A dfbeta is a regression diagnostic measure that quantifies how much each individual regression coefficient changes when a single observation is deleted from the model. For observation i and coefficient j, it is computed as dfbeta_j(i) = (beta_j - beta_j(i)) / SE(beta_j(i)), where beta_j is the original coefficient and beta_j(i) is the coefficient estimated with observation i removed. The denominator standardizes the change so that coefficients on different scales can be compared. Values exceeding ±2 flag influential observations for each predictor. This construct persists through statistical software packages, regression analysis practice, and the methodological literature on regression diagnostics. [formal: df-beta | substrate: mind | horizon: a moment | explicit: yes | epoch: 0.01]
Accepted ontology entry
dfbeta
A dfbeta is a regression diagnostic measure that quantifies how much each individual regression coefficient changes when a single observation is deleted from the model. For observation i and coefficient j, it is computed as dfbeta_j(i) = (…
Definition
Why it is in scope
A human-made statistical measure in regression diagnostics that quantifies the change in each regression coefficient when a single observation is deleted. For observation i and coefficient j, dfbeta_j(i) = (beta_j - beta_j(i)) / SE(beta_j(i)), enabling detection of observations that disproportionately influence individual predictors.
Names and aliases
- dfbetaen · CANONICAL
Relations from this entry
- cmrsx7h5m00k5145rf9y8qelqDERIVED_FROM →
Leverage existed first and mathematically feeds into dfbeta. The dfbeta formula uses leverage (h_ii) as a core component: dfbeta_j(i) = (r_i / (1 - h_ii)) * (x_ji / sqrt(MSE * (1 - h_ii))). Leverage was developed first as a measure of an observation's extremity in predictor space; dfbeta was derived to extend that influence analysis to individual regression coefficients.
- cmsk6gz0j03yknobp6dik93doINSTANCE_OF →
dfbeta is a specific kind of regression diagnostic tool — it quantifies coefficient change on leave-one-out deletion, fitting the diagnostic plot category. A competent speaker would call it a diagnostic.
- cmsesl4wm05uq3vv3rv0svp7mDERIVED_FROM →
dfbeta is mathematically derived from residuals — the leave-one-out coefficient change is computed from the residual of the deleted observation. Residuals existed first and fed into this metric.
- cmsdai2d503n23vv3e00xn5baSERVES →
dfbeta measures the change in each regression coefficient when an observation is deleted. Its designed purpose is to serve regression analysis by identifying observations that disproportionately influence parameter estimates. For whose sake? regression.
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Record identity
- Created
- Aug 8, 2026, 3:58 PM UTC
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- b82083e8a58ce951c6d36a6aaff87ace7e2004586a03fe89caf063ae2b0363c6