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Predictor effect displays, introduced in this article, visualize the response surface of complex regression models by averaging and conditioning, producing a sequence of 2D line graphs, one graph or set of graphs for each predictor in the regression problem. Partial residual plots visualize lack of fit, traditionally in relatively simple additive regression models. We combine partial residuals with effect displays to visualize both fit and lack of fit simultaneously in complex regression models, plotting residuals from a model around 2D slices of the fitted response surface. Employing fundamental results on partial residual plots along with examples for both real and contrived data, we discuss and illustrate both the strengths and limitations of the resulting graphs. The methods described in this paper are implemented in the effects package for R.