Robust Locally Weighted Regression and Smoothing Scatterplots

Abstract

Abstract The visual information on a scatterplot can be greatly enhanced, with little additional cost, by computing and plotting smoothed points. Robust locally weighted regression is a method for smoothing a scatterplot, (x i , y i ), i = 1, …, n, in which the fitted value at z k is the value of a polynomial fit to the data using weighted least squares, where the weight for (x i , y i ) is large if x i is close to x k and small if it is not. A robust fitting procedure is used that guards against deviant points distorting the smoothed points. Visual, computational, and statistical issues of robust locally weighted regression are discussed. Several examples, including data on lead intoxication, are used to illustrate the methodology.

Keywords

SmoothingRobust regressionMathematicsPolynomial regressionRegressionRegression analysisPolynomialStatisticsValue (mathematics)Least-squares function approximationLinear regressionComputer scienceAlgorithmApplied mathematicsMathematical analysis

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Publication Info

Year: 1979
Type: article
Volume: 74
Issue: 368
Pages: 829-836
Citations: 10611
Access: Closed

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APA Style

                            
                                    William S. Cleveland
                                
                            (1979). 
                            Robust Locally Weighted Regression and Smoothing Scatterplots. 
                            Journal of the American Statistical Association
                            , 74
                            (368)
                            , 829-836.
                            https://doi.org/10.1080/01621459.1979.10481038

Identifiers

DOI: 10.1080/01621459.1979.10481038