Year Boats Kills 1977 447 13 1978 460 21 1979 481 24 1980 49

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:

Solution

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]