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\title{Final Project, 36-402}
\author{}
\maketitle
\begin{center}
{\large \bf Due no later than: Thursday, May 2, 1996, 9am}\\
{\large \bf Late projects will NOT be accepted.}\\
\end{center}

This is your final project.  Please present your own work and do not
discuss the problem with anyone other than Mike Meyer.  You should
prepare a preliminary analysis by April 18, 1996.  The preliminary
report should show your initial explorations and give some indication
of how you intend to complete the analysis.  It should be no more than
2 pages long.  If you fail to submit a preliminary report you will not
be directly penalized, but you will be indirectly penalize because you
will not get feedback on your work.

The final report must contain an executive summary (something that a
non-technical person like you boss can understand) together with a
technical summary.  All tables and detailed output should be place in
an appendix.


\section*{Effects of Skidders on Two Types of Forest Soils}


\subsection*{Description}

Modern forestry requires considerable specialized equipment.  First, a
feller cuts trees and lays them down on the ground.  Then, a skidder pulls
those trees to bring them to the road where the branches will be removed by
a delimber.  The skidders ride on trails where they must make many round
trips.  These trails are not made of asphalt or gravel, but rather of soil.
The intensive use of these trails leads to the formation of ruts and soil
compaction on the surface which can be damaging.  In this study, FERIC
(Forest Engineering Research Institute of Canada/Institut canadien de
recherches en g\'{e}nie forestier) with Universit\'{e} du
Qu\'{e}bec in Abitibi-T\'{e}miscamingue, has studied the
modifications to two types of soil caused by the traffic of skidders on
skid trails.

The experimental design is as follows.  Two types of soil were studied:
clay and sand.  For each type of soil, three trails which had never been
used were set up where a mechanical cut with regeneration protection was
performed a few weeks earlier.  Each trail was 30 m long and 4.5 m wide.
On each trail a skidder made 15 round trips; going into the forest, the
skidder was empty, outbound the skidder was full.  Some physical
characteristics of the trail were measured before the first round trip as
well as after trips one, three, five, seven, eleven, and fifteen.

The different measurements taken after each trip previously mentioned are
the following.  The first is the slippage of the wheels of the skidder,
defined as the mean slippage of the four wheels.  The slippage of each
wheel is a function of the total number of spins and the speed of the
skidder.  These quantities are determined from the recordings of two video
cameras on each side of the trail.  Under the weight of the load, the
skidder modifies the ground by forming rims and ruts.  The rut depth as
well as the surface of displaced materials have been computed by taking the
average of these measures for three different transversal profiles as
follows.  For each profile of the width, the height of the ground (with
respect to the level before the first trip of the skidder) has been
measured at 20 points after the return of the skidder.  For a rut, the
height is negative whereas it is positive for a rim.  The depth of the ruts
of a profile is defined as the absolute value of the smallest height among
the 20 measured points.  The surface of displaced materials for a profile
is defined as a function of the absolute value of these 20 heights.  Three
other characteristics of soil have been measured for each of the trips
previously mentioned.  The anhydrous density of the soil is considered as
an indicator of soil compaction.  Measured with a device at depths of 10,
20, and 30 cm under the ruts, only the measurements at 10 cm will be used.
Moreover, resistance to penetration (i.e., the strength that must be used
to stick a needle in the soil) and the limit of shear resistance (the
maximal strength that must be used to provoke a free movement of the soil)
are two other parameters measured in prediction models of the effect of
traffic on soil.  The resistance to penetration is computed by taking means
of pressures at depths 5, 10, 15, 20, 25, and 30 cm in mineral soil, but
only the measurements at 5 cm will be used.  Limit of shear resistance in
the ruts is the mean of 10 readings of a shear measurement device sunk in
about 10 cm of mineral soil.

The objective of this study is to construct prediction models for the
variables describing modifications to the soil in terms of the other
variables.  We want to explain the depth of ruts, the surface of displaced
materials, and the density, all measured after the trip, in terms of the
density of the soil before the trip, the resistance to penetration before
the trip, the slippage, the number of trips of the skidder, and the limit
of shear resistance before the trip.  Note that the measurements being
taken after the trips, the measurements before the trip (density,
resistance to penetration and resistance to cutting) are obtained by
interpolation with respect to the previous trips (except for the first trip
for which we also have the measurements before the trip).  Two different
skidders were used for the sand trails and the clay trails.  

The data set as we received it contains 36 cases with 13 variables, that is
six trips (1, 3, 5, 7, 11, and 15) for each of the three trails and two
types of soil.  Each case corresponds to the measurements (or
interpolations) obtained before or after a trip of the skidder on a
trail.

The variables are: 

              
\begin{enumerate}
        
\item     trail: number of the trail; 
\item     soil: 1 for sand and 2 for clay; 
\item     trip: cumulative number of trips on the trail (including this
          one); 
\item     mean.slip: mean slippage during the trip; 
\item     shearadj: resistance to cutting before the trip (estimated by
          interpolation); 
\item     pen5adj: resistance to penetration at 5 cm before the trip
          (estimated by interpolation); 
\item     rut: maximal depth of ruts after the trip; 
\item     totsur: surface of displaced materials after the trip; 
\item     density: density measured after the trip; 
\item     denadj: density before the trip (estimated by interpolation);
          
\item     diffden: difference between the densities after the trips
          adjusted by the number of trips; 
\item     diffdepth: difference between the depths of ruts adjusted by
          the number of trips; 
\item     difftotsur: difference between the surfaces of displaced
          materials adjusted by the number of trips.

\end{enumerate}

Note that the three variables measuring a difference are adjusted by the
number of trips between the two measurements.  For instance, the difference
after the third trip is the measurement after the third trip minus that
after the first, all divided by two, whereas the difference after the
eleventh trip is the measurement after the eleventh trip minus that of the
seventh divided by four.  The same kind of adjustments are used for
interpolation.


\subsection*{Your task}

Your task is to do a preliminary analyses of these data.  You might
consider  many pictures, linear regression
analyses for each individual dependent variable (depth of ruts, surface of
displaced materials, and density of the soil after the trip) with model
selection techniques, and/or separate analyses  for the sand and
clay trails.   Transformations of variables might be
considered.  In particular, in the case of sand trails, the difference in
rut depths might be used instead of the depth itself.  
Are there appropriate ANOVA models for these data?  Are there discrete
data components to the problem?  Can you use survival methods?  


\subsection*{The data}
The data are available in {\tt /afs/andrew/stat/data/402/ferice.dat}
This problem statement is in {\tt /afs/andrew/stat/data/402/final.tex}
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