Residuální

Residuální is an adjective used in several languages, notably Czech and Slovak, to describe something that remains after a process, calculation, or transformation. It derives from Latin residuum, meaning the remainder. In technical contexts, residuální often corresponds to the English term residual and is applied across disciplines to denote what is left over after an estimation, filtering, or modeling step.

In statistics and data analysis, residuální values (residuals) are the differences between observed values and those predicted by a model. For a response variable y_i and a fitted value ŷ_i, the residual is e_i = y_i − ŷ_i. Residuals are used to assess model fit, diagnose misspecification, identify outliers, and check assumptions such as linearity, homoscedasticity, and independence. Variants include standardized and studentized residuals, which scale residuals to help compare observations.

In time series and signal processing, residuální concepts refer to the portion of a signal not captured by a model or predictor. The residual signal reflects noise, measurement error, or unmodeled structure and is often analyzed to improve forecasting or compression.

In other domains, residuální can describe residues or remnants left after chemical reactions, industrial processing, or filtration. In medicine, the term appears in phrases like residual tumor or residual disease, indicating disease that remains after treatment. Overall, residuální conveys the notion of what persists after an initial operation, estimation, or transformation.