\name{plot.lm}
\alias{plot.lm}
\alias{plot.mlm}%which is .NotYetImplemented()
\title{Plot Diagnostics for an lm Object}
\usage{
\method{plot}{lm}(x, which = 1:4,
     caption = c("Residuals vs Fitted", "Normal Q-Q plot",
                 "Scale-Location plot", "Cook's distance plot"),
     panel = points,
     sub.caption = deparse(x$call), main = "",
     ask = prod(par("mfcol")) < length(which) && dev.interactive(),
     \dots,
     id.n = 3, labels.id = names(residuals(x)), cex.id = 0.75,
     cook.levels = c((0.5, 1), label.pos = c(4, 2))
}
\arguments{
  \item{x}{\code{lm} object, typically result of \code{\link{lm}} or
    \code{\link{glm}}.}
  \item{which}{If a subset of the plots is required, specify a subset of
    the numbers \code{1:5}.}
  \item{caption}{Captions to appear above the plots}
  \item{panel}{Panel function.  A useful alternative to
    \code{\link{points}} is \code{\link{panel.smooth}}.}
  \item{sub.caption}{common title---above figures if there are multiple;
    used as \code{sub} (s.\code{\link{title}}) otherwise.}
  \item{main}{title to each plot---in addition to the above
    \code{caption}.}
  \item{ask}{logical; if \code{TRUE}, the user is \emph{ask}ed before
    each plot, see \code{\link{par}(ask=.)}.}
  \item{\dots}{other parameters to be passed through to plotting
    functions.}
  \item{id.n}{number of points to be labelled in each plot, starting
    with the most extreme.}
  \item{labels.id}{vector of labels, from which the labels for extreme
    points will be chosen.  \code{NULL} uses observation numbers.}
  \item{cex.id}{magnification of point labels.}
  \item{cook.levels}{levels of Cook's distance at which to draw
    contours.}
  \item{label.pos}{positioning of labels, for the left half and right
    half of the graph respectively, for plots 1-3.}
}
\description{
  Six plots (selectable by \code{which}) are currently available: a plot
  of residuals against fitted values, a Scale-Location plot of
  \eqn{\sqrt{| residuals |}} against fitted values, a Normal Q-Q plot, a
  plot of Cook's distances versus row labels, a plot of residuals
  against leverages, and a plot of Cook's distances against
  leverage/(1-leverage).  By default, the first four of these are
  provided.
}
\details{
  \code{sub.caption}---by default the function call---is shown as
  a subtitle (under the x-axis title) on each plot when plots are on
  separate pages, or as a subtitle in the outer margin (if any) when
  there are multiple plots per page.

  The \dQuote{Scale-Location} plot, also called \dQuote{Spread-Location} or
  \dQuote{S-L} plot, takes the square root of the absolute residuals in
  order to diminish skewness (\eqn{\sqrt{| E |}} is much less skewed
  than \eqn{| E |} for Gaussian zero-mean \eqn{E}).

  The \sQuote{S-L}, the Q-Q, and the Residual-Leverage plot, use
  \emph{standardized} residuals which have identical variance (under the
  hypothesis).  They are given as
  \eqn{R_i / (s \times \sqrt{1 - h_{ii}})}{R[i] / (s*sqrt(1 - h.ii))}
  where \eqn{h_{ii}}{h.ii} are the diagonal entries of the hat matrix,
% bug in Rdconv: "$" and \link inside \code fails; '\$' doesn't help :
  \code{\link{influence}()}\code{$hat}, see also \code{\link{hat}}.

  The Residual-Leverage plot shows contours of equal Cook's distance,
  by default for values of 0.5 and 1.  In the Cook's distance vs
  leverage/(1-leverage) plot, contours of standardized residuals that
  are equal in magnitude are lines through the origin.  The contour
  lines are labeled with the magnitudes. 
}
\references{
  Belsley, D. A., Kuh, E. and Welsch, R. E. (1980)
  \emph{Regression Diagnostics.}  New York: Wiley.

  Cook, R. D. and Weisberg, S. (1982)
  \emph{Residuals and Influence in Regression.}
  London: Chapman and Hall.

  Firth, D. (1991) Generalized Linear Models.  In Hinkley, D. V. and
  Reid, N. and Snell, E. J., eds: Pp. 55-82 in Statistical Theory and
  Modelling. In Honour of Sir David Cox, FRS.  London: Chapman and Hall.

  Hinkley, D. V. (1975) On power transformations to
  symmetry. \emph{Biometrika} \bold{62}, 101--111.

  McCullagh, P. and Nelder, J. A. (1989)
  \emph{Generalized Linear Models.}
  London: Chapman and Hall.
}
\author{
  John Maindonald and Martin Maechler.
}
\seealso{\code{\link{termplot}}, \code{\link{lm.influence}},
  \code{\link{cooks.distance}}, \code{\link{hatvalues}}.
}
\examples{
## Analysis of the life-cycle savings data
## given in Belsley, Kuh and Welsch.
plot(lm.SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings))

## 4 plots on 1 page; allow room for printing model formula in outer margin:
par(mfrow = c(2, 2), oma = c(0, 0, 2, 0))
plot(lm.SR)
plot(lm.SR, id.n = NULL)               # no id's
plot(lm.SR, id.n = 5, labels.id = NULL)# 5 id numbers

## Replace Cook's distance plot by Residual-Leverage plot
plot(lm.SR, which=c(1:3, 5))

## Fit a smooth curve, where applicable:
plot(lm.SR, panel = panel.smooth)
## Gives a smoother curve
plot(lm.SR, panel = function(x,y) panel.smooth(x, y, span = 1))

par(mfrow=c(2,1))# same oma as above
plot(lm.SR, which = 1:2, sub.caption = "Saving Rates, n=50, p=5")
}
\keyword{hplot}
\keyword{regression}