Exploring partial residual plots

R. Dennis Cook

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


Partial residual plots have a long history and, judging from their prominence in the literature, are frequently used. In this article, I explore the structure and usefulness of partial residual plots and augmented partial residual plots as basic tools for dealing with curvature as a function of selected covariates x2 in regression problems in which the covariate vector x is partitioned as xr = (x1T, x2T). The usefulness of these plots for obtaining a good impression of curvature can depend on the behavior of the covariates through the conditional expectation E(x1/x2). Partial residual plots seem to perform best under linear conditional expectations. Augmented partial residual plots allow E(x1/x2) to be a quadratic function of x2. This de­velopment leads to a new class of plots, called CERES plots, that includes partial and augmented partial residual plots as spccial eases. CERES plots may be useful for obtaining an impression of curvature as a function of x2 when the conditional expectations E(x1/x2) are neither linear nor quadratic. The relationship between these developments and generalized additive models is discussed as well. © 1993 American statistical association and the American society for quality control.

Original languageEnglish (US)
Pages (from-to)351-362
Number of pages12
Issue number4
StatePublished - 1993


  • Augmented partial residual plots: CERES plots: component-plus-residual plots
  • Generalized additive models
  • Regression diagnostics
  • Regression graphics


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