This lab analyzes a data sets from Weisberg's book
  <CITE>Applied Linear Regression.</CITE> Weisberg writes:

<BLOCKQUOTE> Aerial survey methods are regularly used to estimate the
number of snow geese in their summer range areas west of Hudson Bay in
Canada.  To obtain estimates, small aircraft fly over the range and,
when a flock of geese is spotted, an experienced person estimates the
number of geese in the flock.  To investigate the reliability of this
method of counting, an experiment was conducted in which an airplane
carrying two observers flew over n=45 flocks, and each observer made
an independent estimate of the number of birds in each flock.  Also, a
photograph of the flock was taken so that an exact count of the number
of birds in the flock could be made.  The columns in the data set are
Photo, Observer 1 and Observer 2, in order.  </BLOCKQUOTE>

 <P>
Begin by reading in the data
 <P>
<B>
photo <- c (56,  38,  25,  48,  38,  22,  22,  42,  34,  14, <BR>
            30,  9,   18,  25,  62,  26,  88,  56,  11,  66,<BR> 
            42,  30,  90,  119, 165, 152, 205, 409, 342, 200,<BR>
            73,  123, 150, 70,  90,  110, 95,  57,  43,  55, <BR>
            325, 114, 83,  91,  56 )<BR>
<BR>
observer1 <- c ( 50,  25,  30,  35,  25,  20,  12,  34,  20,  10, <BR>
                 25,  10,  15,  20,  40,  30,  75,  35,  9,   55,<BR> 
                 30,  25,  40,  75,  100, 150, 120, 250, 500, 200,<BR>
                 50,  75,  150, 50,  60,  75,  150, 40,  25,  100,<BR>
                 200, 60,  40,  35,  20 )<BR>
<BR>
observer2 <- c ( 40,  30,  40,  45,  30,  20,  20,  35,  30,  12, <BR>
                 30,  10,  18,  30,  50,  20,  120, 60,  10,  80, <BR>
                 35,  30,  120, 200, 200, 150, 200, 300, 500, 300,<BR>
                 40,  80,  120, 60,  100, 120, 150, 40,  35,  110,<BR>
                 400, 120, 40,  60,  40 )
</B>
 <P>

Make scatter plots of Y=photo count versus X=observer1 and versus
X=observer2.  Do these plots suggest that linear regression is
appropriate?  Why or why not?
 <P>

Make scatter plots of Y=sqrt(photo count) versus X=sqrt(observer1) and versus
X=sqrt(observer2).  Do these plots suggest that linear regression is
appropriate?  Why or why not?
 <P>

Make scatter plots of Y=log(photo count) versus X=log(observer1) and versus
X=log(observer2).  Do these plots suggest that linear regression is
appropriate?  Why or why not?
 <P>

Make a scatter plot of observer1 versus observer2.  Use the log scale
if you like.  Add the 45 degree line to the plot using the command
<B>abline(0,1)</B> immediately after the plot command.  Does one
observer tend to guess higher than the other?  Which one?<BR>
 <P>
Use the regression of Y=log(photo count) versus X=log(observer1) to answer
the following questions.  
<UL>

<LI> What is the log of 90?

<LI> Suppose a new flock of geese is found.  Observer 1 estimates that
it has 90 geese.  What is your best guess of the log of the exact
number of geese in the flock?

<LI> What is your best guess of the exact number of geese in the
flock?  (Hint: the exp() function is the inverse of the log()
function.  For example, exp(4)=54.59815 and log(54.59815)=4.)

<LI> Of all the flocks that Observer 1 estimates to have 90 geese,
about 95% of them will have log of the exact number of geese beween
what and what?  About 95% of them will have the exact number of geese
between what and what?

</UL>
 <P>

Weisberg continues: <BLOCKQUOTE> As a result of this experiment, the
practice of using visual counts of flock size to determine population
estimates was discontinued in favor of using photographs.
</BLOCKQUOTE>