How Loess Works

x

0

α

λ

0

1

2

Loess (or lowess, Locally Weighted Scatterplot Smoothing) is a scatterplot smoother, which provides a flexible method for nonparametric regression.

Elements in the graphic:

• blue points: data points under the smoother

• black points: data points not under the smoother

• black curve: the loess smoother

• dark red dot: the loess fit at the current position

• dark red line or curve: the loess curve with parameters fixed at those corresponding to the red dot

• purple bars: window shape and the corresponding loess weights, with scale indicated on the right axis

Controls:

•

x

0

, the position at which the point on the loess curve is calculated. As you slide

x

0

, notice how the window width changes. The number of points in the window, whose positions are indicated by the green bars, remains constant.

•

α

, the fraction of data under the smoother. As

α

increases, the window width increases and more smoothing is done.

λ=0,1,or2

indicates the degree of the local polynomial.