This function performs the computations for the
*LOWESS* smoother which uses locally-weighted polynomial
regression (see the references).

`lowess(x, y = NULL, f = 2/3, iter = 3, delta = 0.01 * diff(range(x)))`

x, y

vectors giving the coordinates of the points in the scatter plot.
Alternatively a single plotting structure can be specified -- see
`xy.coords`

.

f

the smoother span. This gives the proportion of points in the plot which influence the smooth at each value. Larger values give more smoothness.

iter

the number of ‘robustifying’ iterations which should be
performed.
Using smaller values of `iter`

will make `lowess`

run faster.

delta

See ‘Details’. Defaults to 1/100th of the range
of `x`

.

`lowess`

returns a list containing components
`x`

and `y`

which give the coordinates of the smooth.
The smooth can be added to a plot of the original
points with the function `lines`

: see the examples.

`lowess`

is defined by a complex algorithm, the Ratfor original
of which (by W. S. Cleveland) can be found in the R sources as file
`src/appl/lowess.doc`

. Normally a local linear polynomial fit is
used, but under some circumstances (see the file) a local constant fit
can be used. ‘Local’ is defined by the distance to the
`floor(f*n)`

th nearest neighbour, and tricubic weighting is used
for `x`

which fall within the neighbourhood.

The initial fit is done using weighted least squares. If
`iter > 0`

, further weighted fits are done using the product of
the weights from the proximity of the `x`

values and case weights
derived from the residuals at the previous iteration. Specifically,
the case weight is Tukey's biweight, with cutoff 6 times the MAD of the
residuals. (The current R implementation differs from the original
in stopping iteration if the MAD is effectively zero since the
algorithm is highly unstable in that case.)

`delta`

is used to speed up computation: instead of computing the
local polynomial fit at each data point it is not computed for points
within `delta`

of the last computed point, and linear
interpolation is used to fill in the fitted values for the skipped
points.

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988).
*The New S Language*.
Wadsworth & Brooks/Cole.

Cleveland, W. S. (1979).
Robust locally weighted regression and smoothing scatterplots.
*Journal of the American Statistical Association*, **74**,
829--836.
10.1080/01621459.1979.10481038.

Cleveland, W. S. (1981)
LOWESS: A program for smoothing scatterplots by robust locally
weighted regression.
*The American Statistician*, **35**, 54.
10.2307/2683591.

`loess`

, a newer
formula based version of `lowess`

(with different defaults!).

```
# NOT RUN {
require(graphics)
plot(cars, main = "lowess(cars)")
lines(lowess(cars), col = 2)
lines(lowess(cars, f = .2), col = 3)
legend(5, 120, c(paste("f = ", c("2/3", ".2"))), lty = 1, col = 2:3)
# }
```

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