Year Boats Kills 1977 447 13 1978 460 21 1979 481 24 1980 498 16 1981 513 24 198
ID: 3440316 • Letter: Y
Question
Year Boats Kills
1977 447 13
1978 460 21
1979 481 24
1980 498 16
1981 513 24
1982 512 20
1983 526 15
1984 559 34
1985 585 33
1986 614 33
1987 645 39
1988 675 43
1989 711 50
1990 719 47
1991 681 53
1992 679 38
1993 678 35
1994 696 49
1995 713 42
1996 732 60
1997 755 54
1998 809 66
1999 830 82
2000 880 78
2001 944 81
2002 962 95
2003 978 73
2004 983 69
2005 1010 79
2006 1024 92
2007 1027 73
2008 1010 90
2009 982 97
The correlation is r = 0.951.
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 33 years.
Choose the correct answer below:
? = ?43.17 + 0.129x
? = ?50.15 + 0.1412x
? = ?70.28 + 0.3120x
? = ?25.27 + 0.2378x
Step 2:
In 2009, experts predicted that the number of boats registered in Florida would be 975,000 in 2010.
Predict the number of manatees killed by boats in 2010.
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. Your selections:
Table 4.1 gives 33 years of data on boats registered in Florida and manatees killed by boats.
Data Set
Year Boats Kills
1977 447 13
1978 460 21
1979 481 24
1980 498 16
1981 513 24
1982 512 20
1983 526 15
1984 559 34
1985 585 33
1986 614 33
1987 645 39
1988 675 43
1989 711 50
1990 719 47
1991 681 53
1992 679 38
1993 678 35
1994 696 49
1995 713 42
1996 732 60
1997 755 54
1998 809 66
1999 830 82
2000 880 78
2001 944 81
2002 962 95
2003 978 73
2004 983 69
2005 1010 79
2006 1024 92
2007 1027 73
2008 1010 90
2009 982 97
Figure 4.2 (page 103) shows a strong positive linear relationship.
The correlation is r = 0.951.
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 33 years.
Choose the correct answer below:
? = ?43.17 + 0.129x
? = ?50.15 + 0.1412x
? = ?70.28 + 0.3120x
? = ?25.27 + 0.2378x
Step 2:
In 2009, experts predicted that the number of boats registered in Florida would be 975,000 in 2010.
Predict the number of manatees killed by boats in 2010.
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. Your selections:
Explanation / Answer
1.
Using technology, we get
slope = 0.129208185
intercept = -43.17757221
Thus, the regression line is
y^ = 0.129208185 x - 43.17757221 [OPTION A, ANSWER]
*********************
2.
Thus, if x = 975
Then
y^ = 82.8004078 = 83 [answer]
******************
3.
The prediction is reliable because of the strong linear association visible in the scatterplot. [OPTION B]
r2 is very close to 1, thus ensuring a high prediction accuracy. [OPTION D]
Thus, there are two answers, B and D.
**************
4.
If x = 0,
y^ = - 43.17757221 = -43.18 [ANSWER]
***************
5.
The answers are option A and C.
Because x = 0 is far outside the range of values of the explanatory variable. [OPTION A]
Because a negative number of deaths makes no sense. [option c]
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