A component-plus-residual plot (CPR plot) is a regression diagnostic visualization constructed by plotting each predictor variable against the quantity ŷ + ε̂, where ŷ is the model's fitted value and ε̂ is the residual. The plot overlays a lowess or LOESS smooth line to reveal departures from linearity — a straight reference line through the observed relationship indicates the linear model specification is adequate for that predictor, while curvature signals a misspecified functional form. The parameters are: (1) a fitted linear regression model, (2) a chosen predictor variable, and (3) the smoothing method for the reference curve. The construct persists through statistical software implementations (e.g., R's , Python's statsmodels) and publication in statistical practice. It extends the partial residual plot by adding the fitted value, making the scale match the response variable's units for direct interpretability. [formal: component-plus-residual plot | substrate: mind | horizon: hours | explicit: yes | epoch: 0.01]
Accepted ontology entry
component-plus-residual plot
A component-plus-residual plot (CPR plot) is a regression diagnostic visualization constructed by plotting each predictor variable against the quantity ŷ + ε̂, where ŷ is the model's fitted value and ε̂ is the residual. The plot overlays a…
Definition
Why it is in scope
A human-made visualization in regression analysis that displays the relationship between a single predictor and the response variable by plotting the predictor values against the sum of the fitted values and the residuals — designed to help detect non-linear relationships and assess the functional form of predictors in a regression model.
Names and aliases
- component-plus-residual ploten · CANONICAL
Relations from this entry
- cmse8ujmb04y43vv3c4renvx3INSTANCE_OF →
A component-plus-residual plot IS a specific kind of residual plot used in regression diagnostics. It displays the relationship between a response variable and a predictor, adding the predictor's linear effect. Direction: specific→general. Law 9.
- cmsdai2d503n23vv3e00xn5baDERIVED_FROM →
A component-plus-residual plot (also called a partial residual plot) is a regression diagnostic tool that derives from regression analysis. Regression as a statistical method existed first and fed into the development of diagnostic visualization techniques. The plot shows the relationship between a predictor and the response AFTER accounting for other predictors in the regression model — it is a derivative visualization built on the regression framework.
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Record identity
- Created
- Aug 8, 2026, 8:52 PM UTC
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- 8151f1041cdeac4dbad4e807c234c943a7249ea841e2236bc104c0acb7390324