Other bivariate smoothers

Loess is one of a number of smoothers (including linear regression as an end-member) that can be used.  The different smoothers vary in the assumptions they make about

• the form of the relationship
• the influence of individual points

The other scatter diagram smoothers include a straight, or "least-squares" line, a low-order polynomial least-squares line, and the "smoothing spline".  Each can be viewed as special cases of the more flexible loess-type smoothers in which the curve is very simple.  The best way to understand these different smoothers is to compare them:

Least-squares line

attach(ortann)
plot(tann ~ elevation)
abline(lm(tann ~ elevation), col="red")

Least-squares polynomial

# second order polynomial
poly2.model <- lm(tann ~ elevation+ I(elevation^2))
poly2.model
poly2.hat <- predict(poly2.model)
lines(elevation[order(elevation)], poly2.hat[order(elevation)],
     col="purple")

Smoothing spline

spline.model <- smooth.spline(elevation, tann)
spline.model
lines(spline.model, col="green")