FR 3218/5218 Spring 2008

Need not turn in

This assignment's purpose is to assist you in review of statistics. You do not turn the assignment in. However, you will be held responsible for knowing the methods reviewed in this assignment. Most of these methods are covered in Chapter 2 of your textbook.

You should do question 1. by hand and check your results using Excel or a statistics package. You can do all of question 2. using Excel or a statistics package except where noted. It is suggested that you ALSO compute the regression coefficients for the simple linear regression and the intercept-less regression by hand.

1. Data have been compiled over time on hunter success (quail bagged per hunt) in two reserves located in southeastern Arizona:

        Oracle Junction             Pinnacle Peak
        ---------------             -------------
1958         3.81                        3.53
1959         2.70                        2.37
1960         6.40                        4.74
1961         2.57                        1.80
1962         6.09                        3.83
1963         4.84                        2.70
1964         2.91                        2.60

Summarize the data from each reserve (separately) by computing an average, standard deviation, and coefficient of variation. Compute a 90% confidence interval for mean hunter success for each reserve.

If a "hunting party" is defined to be TWO HUNTERS, estimate mean quail/trip and a standard error for Oracle Junction "hunting parties."

2. Data were compiled on recreational use (visitor hours) for a park during certain days in July and August. Electronic traffic counters are in place at all entrances to the park. It is hoped that a relationship can be established between visitor hours and counter reading so that visitor hours can be indirectly predicted for other days during the season.

Observation           Visitor Hours         Traffic Counter Reading
-----------           -------------         -----------------------
      1                     269                      129
      2                     215                      122
      3                     456                      192
      4                     304                      253
      5                     664                      442
      6                     638                      186
      7                    2758                     1440
      8                     756                      534
      9                     304                      311
     10                     307                      491
     11                     374                      423
     12                     106                      201
     13                     364                      311
     14                    1320                      904
     15                     710                      497
     16                    1876                     1155

Estimate the simple linear regression (intercept and slope estimates) of visitor hours on traffic counter reading. Compute the correlation coefficient and standard error about the regression. Construct a residual plot of "studentized residuals" versus predicted values. What is the best estimate of visitor hours given a traffic counter reading of 350 (do this by hand)?

Estimate the regression equation assuming an intercept of zero. How different is the visitor hour estimate using this equation for a counter reading of 350 (do this by hand)? Which is the best estimate? Why?