlation terms, or browse the full statistics glossary.