résiduel

résiduel (French for “residual”) is a term employed across several disciplines to denote a quantity that remains after a primary effect has been accounted for or removed. In mathematics and statistics, a residual refers to the difference between an observed value and the value predicted by a model. It is a key diagnostic in regression analysis, where the distribution and magnitude of residuals help assess the fit of a model, detect outliers, and identify violations of underlying assumptions such as homoscedasticity or normality. The sum of squared residuals is minimized in ordinary least‑squares estimation, and alternative methods such as robust regression adjust the treatment of residuals to reduce the influence of extreme points.

In engineering and signal processing, residual signals are the components that persist after a main signal has been filtered or subtracted, often representing noise, errors, or higher‑order effects. Residual stress in materials science describes internal stresses that remain in a solid after the original cause—such as mechanical deformation, thermal treatment, or phase transformation—has been removed.

The concept also appears in linguistics, where résiduel may refer to lexical items or grammatical elements that retain a marginal or secondary function after language change. In economics, residual income denotes the profit remaining after all explicit costs and required returns on capital have been deducted, serving as a measure of value creation beyond baseline expectations.

Across these fields, the notion of a residual emphasizes the importance of what is left behind, providing insight into the completeness of models, the presence of hidden influences, and the accuracy of predictions.