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{\Large Advanced Data Analysis, II}
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36-402 \hfill Homework 1 \hfill Spring, 1996
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Homework due --- In class, Tuesday February 6.
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The following problems are taken from the book ``Applied Linear
Statistical Models'' by Neter, Wasserman, and Kutner.
The data are available in the directory {\tt /afs/andrew/hss/stat/data/402}.
\begin{enumerate}
\item {\bf Productivity improvement.}  An economist compiled data on
  productivity improvements fro a sample of firms producing electronic
  computing equipment.  The firms were classified according to the
  level of their average expenditures for research and development in
  the past three years (low, moderate, high).  The results of the
  study follow (productivity improvement is measured on a scale from 0
  to 100).   The data are in the file {\tt product.dat}.\\
  \begin{tabular}{lrrrrrrrrrrrr}
   &1& 2& 3& 4& 5& 6& 7& 8& 9& 10& 11& 12\\
   Low & 7.6 & 8.2 & 6.8 & 5.8 & 6.9 & 6.6 & 6.3 & 7.7 & 6.0 \\
   Moderate & 6.7 & 8.1 & 9.4 & 8.6 & 7.8 & 7.7 & 8.9 & 7.9 & 8.3 &
   8.7 & 7.1 & 8.4 \\
   High & 8.5 & 9.7 & 10.1 & 7.8 & 9.6 & 9.5 \\
  \end{tabular}
  \begin{enumerate}
  \item Analyze the data, looking at fitted values, residuals, the
    ANOVA table, and assumptions
  \item Test for a difference between the ``High'' level and the
    others.  Is it significant?  Are there any other important
    contrasts?  What about the multiple comparisons problem.
  \item Summarize the relationship (if any) between research and
    development expenditures and productivity improvement.
  \end{enumerate}
  
\item {\bf Rehabilitation therapy.}  A rehabilitation center
  researcher was interested in examining the relationship between
  physical fitness prior to surgery of persons undergoing corrective
  knee surgery and time required in physical therapy until successful
  rehabilitation .  Patient records in the rehabilitation center were
  examined, and 24 male subjects ranging in age from 18 to 30 years
  who had undergone similar corrective knee surgery during the past
  year were selected for the study.  The number of days required for
  successful completion of the physical therapy and the prior
  physical fitness status (below average, average, above average) for
  each patient follow, and are in {\tt rehab.dat}.\\
  \begin{tabular}{lrrrrrrrrrr}
   &1& 2& 3& 4& 5& 6& 7& 8& 9& 10\\
   Below average & 29 & 42& 38& 40& 43& 40& 30& 42 \\
   Average & 30& 35& 39& 28& 31& 31& 29& 35& 29& 33 \\
   Above average & 26 &32& 21& 20& 23& 22 \\
  \end{tabular}

  \begin{enumerate}
  \item Analyze the data, looking at fitted values, residuals, the
    ANOVA table, and assumptions.
  \item Are there any important differences between the factor levels?
   How did you decide which differences to test?
 \item Summarize the relationship between the factor levels and the
   response. 

  \end{enumerate}

\item {\bf Soft Drinks.} A soft drink manufacturer uses five agents (1,2,3,4,5) to handle
  the distribution of its various products.  The marketing director
  desired to study the timeliness with which the products are
  distributed.  Twenty transactions for each agent were selected at
  random, and the time lapse (in days) for handling each transaction
  was determined.  The results are available in {\tt
    premium.dat}.  The first column is the time lag, the second column
  is the agent number.   {\em This is a random effects model, because
    of the random sample of times for each agent}. 

  \begin{enumerate}
  \item Analyze the data, looking at fitted values, residuals, the
    ANOVA table, and assumptions.
  \item Are there any important differences between the agents?
   How did you decide which differences to test?
 \item Summarize the relationship between the agents and the
   response.  If you had to select one agent to represent your
   product, which would you choose, or would you even care?
  \end{enumerate}



\end{enumerate}
 Let me know how things are going!
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