# Exponentially
Weighted Moving Average Line

This type of moving average can be considered to be a generalization
of the simple moving average. Specifically, we could compute each data
point for the plot as:

zt = l*x-bart + (1-l)*zt-1

In this formula, each point zt
is computed as l
(lambda) times the respective
mean x-bart, plus one minus l times the previous
(computed) point in the plot. The parameter l (lambda)
here should assume values greater than 0 and less than 1. You may recognize
this formula as the common exponential
smoothing formula. Without going into detail (see Montgomery, 1985,
p. 239), this method of averaging specifies that the weight for historically
"old" sample means decreases geometrically as one continues
to draw samples. This type of moving average line also smoothes
the pattern of means across samples, and allows the engineer to detect
trends more easily.