% File src/library/stats/man/effects.Rd
% Part of the R package, https://www.R-project.org
% Copyright 1995-2007 R Core Team
% Distributed under GPL 2 or later

\name{effects}
\title{Effects from Fitted Model}
\usage{
effects(object, \dots)

\method{effects}{lm}(object, set.sign = FALSE, \dots)
}
\alias{effects}
\alias{effects.lm}
\alias{effects.glm}
\arguments{
 \item{object}{an \R object; typically, the result of a model fitting function
   such as \code{\link{lm}}.}
 \item{set.sign}{logical. If \code{TRUE}, the sign of the effects
   corresponding to coefficients in the model will be set to agree with the
   signs of the corresponding coefficients, otherwise the sign is
   arbitrary.}
 \item{\dots}{arguments passed to or from other methods.}
}
\description{
  Returns (orthogonal) effects from a fitted model, usually a linear
  model. This is a generic function, but currently only has a methods for
  objects inheriting from classes \code{"lm"} and \code{"glm"}.
}
\details{
  For a linear model fitted by \code{\link{lm}} or \code{\link{aov}},
  the effects are the uncorrelated single-degree-of-freedom values
  obtained by projecting the data onto the successive orthogonal
  subspaces generated by the QR decomposition during the fitting
  process. The first \eqn{r} (the rank of the model) are associated with
  coefficients and the remainder span the space of residuals (but are
  not associated with particular residuals).

  Empty models do not have effects.
}
\value{
  A (named) numeric vector of the same length as
  \code{\link{residuals}}, or a matrix if there were multiple responses
  in the fitted model, in either case of class \code{"coef"}.

  The first \eqn{r} rows are labelled by the corresponding coefficients,
  and the remaining rows are unlabelled.  Note that in rank-deficient
  models the corresponding coefficients will be in a different
  order if pivoting occurred.
}
\references{
  \bibshow{R:Chambers+Hastie:1992}
}
\seealso{\code{\link{coef}}}
\examples{
y <- c(1:3, 7, 5)
x <- c(1:3, 6:7)
( ee <- effects(lm(y ~ x)) )
c( round(ee - effects(lm(y+10 ~ I(x-3.8))), 3) )
# just the first is different
}
\keyword{models}
\keyword{regression}
