\HeaderA{summary.nls}{Summarizing Non-Linear Least-Squares Model Fits}{summary.nls}
\aliasA{print.summary.nls}{summary.nls}{print.summary.nls}
\keyword{regression}{summary.nls}
\keyword{models}{summary.nls}
\begin{Description}\relax
\code{summary} method for class \code{"nls"}.
\end{Description}
\begin{Usage}
\begin{verbatim}
## S3 method for class 'nls':
summary(object, correlation = FALSE, symbolic.cor = FALSE, ...)

## S3 method for class 'summary.nls':
print(x, digits = max(3, getOption("digits") - 3),
      symbolic.cor = x$symbolic.cor,
      signif.stars = getOption("show.signif.stars"), ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{object}] an object of class \code{"nls"}.
\item[\code{x}] an object of class \code{"summary.nls"}, usually the result of a
call to \code{summary.nls}.
\item[\code{correlation}] logical; if \code{TRUE}, the correlation matrix of
the estimated parameters is returned and printed.
\item[\code{digits}] the number of significant digits to use when printing.
\item[\code{symbolic.cor}] logical.  If \code{TRUE}, print the correlations in
a symbolic form (see \code{\LinkA{symnum}{symnum}}) rather than as numbers.
\item[\code{signif.stars}] logical.  If \code{TRUE}, \sQuote{significance stars}
are printed for each coefficient.
\item[\code{...}] further arguments passed to or from other methods.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The distribution theory used to find the distribution of the
standard errors and of the residual standard error (for t ratios) is
based on linearization and is approximate, maybe very approximate.

\code{print.summary.nls} tries to be smart about formatting the
coefficients, standard errors, etc. and additionally gives
\sQuote{significance stars} if \code{signif.stars} is \code{TRUE}.

Correlations are printed to two decimal places (or symbolically): to
see the actual correlations print \code{summary(object)\$correlation}
directly.
\end{Details}
\begin{Value}
The function \code{summary.nls} computes and returns a list of summary
statistics of the fitted model given in \code{object}, using
the component  \code{"formula"} from its argument, plus
\begin{ldescription}
\item[\code{residuals}] the \emph{weighted} residuals, the usual residuals
rescaled by the square root of the weights specified in the call to
\code{nls}.
\item[\code{coefficients}] a \eqn{p \times 4}{p x 4} matrix with columns for
the estimated coefficient, its standard error, t-statistic and
corresponding (two-sided) p-value.
\item[\code{sigma}] the square root of the estimated variance of the random
error
\deqn{\hat\sigma^2 = \frac{1}{n-p}\sum_i{R_i^2},}{sigma^2 = 1/(n-p) Sum(R[i]^2),}
where \eqn{R_i}{R[i]} is the \eqn{i}{}-th weighted residual.
\item[\code{df}] degrees of freedom, a 2-vector \eqn{(p, n-p)}{}.  (Here and
elsewhere \eqn{n}{} omits observations with zero weights.)
\item[\code{cov.unscaled}] a \eqn{p \times p}{p x p} matrix of (unscaled)
covariances of the parameter estimates.
\item[\code{correlation}] the correlation matrix corresponding to the above
\code{cov.unscaled}, if \code{correlation = TRUE} is specified and
there are a non-zero number of residual degrees of freedom.
\item[\code{symbolic.cor}] (only if \code{correlation} is true.)  The value
of the argument \code{symbolic.cor}.
\end{ldescription}
\end{Value}
\begin{SeeAlso}\relax
The model fitting function \code{\LinkA{nls}{nls}}, \code{\LinkA{summary}{summary}}.

Function \code{\LinkA{coef}{coef}} will extract the matrix of coefficients
with standard errors, t-statistics and p-values.
\end{SeeAlso}

