Bald Eagles and DDT

(Adapted from Mooney and Swift, A Course In Mathematical Modeling.)

Background

The pesticide DDT was used for many years until it was determined to be responsible for a decline in many raptor populations including eagles and falcons. It was believed that DDT softened the shells of bird eggs which resulted in a lowering of the reproduction rate. DDT was eventually banned on December 31, 1972. The birthrate of the eagle population in northwestern Ontario has been measured annually since 1966. In this project, you will examine the data collected between 1966 and 1981 to determine whether DDT (and banning it) had any effect on the bald eagle population.

Data

The data in the table below is taken from [J. Grier, "Ban of DDT and Subsequent Recovery of Reproduction in Bald Eagles", Science, Vol. 218, Issue 4578, December 17, 1982, pp. 1232-1235]. For each year, the table gives the average number of bald eagle young per breeding area (essentially, per nest).

Year	Young per breeding area
1966	1.26
1967	0.73
1968	0.89
1969	0.84
1970	0.54
1971	0.60
1972	0.54
1973	0.78
1974	0.46
1975	0.77
1976	0.86
1977	0.96
1978	0.82
1979	0.98
1980	1.12
1981	0.82

Problems

1. Plot this data.

2. Compute two regression lines: one for the years up to (and including) 1972, and one for the years from 1973 on. Graph these two lines with your data, on the plot from question 1. What do the slopes of the lines mean?

3. Discuss how well the regression lines fit the data, using r and r². Plot the residuals, and discuss what these plots tell you about the linear models.

4. Using your results, write a paragraph or two on the effect of banning DDT on eagle reproduction. These should be complete, coherent, grammatically correct paragraphs.

You may do this project as a group of up to 4 people, and turn in one report for the entire group. Each member of the group will receive the same grade.

Graded out of 30 points