Data Smoothing: Loess

Overview of the Loess Analysis

The Loess analysis is intended for scatter plot smoothing. Given bivariate data $(x_ i, y_ i), i=1, \ldots , n$, the Loess analysis fits a regression function f whose value at a point x is obtained by evaluating a local regression function at that point. This function is constructed based on data within a neighborhood of x. Although the fit in each local neighborhood is parametric, the construction of the function f depends on many neighborhoods. Consequently, the resulting function is nonparametric.

You can run a Loess analysis by selecting AnalysisData SmoothingLoess from the main menu. The computation of the loess regression function, confidence limits, and related statistics is implemented by calling the LOESS procedure in SAS/STAT software. See the LOESS procedure documentation in the SAS/STAT User's Guide for additional details.

Note: Fitting a loess curve to data sets with more than several thousand observations might require you to wait a while for the computation to finish, especially if you are computing confidence limits or performing an exhaustive search to find the optimal value of the smoothing parameter. Because of this, the Loess analysis presents a warning message (shown in Figure 18.1) when your data contain more than 5,000 observations. A similar warning appears if you are performing an exhaustive search and there are more than 1,000 observations.

Figure 18.1: A Warning Message

A Warning Message