Robust Locally-Weighted Regression

Exploratory LOWESS Charts

  • Exploratory LOWESS is an XY scatter graph with the built-in robust locally-weighted bivariate smoother and exploratory features such as:
    • Allowing interactive modification of smoothing bandwidth
    • Allowing interactive modification of number of iterations
    • Ability for exploratory X-zooming

    Exploratory LOWESS graph types include:

  • LOWESS scatter chart
  • Residuals vs. original predictor variable (which can be used as a useful diagnostic tool for controlling the LOWESS fitting process).
  • Absolute values of residuals vs. the LOWESS fitted values
  • Display of confidence interval (weighted or un-weighted)
  • In any application of LOWESS, the choice of Alpha (the local smoothing width) must be based on a combination of judgment and trial and error*.
    • Allowing interactive modification of the value of Alpha and viewing on the fly (i) the original LOWESS fit and (ii) the plot of LOWESS of residuals from the original LOWESS fit, is the most interactive process for selecting the appropriate Alpha on a case-by-case basis.

* Cleveland, W. S. (1993). Visualizing Data. Hobart Press, Summit, NJ.

Examples of LOWESS Curve Fit and Residuals

LOWESS Curve Fit to a Given Data Set and the Corresponding Residuals vs. Original Predictor Variable

(a) LOWESS Chart

Exploratory LOWESS Chart

(b) The Corresponding Residuals

Residuals vs. Original Predictor Variable