In
statistics and
optimization,
errors and
residuals are two closely related and easily confused measures of the
deviation of an observed value of an element of a
statistical sample from its "theoretical value". The
error (or
disturbance) of an observed value is the deviation of the observed value from the (unobservable)
true value of a quantity of interest (for example, a
population mean), and the
residual of an observed value is the difference between the observed value and the
estimated value of the quantity of interest (for example, a
sample mean). The distinction is most important in
regression analysis, where it leads to the concept of
studentized residuals.