Quiz #5 STA2023
Regression Line and Correlation
Name________________________
Times/Days attend class________________________
Date________________________
Provide all of your answers/explanations/work in the spaces provided. However,
you may attach additional work if you want to. Don’t put down just answers, i.e.
Show all work for full credit! There are two printed pages to this quiz.
1. Many manatees are killed or
injured by motorboats. Part of
this table gives data on powerboat
registrations (in thousands) and
the number of manatees killed by
boats in Florida in the years 1977
to 1991.
Make a scatterplot of these data
with powerboat registrations as
the explanatory variable and the
number of manatee deaths as the
response variable (you do not
have to turn in the scatterplot).
a.
Year Boats Manatees
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
716
53
Fuel
21.00
13.00
10.00
8.00
7.00
5.90
6.30
6.95
7.57
8.27
9.03
9.87
10.79
11.77
12.83
Speed
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
(5 pts.) State and interpret the association for this scatterplot.
b. (3 pts.) What percent of the variation in manatee
deaths can be explained by the number of power
boats registered? Show what made you decide.
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c.
(4 pts.) Write down the least squares regression line.
d. (4 pts.) Predict the number of manatees that will be killed by boats in a year when
716,000 powerboats are registered (round your final answer to the nearest integer,
including the appropriate unit of measure).
e.
(6 pts.) State the value of the slope of the regression line:_________. Interpret
the slope with regards to the story problem situation. Remember to use units of
measure in your answer.
2. (3 pts.) Note the Fuel and Speed lists from the table on page 1. This is data for a
British Ford Escort. Speed is measured in kilometers per hour and fuel consumption
is measured in liters of gasoline used per 100 kilometers traveled. Eric Lang is a
statistician that wonders how fuel consumption changes as speed increases. As a part
of his research he calculates the correlation value for Fuel versus Speed and
concludes from its value that Fuel and Speed share a weak linear relationship. Why is
it wrong for Eric Lang to use the correlation number in this situation?
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