\HeaderA{predict.lm}{Predict method for Linear Model Fits}{predict.lm}
\aliasA{predict.mlm}{predict.lm}{predict.mlm}
\keyword{regression}{predict.lm}
\begin{Description}\relax
Predicted values based on linear model object.
\end{Description}
\begin{Usage}
\begin{verbatim}
## S3 method for class 'lm':
predict(object, newdata, se.fit = FALSE, scale = NULL, df = Inf, 
        interval = c("none", "confidence", "prediction"),
        level = 0.95, type = c("response", "terms"),
        terms = NULL, na.action = na.pass, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{object}] Object of class inheriting from \code{"lm"}
\item[\code{newdata}] An optional data frame in which to look for variables with
which to predict.  If omitted, the fitted values are used.
\item[\code{se.fit}] A switch indicating if standard errors are required.
\item[\code{scale}] Scale parameter for std.err. calculation
\item[\code{df}] Degrees of freedom for scale
\item[\code{interval}] Type of interval calculation.  \code{"prediction"} is
only allowed if \code{newdata} is supplied.
\item[\code{level}] Tolerance/confidence level
\item[\code{type}] Type of prediction (response or model term).
\item[\code{terms}] If \code{type="terms"}, which terms (default is all terms)
\item[\code{na.action}] function determining what should be done with missing
values in \code{newdata}.  The default is to predict \code{NA}.
\item[\code{...}] further arguments passed to or from other methods.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
\code{predict.lm} produces predicted values, obtained by evaluating
the regression function in the frame \code{newdata} (which defaults to
\code{model.frame(object)}.  If the logical \code{se.fit} is
\code{TRUE}, standard errors of the predictions are calculated.  If
the numeric argument \code{scale} is set (with optional \code{df}), it
is used as the residual standard deviation in the computation of the
standard errors, otherwise this is extracted from the model fit.
Setting \code{intervals} specifies computation of confidence or
prediction (tolerance) intervals at the specified \code{level}, sometimes 
referred to as narrow vs. wide intervals.

If the fit is rank-deficient, some of the columns of the design matrix
will have been dropped.  Prediction from such a fit only makes sense
if \code{newdata} is contained in the same subspace as the original
data.  That cannot be checked accurately, so a warning is issued.

If \code{newdata} is omitted the predictions are based on the data
used for the fit.  In that case how cases with missing values in the
original fit is determined by the \code{na.action} argument of that
fit.  If \code{na.action = na.omit} omitted cases will not appear in
the residuals, whereas if \code{na.action = na.exclude} they will
appear (in predictions, standard errors or interval limits),
with residual value \code{NA}.  See also \code{\LinkA{napredict}{napredict}}.

The prediction intervals are for a single observation at each case in
\code{newdata} (which must be supplied) with error variance
\eqn{\sigma^2}{sigma^2} as estimated during the fitting.
\end{Details}
\begin{Value}
\code{predict.lm} produces a vector of predictions or a matrix of
predictions and bounds with column names \code{fit}, \code{lwr}, and
\code{upr} if \code{interval} is set.  If \code{se.fit} is
\code{TRUE}, a list with the following components is returned: 
\begin{ldescription}
\item[\code{fit}] vector or matrix as above
\item[\code{se.fit}] standard error of predicted means
\item[\code{residual.scale}] residual standard deviations
\item[\code{df}] degrees of freedom for residual
\end{ldescription}
\end{Value}
\begin{Note}\relax
Variables are first looked for in \code{newdata} and then searched for
in the usual way (which will include the environment of the formula
used in the fit).  As from \R{} 2.0.0 a warning will be given if the
variables found are not of the same length as those in \code{newdata}
if it was supplied.

Offsets specified by \code{offset} in the fit by \code{\LinkA{lm}{lm}}
will not be included in predictions, whereas those specified by an
offset term in the formula will be.
\end{Note}
\begin{SeeAlso}\relax
The model fitting function \code{\LinkA{lm}{lm}}, \code{\LinkA{predict}{predict}},
\code{\LinkA{SafePrediction}{SafePrediction}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
## Predictions
x <- rnorm(15)
y <- x + rnorm(15)
predict(lm(y ~ x))
new <- data.frame(x = seq(-3, 3, 0.5))
predict(lm(y ~ x), new, se.fit = TRUE)
pred.w.plim <- predict(lm(y ~ x), new, interval="prediction")
pred.w.clim <- predict(lm(y ~ x), new, interval="confidence")
matplot(new$x,cbind(pred.w.clim, pred.w.plim[,-1]),
        lty=c(1,2,2,3,3), type="l", ylab="predicted y")
\end{ExampleCode}
\end{Examples}

