Question

3.

(5.15) Manatees are large, gentle, slow-moving creatures found along the coast of Florida. Many manatees are injured or killed by boats. below contains data on the number of boats registered in Florida (in thousands) and the number of manatees killed by boats for the years between 1977 and 2013. (data are distorted):

YEAR	BOATS	MANATEES	YEAR	BOATS	MANATEES	YEAR	BOATS	MANATEES
1977	446	12	1989	712	50	2001	943	81
1978	458	22	1990	718	46	2002	964	95
1979	481	24	1991	683	53	2003	978	72
1980	497	15	1992	680	37	2004	982	70
1981	511	24	1993	677	36	2005	1010	79
1982	512	21	1994	697	48	2006	1025	91
1983	526	16	1995	711	42	2007	1029	73
1984	557	34	1996	732	60	2008	1010	90
1985	586	32	1997	753	54	2009	984	96
1986	615	33	1998	810	65	2010	942	84
1987	647	39	1999	830	81	2011	923	87
1988	674	44	2000	879	77	2012	904	82	2013	917	71

(a) Find the correlation rr (±±0.001)

rr =

(b) Find the equation of the least-squares line (±±0.001) for predicting manatees killed from thousands of boats registered.

yˆy^ = +xx

(c) What would you predict (±±0.1) number of manatees killed by boats to be if there are 900,000 boats registered?

(d) Predict (±±0.1) manatee deaths if there were no boats registered in Florida.

Answer 1

a)

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.955

b)

Least square line equation: ŷ = -44.145 + 0.131*x

c)

predicted value =-44.145 + 0.131*900 = 73.8

d)

predicted value = -44.1 , which is ot meaningful since 0 boats falls outside the scope of this model