Normalized residuals are regression diagnostics obtained by dividing each raw residual r_i by the square root of MSE times (1 - h_ii), where h_ii is the i-th diagonal element of the hat matrix and MSE is the mean squared error of the fitted model. Unlike raw residuals, normalized residuals have approximately unit variance under the regression assumptions, making them suitable for identifying outliers across observations with differing leverage values. Values with absolute magnitude exceeding 2 are typically flagged as outliers. [formal: normalized-residual | substrate: mind | horizon: a life | explicit: yes | epoch: 0.01]
Accepted ontology entry
normalized residual
Normalized residuals are regression diagnostics obtained by dividing each raw residual r_i by the square root of MSE times (1 - h_ii), where h_ii is the i-th diagonal element of the hat matrix and MSE is the mean squared error of the fitte…
Definition
Why it is in scope
A human-made statistical measure in regression analysis where raw residuals are divided by an estimate of their standard deviation, producing scale-invariant quantities that enable comparison across observations with differing leverage
Names and aliases
- normalized residualen · CANONICAL
Relations from this entry
- cmsesl4wm05uq3vv3rv0svp7mDERIVED_FROM →
Normalized residuals are computed from raw residuals by dividing each by sqrt(MSE * (1 - h_ii)). Residuals existed first and fed into the normalization construction. Historical derivational claim.
- cmskmodwa04zunobpymq3i7ifINSTANCE_OF →
A normalized residual IS a specific kind of regression diagnostic — it is a residual that has been scaled to account for heteroscedasticity, making it suitable for diagnostic checking. A competent speaker would call it a diagnostic method for regression models.
- cmskpjusd056nnobpc3khcmusINSTANCE_OF →
A normalized residual IS a specific kind of diagnostic measure — it standardizes a residual (dividing by its estimated standard deviation) to flag observations with unusually large residuals, which is the core purpose of a diagnostic measure. Direction: specific→general. A competent statistician would call a normalized residual 'a diagnostic measure.'
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Record identity
- Created
- Aug 8, 2026, 5:35 PM UTC
- Content hash
- a64b76b2ddbe6fd79ec6931e9fac3f38a964fd512a769901d4469df6d707b852