User`s guide

Smoothing Data
2-15
2 A weighted linear least squares regression is performed. For lowess, the
regression uses a first degree polynomial. For loess, the regression uses a
second degree polynomial.
3 The smoothed value is given by the weighted regression at the predictor
value of interest.
If the smooth calculation involves the same number of neighboring data points
on either side of the smoothed data point, the weight function is symmetric.
However, if the number of neighboring points is not symmetric about the
smoothed data point, then the weight function is not symmetric. Note that
unlike the moving average smoothing process, the span never changes. For
example, when you smooth the data point with the smallest predictor value,
the shape of the weight function is truncated by one half, the leftmost data
point in the span has the largest weight, and all the neighboring points are to
the right of the smoothed value.
The weight function for an end point and for an interior point is shown below
for a span of 31 data points.
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1
1.2
Local Regression Weight Function
The weight function for
the leftmost data point
The weight function for
an interior data point