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\centerline{\Large \bf 36-707 \ \ Homework \#6 \ \ Due Tuesday Nov 27
  15, 2001}
\bigskip

{\large\bf Reading}

We have been moving through material in RPD in approximately this
order:
\begin{itemize}
\item Regression diagnostics and case statistics: Ch 11
\item Transformations (did already), WLS and GLS: Ch 12, esp. 12.5
\item Bootstrap: not in RPD; but see e.g. pp. 142ff. in Venables and Ripley.
\item Polynomial regression (Ch 8) and Nonlinear regresion (Ch 15)
\end{itemize}
\bigskip

{\large\bf Rough plan for rest of semester:}

\hfil
\begin{tabular}{|l|l|}
\hline
Tue        & Thu \\
\hline
\hline
Logistic   
Regression (RPD Sect. 15.5) & Thanksgiving \\
\hline
More Logistic   
Regression (not in RPD) & Variable Selection (Ch 7) \\
\hline
``Fixing''   
Collinearity (Ch 2, 13) & Bayesian view of Regression (not in RPD) \\
\hline
More Bayes,      
or Mixed Effects (maybe Ch 18) & \\
\hline

\end{tabular}

\bigskip

{\large\bf Exercises:}
\begin{enumerate}

\item Read RPD sect 12.5, do problem 12.20, p. 430.  Unfortunately the
  data are not on-line in this form, so you will have to type it in.

\item Deblois and Leggett (1991; as reported in Hamilton, 1992) set up
  experimental aquaria to study dynamics of a simple predator/prey
  system.  They found that rates of predation by amphipods (a small
  crustacean) were nonlinearly related to the density of their prey,
  capelin eggs (capelin are small marine fish).  For theoretical and
  empirical reasons the researchers chose a negative exponential model
\[
        y = \alpha(1-e^{-\beta x})
\]
for the relation between predation rate (capelin eggs eaten per
amphipod) and prey abundance (initial egg density).  The data are in
``eggs.dat'' in the 707 data directory on the web.  The variables are:
\begin{verbatim}
density: the initial density of capelin eggs
ratio: predation rate: ratio of number of eggs eaten to number of amphipods
\end{verbatim}
Fit the model using {\tt nls()} in Splus.  Turn in summaries and
graphs similar to the analyses presented in lecture.  Briefly describe
the fit and (optionally) if you see any way to improve the model or
the fit, try it out.

\end{enumerate}


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