\Header{lm.influence}{Regression Diagnostics}
\keyword{regression}{lm.influence}
\begin{Description}\relax
This function provides the basic quantities which are
used in forming a wide variety of diagnostics for
checking the quality of regression fits.\end{Description}
\begin{Usage}
\begin{verbatim}
lm.influence(lm.obj)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{lm.obj}] an object as returned by \code{\Link{lm}}.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The \code{\Link{influence.measures}()} and other functions listed in
\bold{See Also} provide a more user oriented way of computing a
variety of regression diagnostics.\end{Details}
\begin{Value}
A list containing the following components:
\begin{ldescription}
\item[\code{hat}] a vector containing the diagonal of the ``hat'' matrix.
\item[\code{coefficients}] the change in the estimated coefficients which results
when the i-th case is dropped from the regression is contained in
the i-th row of this matrix.
\item[\code{sigma}] a vector whose i-th element contains the estimate
of the residual standard deviation obtained when the i-th
case is dropped from the regression.
\end{ldescription}
\end{Value}
\begin{Note}\relax
The \code{coefficients} returned by the \R{} version
of \code{lm.influence} differ from those computed by S.
Rather than returning the coefficients which result
from dropping each case, we return the changes in the coefficients.
This is more directly useful in many diagnostic measures.

Note that cases with \code{weights == 0} are \emph{dropped} (contrary
to the situation in S).

if a model has been fitted with \code{na.action=na.exclude} (see
\code{\Link{na.exclude}}), cases excluded in the fit \emph{are}
considered here.\end{Note}
\begin{References}\relax
Belsley, D. A., Kuh, E. and Welsch, R. E. (1980)
\emph{Regression Diagnostics.}
New York: Wiley.\end{References}
\begin{SeeAlso}\relax
\code{\Link{summary.lm}} for \code{\Link{summary}} and related methods;\\
\code{\Link{influence.measures}},\\
\code{\Link{hat}} for the hat matrix diagonals,\\
\code{\Link{dfbetas}},
\code{\Link{dffits}},
\code{\Link{covratio}},
\code{\Link{cooks.distance}},
\code{\Link{lm}}.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
## Analysis of the life-cycle savings data
## given in Belsley, Kuh and Welsch.
data(LifeCycleSavings)
summary(lm.SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi,
                    data = LifeCycleSavings),
        corr = TRUE)
str(lmI <- lm.influence(lm.SR))

## For more `user level' examples, use example(influence.measures)
\end{ExampleCode}
\end{Examples}

