In signal processing, the linear prediction residue is the difference between the actual signal and the predicted signal using linear prediction analysis.
The residue is also called the linear prediction error $e(n)$ :
$
e(n) = s(n) - \sum_{k=1}^{P} a_k s(n-k)
$
The linear prediction residue is the error term that represents the part of the signal that cannot be explained by the linear model. In the [[source-filter model]] the filter implements the linear model and the residue is associated with the excitation.