Question

Manatees are large, gentle sea creatures that live along the Florida coast. Many manateesare killed or injured by powerboats. Here are data on powerboat registrations (in thousands) and the number of manatees killed by boats in Florida in the years 1985-1990.

Powerboat Registrations (in 1000's)(X)	Manatees Killed by Powerboats(Y)
150	13
200	19
225	23
300	28
330	34

a)Make a well-labeled scatterplot of the powerboat and manatee data.

b)Write the regression equation that will predict the number of manatees killed given the number of powerboat registrations. To earn any credit, show all work for slope(b1)and y-intercept(b0),rounding calculations to 4-decimal places,if necessary.

c)Using the regression equation, predict the number of manatees thatwill be killed when there are 250 thousand powerboats registered.

Answer 1

(a) The scatter plot is shown below:

(b) Y = b₀ + b₁ X

We have

and

Following results are obtained:

	X	Y	X2	XY
	150	13	22500	1950
	200	19	40000	3800
	225	23	50625	5175
	300	28	90000	8400
	330	34	108900	11220
SUM	1205	117	312025	30545
Sxx	21620
Sxy	2348

The regression equation is Y = -2.7734 + 0.1086 X

(c) X = 250. Y = -2.7734 + 0.1086 * 250 = 24.38