Question

QUESTION 1:

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	449	13	1989	710	50	2001	943	81
1978	460	22	1990	720	47	2002	962	95
1979	480	23	1991	683	54	2003	980	74
1980	499	16	1992	680	38	2004	982	69
1981	513	24	1993	680	34	2005	1011	78
1982	513	21	1994	697	49	2006	1023	92
1983	527	15	1995	713	43	2007	1025	73
1984	558	34	1996	731	60	2008	1012	90
1985	583	32	1997	755	55	2009	984	98
1986	615	34	1998	807	66	2010	943	83
1987	643	39	1999	828	83	2011	921	88
1988	674	43	2000	880	79	2012	904	82	2013	913	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.

QUESTION 2:

An online article suggested that for each additional person who took up regular running for exercise, the number of cigarettes smoked daily would decrease by 0.174.
If we assume that 46 million cigarettes would be smoked per day if nobody ran, what is the equation of the regression line for predicting number of cigarettes smoked per day from the
number of people who regularly run for exercise?

Denote (new runners) as xx. Do not include commas in your answer.

Answer 1

1 A)The correlation coefficient is r = 0.95

B)By method of least sqaures,the regression line is given as y^= - 45.209 + 0.133x

C)Number of manatees killed by boats when 900,000 boats were registered is -45.209+0.133(900)=74 (app.)

D)Number of manatees killed by boats when 0 boats were registered is -45.209 which makes no sense.

2)The regression line is of the form Y=a+bX

Here Y is the number of cigarettes to be smoked and X is the number of runners

a= 46,000,000 and b = -0.174

Therefore the regression line is given as Y= 46000000 - 0.174 X