\documentstyle[10pt,fullpage]{report}
\begin{document}
\begin{center}
{\Large Advanced Data Analysis, II}
\end{center}

\begin{center}
36-402 \hfill Homework 3 \hfill Spring, 1996
\end{center}
\begin{center}
Homework due --- In class, Thursday March 14.
\end{center}

The following problems are taken from the book ``The Analysis of
Cross-Classified Categorical Data'' by Fienberg.
The data are available in the directory {\tt /afs/andrew/hss/stat/data/402}.
\begin{enumerate}
\item Plackett presented the data below on a random sample of diabetic
  patients.  Fit appropriate loglinear models to these data and
  comment on the influence of family history of diabetes on the other
  two variables, and on the relationship between the other two
  variables.  Data in {\tt t312.dat}.
  \begin{center}
    \begin{tabular}{l l | r r | r r}
\hline
\multicolumn{2}{l|}{Family History of Diabetes} & \multicolumn{2}{c|}{Yes}
&\multicolumn{2}{c}{No} \\ \hline
\multicolumn{2}{l|}{Dependence on Insulin Injections} & Yes & No &
Yes & No \\\hline 
Age at Onset &$<45$  &   6 &  1 & 16 &  2 \\
             &$\geq 45$  &  6  & 36 &  8 & 48\\\hline
    \end{tabular}
  \end{center}

\item In a survey of a large American city, respondents were asked
  the question: ``Are the radio and TV networks doing a good job, just
  a fair job, or a poor job?''  Data for the responses it this
  question were broken down by the color of the respondent, and the
  question was asked in two separate years. Data in {\tt t316.dat}.
  \begin{center}
    \begin{tabular}{l l | r r r}
\hline
 & & \multicolumn{3}{c}{Response} \\
Year & Color & Good & Fair & Poor \\\hline
1959 & Black &  81 & 23 &  4 \\
     & White & 325 & 253 & 54 \\
1971 & Black & 224 & 144 & 24 \\
     & White &  600& 636& 158 \\ \hline
    \end{tabular}
  \end{center}
  \begin{enumerate}
  \item Which variables are explanatory?
  \item Which loglinear models provide an acceptable fit to the data?
  \item In your most parsimonious model that fits the data, look at
    the residuals and fitted values to decide if you like this model.
  \item Interpret your results.
  \end{enumerate}

\item {\em More challenging problem}.  The following data presents
  information about British coal miners between the ages of 20 and 64
  years who were smokers but did not show radiological signs of
  pheumoconiosis.  The data, consisting of information on two symptoms
  (breathlessness and wheeze) and age are given below.   Find a model
  which fits the data, and describe what the model means.  Be careful
  to take into account explanatory and response variables. Data in
  {\tt t43.dat}. 
  \begin{center}
    \begin{tabular}{l | r r | r r }
      \hline
      Age group & \multicolumn{2}{c|}{Breathlessness} &
      \multicolumn{2}{c}{No Breathlessness} \\
      in years & Wheeze & No wheeze & Wheeze & No wheeze \\\hline
      20--24 &9&     7&    95&  1841\\
      25--29 &23&     9&   105&  1654\\
      30--34 & 54&    19&   177&  1863\\
      35--39 &121&    48&   257&  2357\\
      40--44 &169&    54&   273&  1778\\
      45--49 &269&    88&   324&  1712\\
      50--54&404&   117&   245&  1324\\
      55--59 &406&   152&   225&   967\\
      60--64 &372&   106&   132&   526
   \end{tabular}
  \end{center}
\end{enumerate}
 Let me know how things are going!
\end{document}




