residuaalin

Residuaali is a statistical term used in Finnish to describe the difference between an observed value and the value predicted by a model. The genitive singular form residuaalin is used in sentences such as “residuaalin laskenta.” The concept is commonly referred to in English as a residual.

In a data set with response y and model predictions ŷ, the residual for observation i is r_i = y_i − ŷ_i. In linear regression that includes an intercept, the residuals sum to zero. The common measure of overall residual variability is the residual variance s^2 = RSS/(n − p), where RSS is the residual sum of squares, n is the number of observations, and p is the number of estimated parameters.

Residuals are used to assess model fit and to diagnose violations of assumptions such as linearity, homoscedasticity and independence of errors. Diagnostic tools include residuals versus fitted plots and Q-Q plots of residuals. Standardized residuals divide residuals by an estimate of their standard deviation to improve comparability, while studentized residuals adjust for the influence of individual observations. Large absolute standardized or studentized residuals may indicate outliers or model misspecification.

In addition to residuals, influence measures like Cook’s distance or DFFITS quantify how much a single observation affects the fitted model. Residual analysis is common in regression diagnostics but similar ideas apply in time-series and other modeling contexts, with adjustments for model structure.

Finnish usage notes: residuaalin is the genitive singular form of residuaali; jäännös is a common synonym in everyday language. As with any diagnostic tool, residual analysis depends on the chosen model and its assumptions.