text: % File src/library/stats/man/lowess.Rd
  % Part of the R package, https://www.R-project.org
  % Copyright 1995-2013 R Core Team
  % Distributed under GPL 2 or later
  
  \name{lowess}
  \title{Scatter Plot Smoothing}
  \description{
    This function performs the computations for the
    \emph{LOWESS} smoother which uses locally-weighted polynomial
    regression (see the references).
  }
  \usage{
  lowess(x, y = NULL, f = 2/3, iter = 3, delta = 0.01 * diff(range(x)))
  }
  \alias{lowess}
  \arguments{
    \item{x, y}{vectors giving the coordinates of the points in the scatter plot.
      Alternatively a single plotting structure can be specified -- see
      \code{\link{xy.coords}}.}
    \item{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.}
    \item{iter}{the number of \sQuote{robustifying} iterations which should be
      performed.
      Using smaller values of \code{iter} will make \code{lowess} run faster.}
    \item{delta}{See \sQuote{Details}.  Defaults to 1/100th of the range
      of \code{x}.}
  }
  \details{
    \code{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
    \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.  \sQuote{Local} is defined by the distance to the
    \code{floor(f*n)}th nearest neighbour, and tricubic weighting is used
    for \code{x} which fall within the neighbourhood.
  
    The initial fit is done using weighted least squares.  If
    \code{iter > 0}, further weighted fits are done using the product of
    the weights from the proximity of the \code{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.)
  
    \code{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 \code{delta} of the last computed point, and linear
    interpolation is used to fill in the fitted values for the skipped
    points.
  }
  \value{
    \code{lowess} returns a list containing components
    \code{x} and \code{y} which give the coordinates of the smooth.
    The smooth can be added to a plot of the original
    points with the function \code{lines}: see the examples.
  }
  \references{
    Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
    \emph{The New S Language}.
    Wadsworth & Brooks/Cole.
  
    Cleveland, W. S. (1979)
    Robust locally weighted regression and smoothing scatterplots.
    \emph{J. American Statistical Association} \bold{74}, 829--836.
  
    Cleveland, W. S. (1981)
    LOWESS: A program for smoothing scatterplots by robust locally weighted
    regression. \emph{The American Statistician} \bold{35}, 54.
  }
  \seealso{\code{\link{loess}}, a newer
    formula based version of \code{lowess} (with different defaults!).
  }
  \examples{
  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)
  }
  \keyword{smooth}
  