# lowess

##### Scatter Plot Smoothing

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

- Keywords
- smooth

##### Usage

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

##### Arguments

- 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`

.

##### Details

`lowess`

is defined by a complex algorithm, the Ratfor original
of which (by W. S. Cleveland) can be found in the Rsources as file
`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 Rimplementation 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.

##### Value

`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.

##### References

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.
*J. American Statistical Association* **74**, 829--836.

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

##### See Also

`loess`

, a newer
formula based version of `lowess`

(with different defaults!).

##### Examples

`library(stats)`

```
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)
```

*Documentation reproduced from package stats, version 3.3, License: Part of R 3.3*