AbstractLinear least squares regression is among the most well known classical methods. This and other parametric least squares regression models do not perform well when the modeling is too restrictive to capture the nonlinear effect the covariates have on the response. Locally weighted least squares regression (loess) is a modern technique that combines much of the simplicity of the classical least squares method with the flexibility of nonlinear regression. The basic idea behind the method is to model a regression function only locally as having a specific form. This paper discusses the method in the univariate and multivariate case and robustifications of the technique, and provides illustrative examples. Copyright © 2010 John Wiley & Sons, Inc.This article is categorized under:Statistical and Graphical Methods of Data Analysis > Density Estimation