Press residual (also called the studentized deleted residual or leave-one-out residual) is a diagnostic measure in regression analysis that quantifies the discrepancy between an observation's actual value and the value predicted by a model fit to all other observations. Parameters: (1) for observation i, the press residual e_(i|i) = y_i - ŷ_(i), where ŷ_(i) is the predicted value for observation i from a model fitted to the dataset with observation i removed; (2) the press residual can be computed efficiently from ordinary residuals without refitting: e_(i|i) = e_i / (1 - h_ii), where e_i is the ordinary residual and h_ii is the i-th diagonal element of the hat matrix. The persistence mechanism is statistical practice — the measure is computed by regression software packages and cited in diagnostic reporting. [formal: e_(i|i) | substrate: mind | horizon: a moment | explicit: yes | epoch: 0.01]
Accepted ontology entry
press residual
Press residual (also called the studentized deleted residual or leave-one-out residual) is a diagnostic measure in regression analysis that quantifies the discrepancy between an observation's actual value and the value predicted by a model…
Definition
Why it is in scope
A leave-one-out residual in regression analysis — the residual computed by fitting the model to all observations except one and then calculating the difference between the omitted observation's actual value and the prediction made by that reduced model.
Names and aliases
- press residualen · CANONICAL
Relations from this entry
- cmskmodwa04zunobpymq3i7ifINSTANCE_OF →
Test: nearest kind. A press residual IS a specific kind of regression diagnostic — it is a leave-one-out residual measure used to identify influential observations and assess model fit, directly fitting the definition of regression diagnostics. A competent speaker would call it 'a regression diagnostic.'
- cmsesl4wm05uq3vv3rv0svp7mINSTANCE_OF →
A PRESS residual (predicted residual) is a specific kind of residual computed by leaving out the i-th observation and predicting it from the model fit to the remaining data. A competent speaker calls it 'a type of residual.'
Relations to this entry
No accepted relations in this direction.
Record identity
- Created
- Aug 8, 2026, 10:24 PM UTC
- Content hash
- 8245cbbe50ace843ba16849d1884d0be5c126374db887190a662b4c1751b466b