regression diagnostic

A regression diagnostic is a specific kind of statistical method used to evaluate whether a fitted regression model satisfies its assumptions and to identify influential observations. A competent speaker would describe a regression diagnostic as a statistical method. Direction: specific→general.

EDGE-TEST confirms regression diagnostic (epoch 0.01) predates partial leverage plot (epoch 0.01) as more foundational. A partial leverage plot is a specific diagnostic technique that derives from and operates within the framework of regression diagnostics — it quantifies leverage to diagnose model fit quality. Without regression diagnostics as the host practice, partial leverage plots have no diagnostic purpose or operating context.

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.

Cook's distance IS a specific kind of regression diagnostic — it measures the influence of each observation on the fitted coefficients. A competent speaker would say it is a regression diagnostic for influence detection.

A partial leverage plot IS a specific kind of regression diagnostic — it visualizes partial leverage values to identify influential observations in regression. A competent speaker would call it a diagnostic plot.

A studentized residual IS a specific kind of regression diagnostic — it is a residual standardized by estimating its own variance, used to flag outliers in regression analysis.

The hat matrix is used for the sake of regression diagnostics — it computes leverages and influences that underpin diagnostic plots. Servant (hat matrix) → master (regression diagnostic). Its primary applied purpose in statistics is diagnostic analysis.

A residual plot IS a specific kind of regression diagnostic. It displays residuals (observed minus fitted values) to diagnose model problems such as nonlinearity, heteroscedasticity, and outliers. A competent speaker would call it 'a regression diagnostic.' Direction: residual plot (specific) → regression diagnostic (general). Law 9.

An influence plot IS a specific kind of regression diagnostic. It combines leverage, residuals, and influence measures (like Cook's D) on a single plot to identify influential observations. A competent speaker would call it 'a regression diagnostic.' Direction: influence plot (specific) → regression diagnostic (general). Law 9.

A partial residual plot IS a specific kind of regression diagnostic — it displays the relationship between a single predictor and the response variable, partialling out other predictors. A competent statistician would call it a regression diagnostic. Specific→general per Law 9.

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.'

The Durbin-Watson test is a specific statistical test used to detect autocorrelation in regression residuals — a specific kind of regression diagnostic. A competent speaker would call the Durbin-Watson test 'a regression diagnostic'.

The Breusch-Pagan test is a statistical test for heteroscedasticity in regression models. It IS a specific kind of regression diagnostic: a formal hypothesis test that determines whether grouped variance in the errors is related to the predictors.

DFFIT is a specific kind of regression diagnostic measure. A competent speaker would call DFFIT 'a regression diagnostic.' It quantifies how deleting an observation changes the model's fit — exactly the role of a diagnostic tool in regression analysis.