# Robust Locally Weighted Regression and Smoothing Scatterplots

**William S. Cleveland**

CiteWeb id: 20120000009

CiteWeb score: 8623

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.

Links:- amstat.tandfonline.com/doi/pdf/10.1080/01621459.1979.10481038
- synapse.princeton.edu/~sam/cleveland79_JASA_loess.pdf
- www.jstor.org/stable/2286407?seq=6
- home.eng.iastate.edu/~shermanp/STAT447/Lectures/Cleveland%20paper.pdf
- home.engineering.iastate.edu/~shermanp/STAT447/Lectures/Cleveland%20paper.pdf
- www.tandfonline.com/doi/abs/10.1080/01621459.1979.10481038
- amstat.tandfonline.com/doi/abs/10.1080/01621459.1979.10481038
- dx.doi.org/10.1080/01621459.1979.10481038
- ci.nii.ac.jp/naid/30022468356

William S. Cleveland,

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