(5.15) Manatees are large, gentle, slow-moving creatures found along the coast o
ID: 3065075 • Letter: #
Question
(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):
(a) Find the correlation rr (±0.001)
r = ____
(b) Find the equation of the least-squares line (±0.001) for predicting manatees killed from thousands of boats registered.
yˆ = ____+____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. ____
YEAR BOATS MANATEES YEAR BOATS MANATEES YEAR BOATS MANATEES 1977 448 13 1989 709 51 2001 946 82 1978 459 21 1990 721 46 2002 960 95 1979 481 23 1991 680 53 2003 980 74 1980 500 16 1992 679 38 2004 982 70 1981 513 25 1993 678 35 2005 1011 79 1982 511 20 1994 697 48 2006 1025 92 1983 525 15 1995 712 41 2007 1025 73 1984 558 34 1996 732 60 2008 1009 90 1985 585 33 1997 755 53 2009 982 97 1986 615 33 1998 810 67 2010 943 83 1987 647 40 1999 830 82 2011 921 89 1988 677 42 2000 880 78 2012 902 80 2013 914 70Explanation / Answer
By using MINITAB
MTB > Regress;
SUBC> Response 'MANATEES';
SUBC> Nodefault;
SUBC> Continuous 'BOATS';
SUBC> Terms BOATS;
SUBC> Constant;
SUBC> Unstandardized;
SUBC> Tmethod;
SUBC> Tsummary;
SUBC> Tcoefficients;
SUBC> Tequation.
Regression Analysis: MANATEES versus BOATS
Model Summary
S R-sq R-sq(adj) R-sq(pred)
7.99931 90.83% 90.57% 89.69%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -45.00 5.54 -8.13 0.000
BOATS 0.13235 0.00711 18.62 0.000 1.00
Regression Equation
MANATEES = -45.00 + 0.13235 BOATS
a] correlation r = sqrt(R)
= sqrt( 0.9083)
Correlation (r) = 0.9530
b] The equation of the least-squares line (±0.001) for predicting manatees killed from thousands of boats registered,
y hat = -45.00 + 0.13235 X
c] x= 900,000
y hat = -45.00 + 0.13235 X
y hat = -45.00 + 0.13235 * 900
yhat = 74.115
d] no boat = X =0
y hat = -45.00 + 0.13235 x
y hat = -45.00 + 0.13235 * 0
y hat = -45.00
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