lowess {stats} | R Documentation |

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(xy$x[o])))

`x, y` |
vectors giving the coordinates of the points in the scatter plot. Alternatively a single plotting structure can be specified. |

`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`

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.

`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.

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. Amer. Statist. Assoc.* **74**, 829–836.

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

`loess`

, a newer
formula based version of `lowess`

(with different defaults!).

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)

[Package *stats* version 2.5.0 Index]