Data Set
Figure 4.2 (page 108) shows a strong positive linear relationship.

The correlation is r = 0.954.

Step 1:
Find the equation of the least-squares line for predicting manatees killed from thousands of boats registered.
Because the linear pattern is so strong, we expect predictions from this line to be quite accurate - but only if conditions in Florida remain similar to those of the past 37 years.
Choose the correct answer below:

? = ?44.83 + 0.1323x

? = ?50.15 + 0.1412x

? = ?25.27 + 0.2378x

? = ?70.28 + 0.3120x

Step 2:
Experts predict that the number of boats registered in Florida will be 890,000 in 2014.
Predict the number of manatees killed by boats in 2014.
Round your answer to a whole number.

Step 3:
Explain why we can trust this prediction.

The prediction is not reliable because the regression line explains 95.3% of the variations in y.

The prediction is reliable because of the strong linear association visible in the scatterplot.

The regression line always gives a good prediction.

r² is very close to 1, thus ensuring a high prediction accuracy.

Enter the number(s) of the choice(s) you wish to select. Separate multiple selections with commas or semicolons. Your selections:

Step 4:
Predict manatee deaths if there were no boats registered in Florida.
Use the prediction equation in Step 1 of this question and give your answer to 2 decimal places.

Step 5:
Explain why the predicted count of deaths is impossible.
(We use x = 0 to find the intercept of the regression line, but unless the explanatory variable x actually takes values near 0, prediction for x = 0 is an example of extrapolation.)
Choose the correct answer below:

Because x = 0 is far outside the range of values of the explanatory variable.

Because usually, the intercept is a non-accurate prediction.

Because a negative number of deaths makes no sense.

Enter the number(s) of the choice(s) you wish to select. Separate multiple selections with commas or semicolons.
 

Transcribed Image Text:

TABLE 4.1 YEAR 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 BOATS 447 460 481 498 513 512 526 559 585 614 645 675 711 FLORIDA BOAT REGISTRATIONS (THOUSANDS) AND MANATEES KILLED BY BOATS MANATEES 13 21 24 16 24 20 15 34 33 33 39 43 50 YEAR 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 BOATS 719 681 679 678 696 713 732 755 809 830 880 944 962 MANATEES YEAR 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 47 53 38 35 49 42 60 54 66 82 78 81 95 BOATS 978 983 1010 1024 1027 1010 982 942 922 902 897 MANATEES 73 69 79 92 73 90 97 83 88 81 72 TABLE 4.1 YEAR 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 BOATS 447 460 481 498 513 512 526 559 585 614 645 675 711 FLORIDA BOAT REGISTRATIONS (THOUSANDS) AND MANATEES KILLED BY BOATS MANATEES 13 21 24 16 24 20 15 34 33 33 39 43 50 YEAR 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 BOATS 719 681 679 678 696 713 732 755 809 830 880 944 962 MANATEES YEAR 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 47 53 38 35 49 42 60 54 66 82 78 81 95 BOATS 978 983 1010 1024 1027 1010 982 942 922 902 897 MANATEES 73 69 79 92 73 90 97 83 88 81 72

Answer rating: 100% (QA)

Step 1 The regression equation is defined as y b bx Here b x xy i1 12 x x i1 From the data the regre... View the full answer