Residual

machine-learning statistics

Definition

Residual

The residual of a prediction is the signed gap between the predicted value $\hat{y}$ and the observed target $y$:

$$r=y-\hat{y}.$$

A residual is zero for a correct prediction, positive when the model underpredicts ($\hat{y}<y$), and negative when it overpredicts ($\hat{y}>y$). It measures the error on a single observation and is the quantity that loss functions such as quadratic loss and aggregates such as the mean squared error operate on.