A leverage residual is a human-made diagnostic construct in linear regression analysis that combines residual magnitude with observation leverage to flag influential data points. It is computed as r_i * sqrt((1 - h_ii) / h_ii) where r_i is the raw residual for observation i and h_ii is the i-th diagonal element of the hat matrix H = X(X'X)^{-1}X'. The construct persists as a standard computed quantity in statistical software output (R, Python statsmodels, SAS) and in published regression diagnostic tables. [formal: residual_analysis | substrate: mind | horizon: a moment | explicit: yes | epoch: 0.01]
Accepted ontology entry
leverage residual
A leverage residual is a human-made diagnostic construct in linear regression analysis that combines residual magnitude with observation leverage to flag influential data points. It is computed as r_i * sqrt((1 - h_ii) / h_ii) where r_i is…
Definition
Why it is in scope
A leverage residual is a human-made diagnostic construct in regression analysis. It is the product of a raw residual and the square root of the corresponding leverage value (h_ii) from the hat matrix, used to identify observations that exert disproportionate influence on regression coefficient estimates. It persists as a computed quantity within statistical software packages and published regression output tables.
Names and aliases
- leverage residualen · CANONICAL
Relations from this entry
- cmskpjusd056nnobpc3khcmusINSTANCE_OF →
A leverage residual IS a specific kind of diagnostic measure — it computes a derived quantity (residual × sqrt((1-h_ii)/h_ii)) specifically to diagnose influential observations in regression. Direction: specific diagnostic construct → general category (diagnostic measure). Law 9 satisfied.
- cmskb43xn048dnobp35duoxb0DEPENDS_ON →
A leverage residual needs the hat matrix to operate: its formula r_i * sqrt((1-h_ii)/h_ii) requires h_ii (leverage) values from the hat matrix H=X(X'X)^{-1}X'. Remove the hat matrix and you cannot compute the leverage values needed to produce leverage residuals.
- cmsesl4wm05uq3vv3rv0svp7mDEPENDS_ON →
A leverage residual is computed from a raw residual (r_i) multiplied by a leverage-derived scaling factor. Remove residuals from regression and leverage residuals have nothing to compute — the core quantity they modify is the residual itself.
- cmskpj3wa056enobp3qvjo9loSERVES →
Leverage residuals are computed specifically to flag influential observations in regression — their designed purpose is to identify which data points exert disproportionate influence on the model fit. For whose sake? Influential observation detection.
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Record identity
- Created
- Aug 8, 2026, 8:00 PM UTC
- Content hash
- d1dcb849eaff01a579c8fbc33182d782771666b18857834bcd5232b698a3a2c7