EBD - Manatee Deaths Investigation Task

*You will be asked to create several graphs in this investigation.  You can do so by hand on paper or you can use a computer-generated graph.  For example, if you would like to create a scatter plot, you can do a search online, "scatter plot generator."  You will find many sites that will make scatters plots with your data.

The following table gives data on powerboat registrations (in thousands) and the number of manatees killed by boats in Florida in the years 1977 to 1990.

Manatees are passive, slow-moving animals. Most of their time is spent eating, resting, and traveling. They are often shy and reclusive.

1a.  What are you interested in modeling?

1b. Make a scatter plot of your data. Describe the form and direction of the relationship. Is there a linear pattern? Do you see any unusual observations or outliers, if so, list them ?

1c. Explain, in general, what an influential observation is, include a sketch.  Explain how you can check if an observation is influential?

2a. Fit the least squares regression line to your data.  You may use your calculator. Give the equation of your line, round answer to 3 decimal places. Be sure to label your variables.

2b. Explain what the criterion is that is used to find the equation of Least Squares Regression Line. (LSRL).

2c. Explain what the slope of your equation tells you about the change in Manatees killed with respect to the change in number of boats. Give units of the slope.

3a. Use your equation to predict the number of manatee deaths if the number of boats is 585,000. Compute the error you made by using the equation. Did you overestimate or underestimate by using your equation?

3b. Use your equation to predict the number of manatee deaths if the number of boats is 950,000. Clearly explain why this may not be a reasonable prediction.

4a. Compute correlation coefficient r (use calculator). Round answer to 3 decimal places. Explain what r tells about the strength of linear relationship between the number of boats (in thousands) and number of manatee deaths.

4b. Determine the percentage of variation in the number of manatee deaths that is explained by the regression line you found in (2a)? Round answer to 3 decimal places.  Does it mean that the regression line fits well? Explain.

Submit when completed.