Manatees are large sea creatures that live in the shallow wa

Manatees are large sea creatures that live in the shallow water alone 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. Only calculators can be used no minitab or any other software.

1984 559 34 312481 1156 19006
1985 585 33 342225 1089 19305
1986 614 33 376996 1089 20262
1987 645 39 416025 1521 25155
1988 675 43 455625 1849 29025
1989 711 50 505521 2500 35550
1990 719 47 516961 2209 33793

SUMS 4508 279 2925834 11413 182096

a. Find values x , y, Sxx, Syy, and Sxy.

b. Using b1 = Sxy and b0 = y- b1x find the regression equation yˆ =b0 + b1x.

c. What is the coefficient of determination, r2?

I have answered a and b but need help solving question c. I know the answer but I need to know how to solve the problem using a formula. for the coefficient of determination

by answer is not matching the correct answer. which is 0.881645

Solution

Sxx = 22682

Syy = 292.857143

Sxy = 2420

r. = Sxy/ (Sxx * Syy)

= 2420/ ( 22682 * 292.857143)

= 0.881645