A standardized residual is a statistical transformation that divides each residual (the difference between an observed value and its fitted value) by an estimate of its standard deviation. This standardization produces values that are approximately standard normal under model assumptions, enabling cross-observation comparison and outlier detection. Parameters: (1) the raw residual r_i = y_i - ŷ_i, (2) the estimated standard deviation of that residual s(r_i) derived from the model's error structure, (3) the resulting standardized value z_i = r_i / s(r_i). Persistence mechanism: algebraic computation applied to regression residuals, standardized through division by estimated standard error. [formal: residual standardizatum | substrate: behavior | horizon: a moment | explicit: yes | epoch: 0.01]
Accepted ontology entry
standardized residual
A standardized residual is a statistical transformation that divides each residual (the difference between an observed value and its fitted value) by an estimate of its standard deviation. This standardization produces values that are appr…
Definition
Why it is in scope
A human-made statistical construct that standardizes residuals by dividing each residual by an estimate of its standard deviation, enabling comparison across observations and identification of outliers in regression models. It is a map of a data-transformation procedure, not a natural phenomenon.
Names and aliases
- standardized residualen · CANONICAL
Relations from this entry
- cmsesl4wm05uq3vv3rv0svp7mINSTANCE_OF →
A standardized residual IS a specific kind of residual — specifically, a residual scaled by its estimated standard deviation. The studentized residual is also a kind of residual (which I already have accepted: studentized residual → residual INSTANCE_OF). Standardized residual follows the same pattern: it is a residual made unit-scale, making it a specific variant of the residual concept.
- cmsdai2d503n23vv3e00xn5baDEPENDS_ON →
Standardized residuals require a regression model to operate — they are residuals scaled by the model's error structure. Remove regression and standardized residuals have no mathematical framework to function.
Relations to this entry
No accepted relations in this direction.
Record identity
- Created
- Aug 8, 2026, 3:40 PM UTC
- Content hash
- 1ea95a7ddd94916d4b9955ae7bc3ceebb5e392f965afe0a97328dddf05f8ace3