# LOESS smoothing

Two columns must be selected (*x* and *y* values). The algorithm used is “LOWESS” (LOcally WEighted Scatterplot Smoothing; Cleveland 1979, 1981), with its recommended default parameters (including two robustness iterations). Given a number of points *n* and a smoothing parameter *q* specified by the user, the program fits the *nq* points around each given point to a straight line, with a weighting function decreasing with distance. The new smoothed point is the value of the fitted linear function at the original *x* position.

The Bootstrap option will estimate a 95% confidence band for the curve based on 999 random replicates. In order to retain the structure of the interpolation, the procedure uses resampling of residuals rather than resampling of original data points.

#### LOESS or smoothing spline?

This is almost a matter of taste. The spline often gives a more aesthetically pleasing curve because of its continuous derivatives, but can suffer from overshooting near sharp bends in the data.

#### References

Cleveland, W.S. 1979. Robust locally weighted fitting and smoothing scatterplots. *Journal of the American Statistical Association* 74:829-836.

Cleveland, W.S. 1981. A program for smoothing scatterplots by robust locally weighted fitting. *The American Statistician* 35:54.