Regression Error Characteristic Curves

Jinbo Bi and Kristin Bennett

Department of Mathematical Sciences
Rensselaer Polytechnic Institute

Abstract. Receiver Operating Characteristic (ROC) curves provide a powerful tool for visualizing and comparing classification results. Regression Error Characteristic (REC) curves generalize ROC curves to regression. REC curves plot the error tolerance on the x-axis versus the percentage of points predicted within the tolerance on the y-axis. The resulting curve estimates the cumulative distribution function of the error. The REC curve visually presents commonly used statistics. The area-over-the-curve (AOC) is a biased estimate of the expected error. The R-squared value can be estimated using the ratio of the AOC for a given model to the AOC for the null model. Users can quickly assess the relative merits of many regression functions by examining the relative position of their REC curves. The shape of the curve reveals additional information that can be used to guide modelling.

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