\HeaderA{BOD}{Biochemical Oxygen Demand}{BOD}
\keyword{datasets}{BOD}
\begin{Description}\relax
The \code{BOD} data frame has 6 rows and 2 columns giving the
biochemical oxygen demand versus time in an evaluation of water
quality.
\end{Description}
\begin{Usage}
\begin{verbatim}BOD\end{verbatim}
\end{Usage}
\begin{Format}\relax
This data frame contains the following columns:
\describe{
\item[Time] A numeric vector giving the time of the measurement (days).

\item[demand] A numeric vector giving the biochemical oxygen demand (mg/l).

}
\end{Format}
\begin{Source}\relax
Bates, D.M. and Watts, D.G. (1988),
\emph{Nonlinear Regression Analysis and Its Applications},
Wiley, Appendix A1.4.

Originally from Marske (1967), \emph{Biochemical
Oxygen Demand Data Interpretation Using Sum of Squares Surface}
M.Sc. Thesis, University of Wisconsin -- Madison.
\end{Source}
\begin{Examples}
\begin{ExampleCode}
require(stats)
# simplest form of fitting a first-order model to these data
fm1 <- nls(demand ~ A*(1-exp(-exp(lrc)*Time)), data = BOD,
   start = c(A = 20, lrc = log(.35)))
coef(fm1)
print(fm1)
# using the plinear algorithm
fm2 <- nls(demand ~ (1-exp(-exp(lrc)*Time)), data = BOD,
   start = c(lrc = log(.35)), algorithm = "plinear", trace = TRUE)
# using a self-starting model
fm3 <- nls(demand ~ SSasympOrig(Time, A, lrc), data = BOD)
summary( fm3 )
\end{ExampleCode}
\end{Examples}