Manatees are large, gentle, slow-moving creatures found along the coast of Flori

Question

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 445 12 1989 712 51 2001 943 82 1978 461 21 1990 717 46 2002 963 95 1979 481 23 1991 679 52 2003 979 74 1980 498 15 1992 678 37 2004 983 68 1981 511 23 1993 679 35 2005 1009 79 1982 514 20 1994 698 49 2006 1025 92 1983 526 15 1995 711 42 2007 1029 74 1984 561 34 1996 732 59 2008 1009 91 1985 586 34 1997 755 53 2009 983 97 1986 612 34 1998 809 66 2010 943 83 1987 647 40 1999 831 82 2011 920 88 1988 674 42 2000 879 77 2012 902 81 2013 915 72 (a) Find the correlation r r (± ± 0.001) r r = (b) Find the equation of the least-squares line (± ± 0.001) for predicting manatees killed from thousands of boats registered. yˆ y^ = +x x (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.

Explanation / Answer

a.

Step 1: Find XY , X2 and Y2 as it was done in the table below.

Step 2: Find the sum of every column to get:

X=27999 , Y=2038 , XY=1711009 , X2=22456249 , Y2=136902

Step 3: Use the following formula to work out the correlation coefficient.

r = nXYXY/sqrt[nX2(X)2][nY2(Y)2]= 371711009279992038/sqrt[3722456249279992][3713690220382]=0.9546

b.

Step 1: Find XY and X2 as it was done in the table below.

Step 2: Find the sum of every column:

X=27999 , Y=2038 , XY=1711009 , X2=22456249

Step 3: Use the following equations to find a and b:

a=YX2XXY/nX2(X)2=203822456249279991711009/372245624927999245.608

b=nXYXY/nX2(X)2=371711009279992038/3722456249(27999)20.133

Step 4: Substitute a and b in regression equation formula

y = a + bx= 45.608 + 0.133x

c. x=900,000 y=119654.392

d. for x=0, y=-45.608

X Y XY XX YY   445 12 5340 198025 144 712 51 36312 506944 2601 943 82 77326 889249 6724 461 21 9681 212521 441 717 46 32982 514089 2116 963 95 91485 927369 9025 481 23 11063 231361 529 679 52 35308 461041 2704 979 74 72446 958441 5476 498 15 7470 248004 225 678 37 25086 459684 1369 983 68 66844 966289 4624 511 23 11753 261121 529 679 35 23765 461041 1225 1009 79 79711 1018081 6241 514 20 10280 264196 400 698 49 34202 487204 2401 1025 92 94300 1050625 8464 526 15 7890 276676 225 711 42 29862 505521 1764 1029 74 76146 1058841 5476 561 34 19074 314721 1156 732 59 43188 535824 3481 1009 91 91819 1018081 8281 586 34 19924 343396 1156 755 53 40015 570025 2809 983 97 95351 966289 9409 612 34 20808 374544 1156 809 66 53394 654481 4356 943 83 78269 889249 6889 647 40 25880 418609 1600 831 82 68142 690561 6724 920 88 80960 846400 7744 674 42 28308 454276 1764 879 77 67683 772641 5929 902 81 73062 813604 6561 915 72 65880 837225 5184

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