Question: Manatees are large sea creatures that live in the shallow water along the coast of Florida. Many manatees are injured or killed each year by powerboats. Here are the data on manatees killed and powerboat registration (in thousands of boats) in Florida for the period 1984 to 1990.

a. Complete the table.

b. Using the table, find the following values: .

\[\bar{X},\bar{Y},{{S}_{XX}},{{S}_{YY}},{{S}_{XY}}\]

c. Using find the regression equation \(b=\frac{{{S}_{XY}}}{{{S}_{XX}}}\) and \({{b}_{0}}=\bar{Y}-{{b}_{1}}\bar{X}\) find the regression equation \(\hat{y}={{b}_{0}}+{{b}_{1}}x\).

d. What is the coefficient of determination \({{r}^{2}}\) ?

e. If Florida were to limit powerboat registration to a maximum of 700,000 boats (x = 700) how many manatees could we expect to be killed?