Graphical Diagnostics in Locally Weighted Regression

Abstract

We discuss a method for smoothing scatter plots called locally weighted regression. This is a procedure for fitting a regression curve to data by smoothing; the dependent variable is smoothed as a function of the independent variables in a moving fashion. This scatter plot smoothing involves drawing a smooth curve on a scatter plot to summarize a relationship, in a fashion that makes few assumptions initially about the form or strength of the relationship. One of the chief advantages of this method is that the data analyst is not required to specify a global function of any form to fit a model to the data, only to fit segments of the data. However, the locally weighted regression presented here is based on certain assumptions. One is that the errors are independently and normally distributed with constant variance. Another is that the fitted function follows the pattern of the data, that is, provides a nearly unbiased estimate. Such assumptions are checked by graphical approaches. An example is given for illustration.