For questions 13 and 14, use the data table below
Year
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
Temp
8
19
26
4
25
9
4
12
27
31
CO2
336.67
338.57
339.92
341.30
342.71
344.24
345.81
347.11
348.72
351.04
Year
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
Temp
19
36
35
13
13
23
37
29
39
56
31
CO2
352.68
353.97
355.37
356.18
356.69
358.14
360.02
361.95
363.18
365.19
367.86
Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Temp
33
47
56
55
48
63
55
58
44
57
63
CO2
368.83
370.43
372.01
374.45
376.77
378.30
380.83
382.56
384.39
386.34
388.13
The temperature data is called the Global Land-Ocean Temperature Index and is in units of 1/100 of a degree Celsius above the
1950 – 1980 average temperature. For example, in 1979, the 8 means that the temperature that year was 0.08 degrees Celsius above
the average temperature between 1950 and 1980. The Carbon Dioxide data is in ppm (parts per million) which refers to the
concentration of carbon dioxide in the atmosphere. These levels are measured at the Mauna Loa Observatory in Hawaii. Any
concentration higher than 350 ppm is considered unsafe.
13. Using the year and temperature data,
a. Determine which would be the independent and dependent variables.
b. Using a full sheet of graph paper, plot the data on a scatterplot. Be sure to scale and label correctly.
c. What might one reason be for providing the temperature in this manner, rather than simply stating it?
d. What do you notice from the graph?
14. Using the temperature and CO2 data,
a. Determine which would be the independent and dependent variables.
b. Using a full sheet of graph paper, plot the data on a scatterplot. Be sure to scale and label correctly.
c. What do you notice from the graph?
d. How might your graph look different if your y-axis was scaled from 300 to 400 compared to 0 to 400?
5. Find the equation of the line that has a slope of 4 and passes through the point (6, 2).
6. Find the equation of the line that passes through the points (2, -4) and (-6, 20).
7. Find the equation of the line that passes through the points (-8, -3) and (20, -10).
8. Find the equation of the vertical line that passes through the point (3, -5).
9. Find the equation of the horizontal line that passes through the point (8, -2).
10. Explain how you can easily remember the form of the equation of a vertical line and a horizontal line.
11. Find the slope of the line that is perpendicular to the line in question 5 and then use that slope to find
the equation of the line that is perpendicular to the line in question 5 that passes through the point (6, - 2).
12. Write out in your own words the necessary steps to finding the equation of a line through two points.
19. Sam collected data by measuring the pencils of her
classmates. She recorded the length of the painted part of
each pencil and its weight. Her data is shown on the graph
at the right.
a. Describe the association between weight and length of the
pencil. Remember to describe the form, direction, strength,
and outliers in context.
b. Make a conjecture (a guess) about why Sam’s data had an
outlier.
c. What would the units of slope be?
22. Factor 10x2 + x + 3
31. Battle Creek Cereal is trying a variety of packaging sizes for their Crispy Puffs cereal. Below is a list
of six current packages.
Packaging Cardboard (in2) Net Weight of Cereal (g)
34
21
150
198
218
283
325
567
357
680
471
1020
a. Write a few sentences to the executives of Battle Creek Cereal that describe the association.
b. Find an equation the executives can use to predict the net weight of cereal based on the amount of
cardboard used for the package.
c. Tell the executives how much cereal a new experimental “green” package that uses 260 in2 of
cardboard is expected to hold. Use your equation from part b.
32. If it is measured that the 260 in2 box from will actually hold 355 g of cereal,
a. Determine the residual for this box.
b. What does a positive residual tell you in the context of this problem?
c. What does a negative residual tell you in the context of this problem?
d. If you graph both the actual and predicted data point, visually what will the residual represent. Color
this residual in a different color on your graph.
33. What is the residual for the 471 in2 box? Mark the residual on your scatterplot. Be sure to include
units for your residual.
34. The warehouse store wants to offer a super-sized 600 in2 box.
a. The residual for this box is 1005 grams. What is the actual weight of a 600 in2 box?
b. Why do you suppose the residual is so large?
c. Interpret the meaning of the slope and y-intercept of your model in the context of this problem. Does
the y-intercept make sense in the context of the problem?
21. The graph below shows the areas and populations of some of the states of the U. S. A. Use it to
answer the following questions.
a. Estimate the coordinates of the point that represents the state with the highest population.
b. Estimate the coordinates of the point that represents the state with the lowest population of people per
square mile. This value of the number of people per square mile is called the population density.
c. Describe the association.
d. Draw an X on the graph to show the data for Michigan, with an area of 56,802 square miles and a
population of 9,295,277 people.
e. Calculate the number of people per square miles in Michigan, giving your answer to the nearest whole
number.
f. The average number of people per square mile for the U.S. A. is 70, though no state actually has exactly
this population density. Draw a straight line on the graph to show all the possible positions of points
showing 70 people per square mile.
g. The average state area is 68,000 square miles, though no state has exactly this area. If a state with the
average area had the average population density, what would its population be?
h. The data in this graph is for the year 1990. Since then, what data will have stayed the same and what
data may have changed and how would this change the graph?
23. Simplify (2xy2)3
24. Find the vertex of the parabola by completing the square y = x2 + 8x – 3
25. Given f(x) = -x2 + 2x + 3, find f(-1) and f(x) = 0
36. Armen was concerned about the amount of sugar in his diet, so he went to the store and collected data
from several cereal boxes. Armen used the data to create a model that related the sugar in cereal to
calories:
s = –16.9 + 0.23c
where s is the amount of sugar in grams and c is the number of calories in one cup of cereal.
a. What does a negative residual mean in this context? Is a cereal with a positive or negative residual
better for Armen’s diet?
b. Interpret the meaning of the slope and y-intercept in the context of the problem. Does the y-intercept
make sense in the context of the problem?
37. Remember Sam who collected data by measuring the pencils of her classmates? She recorded the
length of the painted part of each pencil and its weight. Her
data is shown on the graph at right.
a. Sam created a line of best fit: w = 1.4 + 0.25l where w is
the weight of the pencil in grams and l is the length of the
paint on the pencil in centimeters. What does the slope
represent in this context?
b. Sam’s teacher has a pencil with 11.5 cm of paint. Predict
the weight of the teacher’s pencil.
c. Interpret the meaning of the y-intercept in context.
d. Would you estimate that a pencil that is approximately 11 cm long would have a positive residual or a
negative residual. Justify your answer.
39. Find the equation of the parabola that has a vertex of (3, -4) and passes through the point (5, -12) and
then use that equation to find the y-intercept.
60. The following table shows data for one season of the El Toro professional basketball team. El Toro
team member Antonio Kusoc was inadvertently left off of the list. Antonio Kusoc played for 2103
minutes. We would like to predict how many points he scored in the season.
Player Name
Minutes Played
Total Points Scored
in a Season
Sordan, Scottie
3090
2491
Lippen, Mike
2825
1496
Karper, Don
1886
594
Shortley, Luc
1641
564
Gerr, Bill
1919
688
Jodman, Dennis
2088
351
Kennington, Steve
1065
376
Bailey, John
7
5
Bookler, Jack
740
278
Dimkins, Rickie
685
216
Edwards, Jason
274
98
Gaffey, James
545
182
Black, Sandy
671
185
Talley, Dan
191
36
checksum 17627
checksum 7560
a. Draw a line of best fit for the data and then use it to
write an equation that models the relationship between
total points in the season and minutes played.
b. Which data point is an outlier for this data? Whose
data does that point represent? What is his residual?
c. Would a player be more proud of a negative or
positive residual?
d. Predict how many points Antonio Kusoc made.
LSRL: _________________________
80. Giulia’s father would like to open a restaurant, and is deciding how much to charge for the toppings
on pizza. He sent Giulia to eight different Italian restaurants around town to find out how much they each
charge. Giulia returned with the following information:
Paolo’s Pizza
Vittore’s Italian
Ristorante Isabella
Bianca’s Place
JohnBoy’s Pizza
Delivery
Ristorante Raffaello
Rosa’s Restaurant
House of Pizza Pie
# Toppings on Pizza
(not including
cheese)
1
3
4
6
3
Cost ($)
5
0
2
16.50
8.00
9.00
10.50
9.00
14.00
15.00
12.50
a. Giulia needs to write an analysis for her father about what he should charge for a two-topping pizza.
Discuss with your team what elements a statistical analysis report should contain.
b. Write the analysis you described in part (a), and predict what Giulia’s father should charge for a twotopping pizza.
81. A residual plot can help you determine if a linear model is a good fit for a scatterplot of data.
Whenever a LSRL line is drawn on a scatterplot, a residual plot can also be created. A residual plot has an
x-axis that is the same as the scatterplot, and a y-axis that plots the residual at that x-value.
a. Match each scatterplot to its corresponding residual plot.
b. For which of the scatterplots does a linear model fit the data best?
c. How does the residual plot help you make that decision?
53. Coach Romero is going to hold tryouts for the football team. Since timing students in the 100 m dash
is time-consuming and inconvenient, he wondered if he could predict 100 m dash times from the number
of push-ups a student can do. He went to the records from previous physical fitness exams and randomly
chose a sample of students.
Push- Ups
4
27
44
22
38
12
15
35
100 m
Dash (sec)
11.7
17.4
16.4
17.3
12.3
14.7
13.7
16.5
Push- Ups
25
3
26
44
14
22
28
35
100 m
Dash (sec)
11.1
15.0
17.2
11.6
17.5
14.5
14.1
12.2
a. Make a scatterplot of this data using a full sheet of paper, be sure to think about which is the
independent variable and which is the dependent variable.
b. Describe the association between 100 m dash times and number of push-ups.
c. Would you use this model to predict 100 m dash times? Why or why not?
d. Draw in a best fit line and find its Least Squares Regression Line.
e. Interpret the slope in context.
f. Calculate the residual for a person who can do 15 push-ups.
67. Charlie’s friend is visiting from Texas and asks him, “What does a hamburger cost in this town?” This
caused Charlie to wonder because the price of a hamburger seems to be different at every eatery. Charlie
thinks there may be an association between the amount of meat in the patty and the cost of the hamburger.
He collected the following data.
a. Interpret the slope and y-intercept in context. Does the y-intercept make sense in this situation?
b. What is the residual for the hamburger with the 3 ounce patty? What does it mean in context?
c. Charlie’s friend says that in his hometown he cam buy a 1 pound hamburger for $14.70. Would this
be a reasonable price in Charlie’s town? Show how you know.
69. Solve the system
a + 4b = 10
3a – 4b = 6
70. Given f(x) = -5x – 4 and g(x) = -x2 + 4x find the following:
g(-5)
f(x) = -4
g(x) = 0
71. Given f(x) = x2 – 2x – 24, algebraically find:
x-intercepts
y-intercept
g(x) – f(x)
vertex
77. Solve: 3(x –
78. Find an exponential function in form that passes through the points (2, 20) and (7, 640).
79. Find the domain of y = 3(x – 1)2 + 4
98. The following scatterplots have correlation r = -0.9, r = -0.6, r = 0.1, and r = 0.6.
Match each scatterplot to one of the correlation coefficients, r, given.
99. Although the correlation coefficient tells us about the strength of a linear relationship, it does not tell
us if the relationship is linear in the first place. It is important to ALWAYS look at the scatterplot and
residual plot, in addition to calculating the correlation. In order to see why we cannot simply use the
correlation coefficient to determine how appropriate a linear model is, we will do a small investigation.
Below are four data sets. Each member of your team should select a different data set and do the
following:
a. For your data set, without making a scatterplot, find the
correlation and the LSRL. Share your results with your team
and record this information for all four data sets on your
paper.
b. Describe what you notice.
c. Use the regression line to predict y for x = 10.
Data Set A
x
y
10
8.04
8
6.95
13
7.58
9
8.81
11
8.33
14
9.96
6
7.24
4
4.26
12 10.84
7
4.82
5
5.68
Data Set B
x
y
10
9.14
8
8.14
13
8.74
9
8.77
11
9.26
14
8.10
6
6.13
4
3.10
12
9.13
7
7.26
5
4.74
Data Set C
x
y
10
7.46
8
6.77
13 12.74
9
7.11
11
7.81
14
8.84
6
6.08
4
5.39
12
8.15
7
6.42
5
5.73
Data Set D
x
y
8
6.58
8
5.76
8
7.71
8
8.84
8
8.47
8
7.04
8
5.25
8
5.56
8
7.91
8
6.89
19 12.50
d. Make a scatterplot for each of the data sets and add the regression line to each plot. Sketch all four of
them on your paper.
e. In which of the four cases would you be willing to use the regression line to describe the dependence of
y on x? Explain your answer in EACH case.
100. At the beginning of the chapter, you completed the pirate problem. Robbie’s data is shown in the
table below.
Distance from wall (in)
Width of field of view (in)
144
132
120
108
96
84
72
60
Checksum 816
20.7
19.6
17.3
16.2
14.8
13.1
11.4
9.3
Checksum 122.4
a. Find the correlation coefficient. Is the association strong or weak?
b. Describe the form, direction, strength, and outliers of the association.
c. You already know a graphical way to determine if the “form” is linear by looking at the residual plot
for the data. A mathematical description of “direction” is the slope. A mathematical description of
“strength” is the correlation coefficient. Describe the form, direction, and strength of the viewing tube
data in more mathematical terms than you did in part (b).
83. Dry ice (frozen carbon dioxide) evaporates at room temperature. Giulia’s father uses dry ice to keep
the glasses in the restaurant cold. Since dry ice evaporates in the restaurant cooler, Giulia was curious
how long a piece of dry ice would last. She collected the following data:
# hours after noon
Weight of dry ice (oz)
0
15.3
1
14.7
2
14.3
3
13.6
4
13.1
5
12.5
6
11.9
7
11.5
8
11.0
9
10.6
10
10.2
a. Sketch the scatterplot and calculate the LSRL of this data.
b. Use your calculator to make a residual plot to determine if a linear model is appropriate. Make a
conjecture about what the residual plot tells you about the shape of the original data Giulia collected.
86. Marissa heard from her summer science camp counselor that the temperature can be determined from
the number of cricket chirps. She emailed several of her relatives to ask them to stay up one night and
record the temperature and the number of cricket chirps per minute. She collected the following data:
Number of
79
200 218 145 156 184 49
211 70
200 100 98
137 checksu
Chirps per
m 1847
Minute
Temperature 54
71
85
65
91
77
66
81
78
90
65
74
79
checksu
(ºF)
m 976
a. Describe the association between number of cricket chirps and the temperature.
b. Interpret the slope.
c. After Marissa collected and analyzed the data, she counted 107 chirps per minute on a night that was
69º F. What was the residual for her data point?
93. Factor and use the zero product property to solve:
2x2 + 9x + 4 = 0
3x2 – 9x = 0
94. Find the equation of the exponential that passes through the points (2, 54) and (9, 118098) with an
asymptote at y = 0.
95. The price of a movie ticket averages $10.50 and is increasing 3% each year.
a. What is the multiplier in this situation?
b. Write a function that represents the cost of a movie ticket n years from now.
c. If tickets continue to increase at the same rate, what will they cost 10 years from now?
103. A team of college students in a Geography class were asked to determine if there is an association
between latitude and mean daily temperature of cities in the United States. Latitude is measured in
degrees, and indicates how far north of the equator the city is. The students gathered data from the
Internet and recorded the mean January temperatures of 142 large cities and each city’s latitude. The
scatterplot appeared to be reasonably linear, so the students created a least squares regression line.
a. Describe the association, including an interpretation of the slope and the correlation coefficient in
context.
b. A city with latitude of 40 degrees has a residual of 35 degrees. Should the city advertise that it is a
warmer than expected in winter, or that it is a winter wonderland of ice and snow because it is colder than
expected in winter?
c. What is the actual mean January temperature for the city in part (b)?
105. Does eating a small breakfast mean that you tend to overeat at dinner on the same day? The school
psychologist asked 13 students what they ate for breakfast and what they ate for dinner on the same day.
She recorded the calories eaten for each meal and did an analysis. Her data follows, where d is the dinner
calories, and b is the breakfast calories. Describe the association.
126. An outbreak of avian flu occurs in a crowded city. Doctors immediately identify 25 patients who are
infected. One week later, there are 2391 people infected.
a. Find the LSRL. How accurate is it? Explain why you did not really need to use the calculator to find it.
b. If we assume that the number of infected patients can be modeled with exponential growth, find the
equation for the exponential model. How accurate is it?
c. What assumption did you make when you made this exponential model. Justify the validity of this
assumption.
d. Use your models to predict the number of infected people after one month. How different are the
results?
e. What might be some downfalls of either of these models, in terms of the context of the problem?
f. What happens if you also know that after two weeks, there are 300,000 people infected? Are either of
your models a good predictor at this point? Which model is closer? Is it important to incorporate this third
piece of information into our model? Why or why not?
127. The CDC (Centers for Disease Control and Prevention) indicates that in the year 2000 there were
41,267 AIDS cases in the United States. In 2001 there were 40,833 cases. In 2002 there were 41,289
cases.
a. Why can you not find a perfect linear equation to model this data?
b. Why can you find a perfect quadratic equation to model this data?
c. Assuming that this data is quadratic, use what you learned in Algebra to find the quadratic equation that
models this data. Record the year as the number of years after 1980. For example, the first piece of data
would correspond to (20, 41267).
d. Use this model to estimate the number of AIDS cases in the United States in 2003.
e. If you then found out that in1999 there were 41,356 AIDS cases and in 2003 there were 43,171 AIDS
cases, calculate the residuals and determine how well your model worked.
f. If you were originally given all 5 data points, could you have found a perfect quadratic model?
118. When Giulia went around town comparing the cost of toppings at pizza parlors, she gathered this
data that you used in problem 80.
# Toppings on Pizza Cost ($)
(not including
cheese)
Paolo’s Pizza
1
10.50
Vittore’s Italian
3
9.00
Ristorante Isabella
4
14.00
Bianca’s Place
6
15.00
JohnBoy’s Pizza
Delivery
Ristorante Raffaello
Rosa’s Restaurant
House of Pizza Pie
3
12.50
5
0
2
16.50
8.00
9.00
a. What is the LSRL?
b. Interpret the y-intercept in context.
c. What is the correlation coefficient?
d. In a problem 77 you wrote a report describing this association. Now improve upon the report by
making it more mathematical. Use slope when describing the “direction” and use the correlation
coefficient when describing the “strength”.
120. A researcher wanted to see if there was an association between the number of hours spent watching
TV and students’ grade point averages. He found that r = -0.72. Interpret the results.
121. One endpoint of a line segment is (8, −1). The point (5, −2) is one-third of the way from that
endpoint to the other endpoint. Find the other endpoint.
122. Find an exponential function f of the form f(t) = a•bt whose graph goes through the ordered pairs
(2, 10) and (11, 23).
138. Enter the data from the following table into the calculator. Examine the scatterplot produced.
x
2
5
8
11
y
1
5.5
19
41.5
a. Sketch your scatter plot. Be sure to include the scale for each axis.
b. Describe how you determined the scale for the axis.
c. Find the exponential function from these data.
d. Graph this function over the scatterplot and add the curve to the graph above.
e. Find the quadratic function from these data.
f. Change your viewing window in the calculator to include negative values. Sketch the graph from the
calculator along with the points from the table above. Be sure to label the function.
g. Which is a better function for these data — an exponential or a quadratic function? Why?
h. How would including the point (-2, 0.25) affect which function you choose? Why?
i. How would including the point (-2, 9) affect which function you choose? Why?
139. Below are three tables.
Table A
x
y
1
1
6
36
11
121
16
256
21
441
Table B
x
1
6
11
16
21
y
3
18
33
48
63
Table C
x
1
6
11
16
21
y
3
27
243
2187
19683
a. Determine which table of values represents a linear function, which table represents a quadratic
function, and which table represents an exponential function. Show your work and explain the methods
you used.
b. Constant differences and ratios can be used to determine whether data fit a linear, quadratic, or
exponential function. You may have
• The ratio between consecutive y-values which is the next y-value divided by the current y-value.
• The difference between consecutive y-values which is the difference between the next y-value and the
current y-value.
• The difference between the differences between consecutive y-values. This is called the second
difference. For example, if 3 consecutive y-values are 4, 9, and 16, the differences between consecutive
pairs are 9 – 4 = 5 and 16 – 9 = 7. The second difference is 7 – 5 = 2.
Describe the relationship between the ratios, differences, and second differences and each function type.
c. When determining if a table of values represents a certain type of function, what is the minimum
number of data points needed? Explain.
d. Test your hypotheses from part b by creating a table of values for each of a linear, quadratic, and
exponential data set. Does your rule still work for the data set you created?
e. What would you expect the r to be for the linear function?
Explain why and verify your hypothesis.
140. Find the inverse of f(x) = 3(x – 5)2+ 4
142. Solve for x:
𝑥
a) 𝑡𝑎𝑛(24) = 34.627
c) 𝑐𝑜𝑠(𝑥) =
48º
b)
38
x
24
25
143. A ball is thrown and reaches a maximum height of 4 feet. It travels a horizontal distance of 20 feet. If
the ball’s path is a parabola, find the equation that represents its vertical height as a function of its
horizontal distance traveled.
144. Factor
10x2 + 13x – 3
2x2 – 8
148. Fire hoses come in different diameters. How far the
hose can throw water depends on the diameter of the hose.
The Smallville Fire Department collected data about their
fire hoses. The residual plot for the data is shown at right.
a. What does the residual plot tell you about the LSRL
model the fire department used?
b. Find the worst prediction made with the LSRL. How different was the worst prediction from what was
actually observed? Explain why in context.
c. Make a conjecture about what the original scatterplot might have looked like and sketch it. Label both
axes.
149. The mayor of Smallville finds the following graph in the town’s annual financial report.
a. Describe the association in the scatterplot.
b. The mayor immediately orders the fire department to send fewer firefighters to each fire so that there is
less damage. Why do you think the mayor said this? Do you agree with the mayor’s decision? Explain
why or why not.
150. A dietician studying the benefits of eating spinach surveyed a large sample of individuals. She
recorded the amount of spinach they ate and their physical strength. The dietician found the spinach eaters
to be much stronger than the non- spinach eaters. The next day the newspaper headline was, “Popeye was
right! Eating spinach does make you stronger!”
a. Do you agree with the newspaper? Do you agree that if you eat more spinach, you will grow stronger
muscles and increase your strength?
b. The dietician correctly found an association. What could explain this association other than spinach
makes you stronger?
A lurking variable is a hidden variable that was not part of the study. The size of the fire in problem 149
and the amount people work out in problem 150 are lurking variables.
151. A medical study found a strong link between the numbers of hours high school students wear a
helmet and the number of concussions (head injuries). However, it is unlikely that wearing helmets causes
head injuries. Can you think of a lurking variable that might explain this association?
155. Here are some more news headlines from real observational studies. Just as you did in problem 151,
determine at least one plausible lurking variable that could explain the cause and effect. Remember, do
not argue about the link expressed in the headline. Accept the association or link as true. Your task is to
find the other variable(s) that could be the actual cause(s).
a. “Teens with own cars more likely to crash”
b. “Bottled water linked to healthier babies”
156. For the statement below, either justify why a causation can be inferred, or explain what might
account for the correlation other than a causal relation.
Researchers have noticed that the number of golf courses and the number of divorcees in the United
States are strongly correlated and both have been increasing over the last several decades. Can you
conclude that the increasing number of golf courses is causing the number of divorcees to increase?
157. A human resources manager recorded the experience and hourly wage for a sample of 10 technology
workers.
Experience 1
2
3
4
5
6
7
8
9
10
(years)
Hourly
12.00
13.25
14.00
16.00
17.00
18.00
19.50
21.00
22.00
23.25
Wage ($)
a. Sketch a scatterplot showing the association between the wage and the years of experience.
b. Describe the association.
c. Sketch the residual plot. Is a linear model appropriate?
d. What is the correlation coefficient? What does it tell you?
158. Marissa went with her friends to the amusement park on
a beautiful spring day. The park was crowded. Marissa
wondered if there was an association between the weather and
attendance. From data she received at the theme park office,
Marissa randomly picked ten Saturdays and analyzed the data.
a. Marissa calculated the least squares regression line a = -14 + 0.41t where a is the attendance (in
thousands) and t is the high temperature (Fº) that day. Interpret the slope in this context.
b. The residual plot Marissa created is shown at right. On days when temperatures were in the 80s, would
you expect the predictions made by Marissa’s model to be too high, too low, or pretty accurate?
c. What was the actual attendance on the day when the temperature was 95ºF?
d. Would you rely on this model to make predictions? Why or why not?
159. Here are some more news headlines from real observational studies. Determine at least one plausible
lurking variable that could explain the cause and effect.
Remember, do not argue about the link expressed in the headline. Accept the association as true. Your
task is to find the other variable(s) that could be the actual cause(s).
a. “The graveyard shift may be aptly named. Working nights will soon be listed as a likely cancer cause”
b. “Daily meat diet tied to higher chance of early death”
160. Suppose you found that the correlation between the life expectancy of citizens in a nation and the
average number of TVs in households in that nation is r = 0.89 . Does that mean that watching TV helps
you live longer?
161. Find the equation of the exponential function that has an asymptote at y = -5 and passes through the
points (10, 22.94) and (13, 49.57).
162. Complete the square to find the vertex of y = 2x2 – 12x + 1
163. Ranger Sarah is responsible for monitoring the population of the elusive Gray’s nightingale in Holly
State Park. She would like to find a relationship between the Maile oak trees (their preferred nesting site)
and the number of nightingales in the park. She randomly selects 7 different areas in the park and
painstakingly counts the Maile Oaks and Gray’s nightengales in each area.
Oaks
8
Nightingales 5
13
9
4
3
5
5
10
7
9
7
4
5
a. Make a scatterplot on graph paper
b. Describe the association.
c. Calculate the LSRL and then sketch the line of best fit on your scatterplot. Round to the nearest tenth.
d. Interpret the slope and y-intercept of your model in context.
164. Consider Ranger Sarah’s situation from the previous problem.
a. About how many nightingales would Ranger Sarah expect to find in a particular area with 6 oaks?
b. Sarah went back to Holly Park and observed 4 nightingales on the plot with 6 oaks. What is the
residual for this particular area?
165. Consider Ranger Sarah’s situation from problem 159. Calculate and interpret the correlation
coefficient.
166. A study shows a positive association between cancer and number of cups of coffee consumed each
day. Does this mean that reducing the amount of coffee you drink will reduce your chances of getting
cancer? Explain.
167. The table shows the foreign and total assets of international companies. Draw a scatterplot to
represent the relationship between the foreign assets and total assets of the companies. Is there a
relationship between a company’s foreign assets and total assets? If so, describe it.
Company
Country
A
Netherlands / UK
Foreign Assets ($
billions)
69
Total Assets ($
billions)
100
B
C
D
E
F
G
H
I
Britain
United States
Japan
Mexico
United States
Switzerland
United States
France
19
44
23
4
23
25
47
22
28
81
77
8
41
31
84
46
Is there a relationship between a company’s foreign assets and total assets? If so, describe it.
168. The table shows the housing affordability of cities in the United States and their latitude.
Affordability is the percentage of homes sold that were within reach of the median income household.
Draw a scatterplot to represent the relationship between affordability and each city’s latitude. Is there a
relationship between latitude and affordability?
CITY
AFFORDABILITY
NORTH LATITUDE
(º)
Lima, Ohio
86%
41
Laredo, Texas
30%
27
Portland, Oregon
36.5%
46
Baton Rouge,
85%
31
Louisiana
San Francisco,
21%
37
California
Melbourne, Florida
83%
28
New York, New
35%
41
York
Kansas City,
83%
38
Missouri
Draw a scatterplot to represent the relationship between affordability and each city’s latitude.
Is there a relationship between latitude and affordability?
169. Which scatterplot shows the relationship between money earned and hours worked if a worker earns
an hourly wage?
170. If a scatterplot of y versus x has a positive correlation, then:
a. as y decreases, x
b. as y decreases, x c. as y increases, x
increases
decreases
decreases
d. both A and C are
true
171. Scientist Robert Boyle examined the relationship between the volume in which a gas is contained
and the pressure in that container. He used a cylindrical container with a moveable top that could be
raised or lowered to change the volume. He measured the height in inches and measured the pressure in
inches of mercury (as in a barometer). Here is some data:
Height
48
44
40
36
32
28
Pressure
29.1
31.9
35.3
39.3
44.2
50.3
Height
24
20
18
16
14
12
Pressure
58.8
70.7
77.9
87.9
100.4
117.
a. Create a scatterplot of the data.
b. Find an appropriate model for this data.
c. Justify the appropriateness of the model.
d. Predict the pressure of a 46 inch container.
e. Calculate the residual of an 18 inch container.
172. The value of a log is based on the number of “board feet” of lumber the log may contain. One board
foot is equivalent to one piece of wood 1inch thick, 12 inches wide and 1 foot long. To estimate the
amount of lumber in a log, buyers measure the diameter inside the bark at the smaller end. Then they look
at a table based on the Doyle Log Scale. Here are the estimates for logs 16 feet long:
Diameter of Log
8”
12”
16”
20”
24”
28”
Board Feet
16
64
144
256
400
576
a. What model does this scale use (for example, linear? Exponential? Quadratic? Other?)?
b. How much lumber would you estimate that a log 10” in diameter contains?
173. Here is some sales data for a tire manufacturer:
a. Find an appropriate model to predict sales from year.
b. Use this model to predict the tire sales in 2014.
c. What might be some issues with this prediction?
Use the following data to answer questions 174 and 175:
Year
Temp
CO2
Year
Temp
CO2
Year
Temp
CO2
1979
8
336.67
1989
19
352.68
2000
33
368.83
1980
19
338.57
1990
36
353.97
2001
47
370.43
1981
26
339.92
1991
35
355.37
2002
56
372.01
1982
4
341.30
1992
13
356.18
2003
55
374.45
1983
25
342.71
1993
13
356.69
2004
48
376.77
1984
9
344.24
1994
23
358.14
2005
63
378.30
1985
4
345.81
1995
37
360.02
2006
55
380.83
1986
12
347.11
1996
29
361.95
2007
58
382.56
1987
27
348.72
1997
39
363.18
2008
44
384.39
1988
31
351.04
1998
56
365.19
2009
57
386.34
1999
31
367.86
2010
63
388.13
The temperature data is called the Global Land-Ocean Temperature Index and is in units of 1/100 of a
degree Celsius above the 1950 – 1980 average temperature. For example, in 1979, the means that the
temperature that year was 0.08 degrees Celsius above the average temperature between 1950 and 1980.
The Carbon Dioxide data is in ppm (parts per million) which refers to the concentration of carbon dioxide
in the atmosphere. These levels are measured at the Mauna Loa Observatory in Hawaii. Any
concentration higher than 350 ppm is considered unsafe.
174. In question 14, you estimated a model to predict temperature from year. Now you will use your
calculator to do this.
a. Determine if a linear model is appropriate. Justify why or why not.
b. If so, find it.
c. Does this indicate that there is global warming occurring?
175. In question 15, you estimated a model to predict temperature from CO2 level. Now you will use your
calculator to do this.
a. Determine if a linear model is appropriate. Justify why or why not.
b. If so, find it.
c. Does this indicate that the rise in CO2 is causing a rise in temperature?
176. Below is the data from the U. S. federal debt. The debt is given in millions of dollars.
Year
Debt
CO2
Year
Debt
CO2
Year
Debt
CO2
1979
829467
336.67
1989
2867800
352.68
2000
5628700
368.83
1980
909041
338.57
1990
3206290
353.97
2001
5769881
370.43
1981
994828
339.92
1991
3598178
355.37
2002
6198401
372.01
1982
1137315
341.30
1992
4001787
356.18
2003
6760014
374.45
1983
1371660
342.71
1993
4351044
356.69
2004
7354657
376.77
1984
1564586
344.24
1994
4643307
358.14
2005
7905300
378.30
1985
1817423
345.81
1995
4920586
360.02
2006
8451350
380.83
1986
2120501
347.11
1996
5181465
361.95
2007
8950744
382.56
1987
2345956
348.72
1997
5369206
363.18
2008
9986082
384.39
1988
2601104
351.04
1998
5478189
365.19
2009
11875851 386.34
1999
5605523
367.86
2010
13528807 388.13
a. For each year, plot the CO2 level with the federal debt from that year in a scatterplot. Be sure to think
about which is the dependent and which is the independent variable.
b. Determine if a linear model is appropriate. Justify why or why not.
c. If so, find it.
d. Does this indicate that the rise in CO2 is causing a rise in the federal debt?
e. In 2013, the federal debt was $16,719.434 millions of dollars and the CO2 level was 396.48. Calculate
the residual and comment on how accurate the model is at making this prediction.
177. The data at the right shows the cooling temperatures of a freshly brewed cup of coffee after it is
poured from the brewing pot into a serving cup. The brewing pot temperature is approximately 180ºF.
The temperatures are measured in ºF and the time is measured in minutes.
Time
0
5
8
11
15
18
22
25
30
34
38
42
45
Temp
179.5 168.7 158.1 149.2 141.7 134.6 125.4 123.5 116.3 113.2 109.1 105.7 102.2
a. Determine an exponential model to represent this data.
b. Use a residual plot to determine if this model is an appropriate model.
c. Based on this equation, what was the initial temperature of the coffee?
d. What is the predicted temperature of the coffee after one hour?
e. What is the predicted temperature of the coffee after four hours? Does this make sense? Why?
f. In 1992 a woman sued McDonald’s for serving coffee at a temperature of 180ºF that caused her to be
severely burned when the coffee spilled. An expert witness at the trial testified that liquids at 180ºF will
cause a full thickness burn to human skin in two to seven seconds. It was stated that had the coffee been
served at 155ºF, the liquid would have cooled and avoided the serious burns. The woman was awarded
over 2.7 million dollars. As a result of this famous case, many restaurants now serve coffee at a
temperature around 155ºF. How long should restaurants wait (after pouring the coffee from the pot)
before serving coffee, to ensure that the coffee is not hotter than 155F?
g. If the temperature in the room is 76ºF, what will happen to the temperature of the coffee, after being
poured from the pot, over an extended period of time?
50
100.5