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Chapter 6 ● Skills Practice 441
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Skills Practice Skills Practice for Lesson 6.1
Name _____________________________________________ Date _________________________
Mia’s Growing Like a WeedDrawing the Line of Best Fit
Vocabulary
Match each definition to its corresponding term.
1. a graph in the coordinate plane in which values a. rate of change
of x and y are plotted as points (x, y)
2. a line that is used to approximate the data as b. model of a data set
close to as many points as possible
3. the equation of the line of best fit c. scatter plot
4. a comparison of two quantities with different d. range of a data set
units that are changing
5. a line of best fit and its equation e. linear regression equation
6. the difference between the greatest number f. line of best fit
and the least number in the data set
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Problem Set
Create a scatter plot representing each table on the given grid. Be sure to label your graph clearly.
1. 2.
Beagle’s Weight (female)
Age (weeks) Weight (kg)
6 1.0
12 3.0
16 4.5
24 6.5
30 8.0
Beagle’s Weight (male)
Age (weeks) Weight (kg)
6 1.0
12 3.5
16 5.0
24 7.0
30 9.0
x3024 27
6
7
8
9
10
12 15
4
5
18 210
3
3 6 9
2
1
y
Age (weeks)
Beagle’s Weight (Female)
Wei
gh
t (k
g)
Chapter 6 ● Skills Practice 443
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3. 4.
Chihuahua’s Weight (male)
Age (weeks) Weight (oz)
6 15
12 30
16 39
24 46
30 51
Chihuahua’s Weight (female)
Age (weeks) Weight (oz)
6 11
12 19
16 25
20 30
24 33
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5. 6.
Dalmatian’s Weight
Age (weeks) Weight (kg)
8 6.5
12 11.5
16 15.4
20 21.5
25 24.5
Pomeranian’s Weight
Age (weeks) Weight (oz)
6 13
12 22.5
16 30
20 35.5
24 39
Chapter 6 ● Skills Practice 445
Name _____________________________________________ Date _________________________
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Use a ruler to draw a line that best fits each scatter plot.
7. 8.
x2520
15
20
25
10
10
150 5
5
y
x2520
15
20
25
10
10
150 5
5
y
9. 10.
x2520
15
20
25
10
10
150 5
5
y
x2520
15
20
25
10
10
150 5
5
y
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Draw a line of best fit for each scatter plot. Then write the equation of the line.
11. (0, 18), (5, 16), (7, 10), (10, 8), (15, 3), (20, 0) 12. (0, 10), (5, 5), (6, 4), (7, 3), (10, 0)
x2520
15
20
25
10
10
150 5
5
y
x2520
15
20
25
10
10
150 5
5
y
Sample Answer: y � � 10 ___ 11
x � 18
13. (0, 0), (1, 2), (2, 4), (3, 6), (5, 10) 14. (0, 0), (5, 5), (7, 8), (8, 6), (10, 10)
x2520
15
20
25
10
10
150 5
5
y
x2520
15
20
25
10
10
150 5
5
y
Chapter 6 ● Skills Practice 447
Name _____________________________________________ Date _________________________
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Use the given equation to answer each question.
15. A grocery store’s earnings in dollars can be modeled by the equation y � 0.75x � 0.15x,
where x represents the number of tomatoes that they sell. If they sell 200 tomatoes in one
day, how much money do they earn?
y � 0.75(200) � 0.15(200) � 150 � 30 � 120
The grocery store earns $120 if they sell 200 tomatoes.
16. The number of T-shirts that a T-shirt company sells can be modeled by the equation
y � �18x � 520, where the price of a T-shirt is represented by x. If they sell their T-shirts
for $8.00 each, how many will they sell?
17. The distance a car can travel in miles is modeled by the equation y � 23x � 6, where
x represents the number of gallons of gas the car uses. If the car traveled 86 miles,
how many gallons of gas did it use?
18. The amount a shoe store charges in dollars to deliver x pairs of shoes can be modeled by
the equation y � 40x � 30. If the total bill was $350 dollars, how many pairs of shoes did
they deliver?
448 Chapter 6 ● Skills Practice
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Chapter 6 ● Skills Practice 449
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Skills Practice Skills Practice for Lesson 6.2
Name _____________________________________________ Date _________________________
Where Do You Buy Your Music?Using Lines of Best Fit
Vocabulary
Define each term in your own words.
1. line of best fit
2. model of a data set
3. x-coordinate
4. y-coordinate
5. y-intercept
6. slope
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Problem Set
Use a ruler to draw the line that best fits the data represented in each scatter plot.
1.
U.S. Gasoline Prices
$0.00$0.50$1.00$1.50$2.00$2.50$3.00$3.50
Feb2006
Mar2006
May2006
Jul2006
Aug2006
Oct2006
Nov2006
Jan2007
Mar2007
Apr2007
Date
Pric
e pe
r G
allo
n
2.
U.S. Gasoline Prices
$0.00
$1.00
$2.00
$3.00
$4.00
Dec2006
Jan2007
Feb2007
Mar2007
Apr2007
May2007
Jun2007
Jul2007
Aug2007
Date
Pric
e pe
r G
allo
n
3.
U.S. Gasoline Prices
$2.50$2.75$3.00$3.25$3.50$3.75$4.00$4.25
Jun2007
Aug2007
Sep2007
Nov2007
Jan2008
Feb2008
Apr2008
Jun2008
Jul2008
Sep2008
Date
Pric
e pe
r G
allo
n
4.
U.S. Gasoline Prices
$1.50$2.00
$2.50$3.00$3.50
$4.00$4.50
Jun2008
Jul2008
Aug2008
Sep2008
Oct2008
Nov2008
Dec2008
Jan2009
Feb2009
Mar2009
Date
Pric
e pe
r G
allo
n
Chapter 6 ● Skills Practice 451
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Estimate the equation of the line of best fit shown in each scatter plot.
5.
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8
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4
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Answers will vary but should be close to the following equation:
y � y 1 � m(x � x 1 ) m � y 2 � y 1 ________ x 2 � x 1
� 2 � 1 _______ 0.5 � 0
� 2
y � 1 � 2(x � 0)
y � 2x � 1
6.
x2016 18
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18
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8 10
8
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12 140 2 4 6
4
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7.
x2016 18
12
14
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18
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8 10
8
10
12 140 2 4 6
4
6
2
y
8.
x2016 18
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18
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8 10
8
10
12 140 2 4 6
4
6
2
y
Chapter 6 ● Skills Practice 453
Name _____________________________________________ Date _________________________
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9.
x2016 18
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18
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8 10
8
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12 140 2 4 6
4
6
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y
10.
x2016 18
12
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18
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8 10
8
10
12 140 2 4 6
4
6
2
y
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Use each line of best fit to make the prediction. Explain your reasoning.
11. Predict the 2005 mathematics SAT score for Connecticut.
Connecticut SAT Scores: Mathematics
508509510511512513514515516
1999 2000
Source: The College Board
2001 2002 2003 2004 2005
Year
SA
T S
core
Answers will vary, but 516 appears to be the next point on the line of best fit. The scores seem to be clustering with an upward trend, and increasing in value, around the line of best fit (except for the one score in 2002).
12. Predict the 2005 mathematics SAT score for New York.
New York SAT Scores: Mathematics
504505506507508509510511
1999 2000 2001 2002 2003 2004 2005
Year
SA
T S
core
Source: The College Board
13. Predict the average monthly sun spots that occurred in 2001.
Average Monthly Sun Spots: 1995-2000
0
20
40
60
80
100
120
140
1994 1995 1996 1997 1998 1999 2000 2001
Year
Nu
mb
er o
f S
un
Sp
ots
Source: National Geophysical Data Center
Chapter 6 ● Skills Practice 455
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14. Predict the average monthly sun spots that occurred in 1905.
Average Monthly Sun Spots: 1900-1904
-5
5
15
25
35
45
55
1899 1900 1901 1902 1903 1904 1905
Year
Nu
mb
er o
f S
un
Sp
ots
Source: National Geophysical Data Center
Compare each pair of graphs. Which line models the data better? Explain your reasoning.
15. Gold Prices
$0.00$100.00$200.00$300.00$400.00$500.00$600.00$700.00$800.00$900.00
$1,000.00
2003 2004 2005
Graph A
2006 2007 2008 2009
Year
Go
ld P
rice
s
Gold Prices
$0.00$100.00$200.00$300.00$400.00$500.00$600.00$700.00$800.00$900.00
$1,000.00
2003 2004 2005 2006 2007 2008 2009
Year
Go
ld P
rice
s
Graph B
Graph B is a better choice for the line of best fit. Graph B has the same number of points above the line as it has below the line and the most points that cluster to the line of best fit.
16. Gold Prices
$250.00$270.00$290.00$310.00$330.00$350.00$370.00$390.00$410.00$430.00
1999 2000 2001 2002 2003 2004 2005
Year
Go
ld P
rice
Graph A
Gold Prices
$250.00$270.00$290.00$310.00$330.00$350.00$370.00$390.00$410.00$430.00
1999 2000 2001 2002 2003 2004 2005
Year
Go
ld P
rice
Graph B
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17. U.S. Gasoline Prices per Gallon
$1.50
$2.00
$2.50
$3.00
$3.50
$4.00
$4.50
Jun 2008 Sep 2008 Dec 2008 Mar 2009
Date
Pri
ce p
er G
allo
n
Graph A
U.S. Gasoline Prices per Gallon
$1.50
$2.00
$2.50
$3.00
$3.50
$4.00
$4.50
Jun 2008 Sep 2008 Dec 2008 Mar 2009
Date
Pri
ce p
er G
allo
n
Graph B
18. U.S. Gasoline Prices per Gallon
$2.50$2.75$3.00$3.25$3.50$3.75$4.00$4.25
Apr2007
Aug2007
Nov2007
Feb2008
Jun2008
Sep2008
Date
Pri
ce p
er G
allo
n
Graph A
U.S. Gasoline Prices per Gallon
$2.50$2.75$3.00$3.25$3.50$3.75$4.00$4.25
Apr2007
Aug2007
Nov2007
Feb2008
Jun2008
Sep2008
Date
Pri
ce p
er G
allo
n
Graph B
Use the given equation to answer each question.
19. A computer parts company estimates its profits using the equation y � 0.85x � 125, where
x is the number of parts they sell. If they sell 200 parts to computer repair store A and
160 parts to computer repair store B, what was the parts company’s profit?
Total parts sold: 200 � 160 � 360
y � 0.85(360) � 125 � 306 � 125 � 181
The parts company made $181 in profit.
20. A restaurant uses the equation y � 35x � 325 to approximate its profit for a day, where x is
the number of customers. On Friday, if they have 11 customers for lunch and 25 customers
for dinner, how much did they earn in profit?
Chapter 6 ● Skills Practice 457
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21. An artist’s paintings increase in price as he becomes more popular. He estimates the price
of each painting using the equation y � 0.75x � 300, where x is the number of paintings
he has already sold. If his latest painting is selling for $317.25, how many paintings has he
already sold?
22. Your grandmother gives you money for college every year. She determines the amount
based on your age, x, using the equation y � 15x � 45. How old will you be when she gives
you $270?
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Chapter 6 ● Skills Practice 459
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Skills Practice Skills Practice for Lesson 6.3
Name _____________________________________________ Date _________________________
Stroop TestPerforming an Experiment
Vocabulary
Provide an example of each term.
1. matching list of a Stroop Test
2. non-matching list of a Stroop Test
3. mean
4. experiment
5. linear regression equation
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Problem Set
Create a scatter plot of the ordered pairs on the grid provided, and estimate the equation of the line of best fit. Use your equation to answer each question. Be sure to label your graph clearly.
1. Your little sister’s classroom has a pet baby turtle. They let it swim in a tank and record its
distance at certain times. Using your line of best fit, predict how far the baby turtle will swim
in 30 seconds.
Tracking a Turtle
Time (seconds) Distance (meters)
5 3
6 3.3
10 4.1
11 4.5
15 6.3
20 7.9
Answers for line of best fit will vary.
Sample line of best fit using first and last data points:
y � mx � b
m � 7.9 � 3 _______ 20 � 5
� 4.9 ___ 15
� 0.33
3 � 0.33(5) � b
3 � 1.65 � b
b � 1.35
y � 0.33x � 1.35
Sample solution to distance traveled after 30 seconds:
y � 0.33(30) � 1.35 � 11.25
In 30 seconds, the turtle will swim approximately 11.25 meters.
x2016 18
12
14
16
18
20
8 10Time (seconds)
8
10D
ista
nce
(m
eter
s)
12 140 4 62
4
6
2
y
Chapter 6 ● Skills Practice 461
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2. Your class conducts an experiment. You ask shoppers at different stores how much change
they have, and you record the total number of shoppers and the total dollar amount of
change among them. If you encountered 25 shoppers, how much change, in dollars, would
you expect them to have altogether? Use your line of best fit to approximate a solution.
Counting Change
Number of Shoppers Total Change (dollars)
2 1.5
5 3
7 4.2
10 4.5
14 7
18 11
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3. Jeremiah prints his digital pictures. After they start printing, he starts recording the time
elapsed and the total number of pictures printed. Using your line of best fit, if he prints
30 pictures, approximately how much time, in seconds, will it take?
Printing Pictures
Time (seconds)Number of Pictures
Printed
7 6.5
12 9.4
15 11.5
17 13.2
20 15
22 17.3
Chapter 6 ● Skills Practice 463
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4. A fundraiser uses telemarketers to raise money. Every so often, they stop to determine how
many phone calls they’ve made and how much money they’ve collected. Using your line
of best fit, if the telemarketers raised $250, approximately how many phone calls did they
make?
Fundraising Totals
Number of Phone Calls
Money Collected (dollars)
5 60
10 82.30
12 92
13 98.70
15 100.30
20 146
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Write an equation for each line of best fit.
5.
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Answers will vary but should be close to the following equation:
y � y 1 � m(x � x 1 ) m � y 2 � y 1 ________ x 2 � x 1
� 6 � 5 ________ 12 � 10
� 0.5
y � 5 � 0.5(x � 10)
y � 0.5x
6.
x2016 18
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8
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Chapter 6 ● Skills Practice 465
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7.
x2016 18
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4
6
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y
8.
x2016 18
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18
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8 10
8
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12 140 4 62
4
6
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y
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Use the given equation to answer each question.
9. Your sister is moving into a new apartment. To estimate her average heating costs each
month in dollars, she uses the equation y � 0.14x, where x is the square footage of her
apartment. How much more will it cost her to heat an apartment that is 900 square feet than
one that is 700 square feet?
Difference in square footage: 900 ft2 � 700 ft2 � 200 ft2
Cost to heat this extra square footage: y � 0.14(200) � $28
She estimates it will cost her $28 more per month to heat the 900 square foot apartment than the 700 square foot apartment.
10. Your brother has found a new apartment to rent. It is 800 square feet, and the electricity
costs in dollars per month will be approximately y � 0.08x, where x is the square footage of
the apartment. He doesn’t want to pay more than $60 a month for electricity. Should he rent
this apartment?
11. Alice and Monique run a race. Alice’s distance in meters can be approximated using the
equation a � 6x and Monique’s distance in meters can be approximated using the equation
m � 7x, where x is the time in seconds. If the two girls raced in a 400-meter sprint, who
would finish first?
Chapter 6 ● Skills Practice 467
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12. Francis and Mario are competing in a 200-meter sprint. Francis’s distance in meters can
be approximated by the equation f � 9.09x and Mario’s distance can be approximated by
the equation m � 8.89x, where x is the time in seconds. Who would win the 200-meter race
between the two boys?
Use the given information about the experiments to answer each question.
13. A professor is interested in determining the average reading time of his students. He
performs two experiments. In the first experiment, students read in a quiet room and are
uninterrupted. In the second experiment, students read in a busy cafeteria.
The line of best fit for the first experiment is w 1 � 259.5t � 53.2, and the line of best fit for
the second experiment is w 2 � 178.8t � 12, where w equals the total number of words
read, and t is the time in minutes. Explain the difference between the number of words read
in 20 minutes by a student in each experiment.
Experiment 1:
w � 259.5(20) � 53.2 � 5136.8
Experiment 2:
w � 178.8(20) � 12 � 3576 � 12 � 3588
The difference between the number of words read by a student in experiment 1 and a student in experiment 2 is 5136.8 � 3588 � 1548.8 words. A student in the first experiment reads 1548.8 more words than a student in the second experiment. A student in the first experiment is reading in a quiet room and should be able to read at a faster rate than a student who is reading in a busy cafeteria. Because students in the first experiment read at a faster rate, they will read more words in the same amount of time.
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14. A car review website wants to compare the total gas used between small cars and pick-up
trucks. They conduct two experiments. In the first experiment, they record the number of
miles driven and the total gas used by small cars. In the second experiment, they record
the number of miles driven and the total gas used by pick-up trucks. The line of best fit for
the first experiment is d 1 � 29.4g � 3.9, and the line of best fit for the second experiment
is d 2 � 17.4g � 2.2, where d equals the total number of miles driven, and g is the amount
of gasoline in gallons. Explain the difference between the number of miles driven by a small
car and a pick-up truck if both vehicles use 10 gallons of gasoline.
15. A teacher wants to determine how far her students travel to school. She collects the
times and distances traveled for students who walk, and she separately collects the
times and distances traveled for students who ride the bus. For the students who walk, the
line of best fit is d w � 2.5t � 0.15, and for students that ride the bus, the line of best fit is
d b � 17.6t � 0.7, where d is the distance in miles and t is the time in hours. If two students,
one walking and one riding the bus, take 15 minutes (or 0.25 hours) to get to school, how
much further does the student travel who rides the bus?
Chapter 6 ● Skills Practice 469
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16. Two experiments are conducted to compare how long it takes inkjet printers to print in
black-and-white and how long it takes them to print in color. The number of pages printed
using black-and-white can be expressed by the line of best fit p b � 33.8t � 5.3, and the
number of pages printed using color can be expressed by the line of best fit p c � 21t � 2.7,
where p is the total number of pages printed, and t is the time in minutes. If you only have 15
minutes to use an inkjet printer, how many more black-and-white pages could you print than
color pages?
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Chapter 6 ● Skills Practice 471
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Skills Practice Skills Practice for Lesson 6.4
Name _____________________________________________ Date _________________________
JumpingCorrelation
Vocabulary
Draw a graph to illustrate each term.
1. positive correlation 2. negative correlation
3. no correlation 4. line of best fi t
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Problem Set
Determine whether the points in each scatter plot have a positive correlation, a negative correlation, or no correlation. Explain your answer.
1.
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4
6
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x2520
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25
10
10
150 5
5
y
The points in this scatter plot have a negative correlation because the line of best fit has a negative slope.
3.
x2016 18
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4
6
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y 4.
x2016 18
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Chapter 6 ● Skills Practice 473
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5.
x2016 18
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8 10
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4
6
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y 6.
x2016 18
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8
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4
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y
7.
x2016 18
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18
20
8 10
8
10
12 140 4 62
4
6
2
y 8.
x2016 18
12
14
16
18
20
8 10
8
10
12 140 4 62
4
6
2
y
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9.
x2016 18
12
14
16
18
20
8 10
8
10
12 140 4 62
4
6
2
y 10.
x2016 18
12
14
16
18
20
8 10
8
10
12 140 4 62
4
6
2
y
Use a ruler to draw the line that best fits the data represented in each scatter plot. Explain what your graph and line of best fit indicate about the relationship between the two variables.
11.
Unemployment Rates (1992-2000)
4
4.5
5
5.5
6
6.5
7
7.5
8
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Year
Per
cent
of P
eopl
e U
nem
ploy
ed
(ove
r 16
yea
rs o
ld)
x
y
The negative slope indicates there is a negative correlation between these two variables. The percent of people unemployed in the United States steadily decreased between 1992 and 2000.
Chapter 6 ● Skills Practice 475
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12.
U.S. Unemployment Rates: 2000-2004
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
1999 2000 2001 2002 2003 2004 2005
Year
Per
cent
age
of P
eopl
e U
nem
ploy
ed
(ove
r 16
yea
rs o
ld)
x
y
13.
Price of Electricity (1979-1996)
0
10
20
30
40
50
60
1975 1980 1985 1990 1995 2000Year
Pric
e pe
r 50
0 kw
hs
x
y
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14.
U.S. Hurricanes
0
2
4
6
8
10
12
14
16
18
1951-1960 1961-1970 1971-1980 1981-1990 1991-2000Year
Num
ber
of H
urric
anes
x
y
Estimate the equation of the line of best fit for each scatter plot shown.
15.
x3024 27
6
7
8
9
10
12 15
4
5
18 210 6 93
2
3
1
y
Answers will vary but should be close to the following equation:
y � y 1 � m(x � x 1 ) m � y 2 � y 1 ________ x 2 � x 1
� 5.5 � 2 _______ 20 � 8
� 0.29
y � 2 � 0.29(x � 8)
y � 0.29x � 0.32
Chapter 6 ● Skills Practice 477
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16.
x3024 27
6
7
8
9
10
12 15
4
5
18 210 6 93
2
3
1
y
17.
x2016 18
120
140
160
180
200
8 10
80
100
12 140 4 62
40
60
20
y
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18.
x2016 18
120
140
160
180
200
8 10
80
100
12 140 4 62
40
60
20
y
19.
x108 9
6
7
8
9
10
4 5
4
5
6 70 2 31
2
3
1
y
Chapter 6 ● Skills Practice 479
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20.
x108 9
6
7
8
9
10
4 5
4
5
6 70 2 31
2
3
1
y
Use the given equation to solve each problem.
21. The average speed of a cheetah is 72 miles per hour. The total distance traveled by a
cheetah is given by the equation d � 72h, where h is the number of hours. If cheetahs
can only maintain this speed for a total distance of 3.5 miles, for how long can they run at
72 miles per hour? Round your answer to the nearest hundreth.
3.5 � 72h
h � 3.5 ÷ 72 � 0.05
Cheetahs can run at a speed of 72 miles per hour for 0.05 hours (or approximately 3 minutes).
22. A gazelle runs at an average speed of 35 miles per hour. The total distance traveled by
the gazelle is given by the equation d � 35h, where h represents the time in hours. If the
gazelle’s total distance traveled is 3.5 miles, for how long did it run?
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23. You make an investment of $50 in your friend’s business. According to your friend, you will
have a total of p � 50 � 0.5m dollars if you invest in the business for m months. After
24 months, what is your investment worth?
24. Your uncle put aside some college savings for you when you were born. The total amount
saved is A � 5000 � 150y, where y is the time in years. If you go to college when you are
18 years old, how much money will you have for college?
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Skills Practice Skills Practice for Lesson 6.5
Name _____________________________________________ Date _________________________
Human Chain: Wrist ExperimentUsing Technology to Find a Linear Regression, Part 1
Vocabulary
Define each term in your own words.
1. least squares method
2. linear regression equation
3. correlation coefficient
4. domain of a function
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Problem Set
Create a scatter plot of each table. Then use your ruler to draw a line of best fit. Write the equation of your line. Be sure to label your graph clearly.
1.
Mean Temperatures in Anchorage, Alaska
Month Temperature (°F)
Jan (1) 15.8
Feb (2) 18.7
Mar (3) 25.9
Apr (4) 36.3
May (5) 46.9
Jun (6) 54.7
Jul (7) 58.4
Sample equation of line of best fit through points (2, 18.7), (5, 46.9):
y � mx � b
m � 46.9 � 18.7 ___________ 5 � 2
� 28.2 _____ 3 � 9.4
y � 9.4x � b
18.7 � (9.4)(2) � b
18.7 � 18.8 � b
b � �0.1
y � 9.4x � 0.1
x2016 18
60
70
80
90
100
8 10
40
50
12 140
30
2 4 6
20
10
y
Month
Mean Temperatures in Anchorage, Alaska
Tem
per
atu
re (
deg
rees
Fah
ren
hei
t)
Chapter 6 ● Skills Practice 483
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2.
Mean Temperatures in Phoenix, Arizona
Month Temperature (°F)
Jan (1) 54.2
Feb (2) 58.2
Mar (3) 62.7
Apr (4) 70.2
May (5) 79.1
Jun (6) 88.6
Jul (7) 92.8
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3.
Average Number of Books Read by Students
Age of Student (years)
Number of Books Read
6 3
8 12
10 35
12 60
14 71
16 80
18 87
Chapter 6 ● Skills Practice 485
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4.
Average Number of Movies Watched by Students
Age of Student (years)
Number of Movies Watched
2 3
4 5
6 10
8 22
10 30
12 38
14 50
16 75
For each value of the correlation coefficient r, indicate how close the data are to being a straight line. Use a complete sentence in your explanation.
5. r � 0.1
The data are not close to being a straight line because the value of r is closer to 0 than to 1.
6. r � 0.9
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7. r � �0.1
8. r � �0.9
9. r � 0.4
10. r � �0.4
Use your graphing calculator to determine the linear regression equation for the given data values. Write the values for a, b, r2, and r that are provided by your calculator. Explain your results.
11. (1, 6) and (2, �2)
y � ax � b
a � �8
b � 14
r 2 � 1
r � �1
The linear regression equation is y � �8x � 14. The values of r 2 and r show that the data are in a straight line through the two points with a negative slope.
12. (3, 4) and (4, 5)
Chapter 6 ● Skills Practice 487
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13. (1, 4), (3, 11), (5, 10), and (7, 15)
14. (1, 3), (3, 6), (4, 6), and (10, 2)
Use your graphing calculator and the data from each table to calculate the linear regression equation. Round to the nearest hundredth, if necessary.
15. The daily recommended hours of sleep by one source for different ages are listed below.
Average Number of Hours of Sleep Needed by Age
Age (years) Hours of Sleep
0.5 15
1.5 12.5
4 11.5
9 10
15 10
20 8
Answers will vary but should be close to the equation: y � �0.28x �13.50.
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16. An office records the number of bagels that were consumed by different numbers of
employees.
Number of Bagels Consumed by Employees
Number of EmployeesNumber of Bagels
Consumed
1 1
3 2
5 5
6 7
9 8
14 10
17 15
17. A school cafeteria records the number of students in the cafeteria and the number of hot
lunches that were purchased.
Hot Lunches Purchased by Students
Number of StudentsNumber of Hot Lunches
Purchased
120 87
315 208
411 270
459 300
502 360
530 350
603 399
Chapter 6 ● Skills Practice 489
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18. A class records the total number of papers written and the total number of English classes
taken by each student.
Number of Papers Written per Student
Number of English Classes Taken Number of Papers Written
2 9
2 10
3 16
4 18
4 22
5 30
5 27
Use the graphing calculator screenshot to write the corresponding linear regression equation. Then use the linear regression equation to answer each question.
19. A research company collected data to study the relationship between the total number of
hours students spend studying per week, x, and their average test grade (out of 100), y.
The screenshot below shows the graphing calculator output when determining the linear
regression equation for these data.
y � ax � b
a � 2.21
b � 66.7
r2 � 0.96
r � 0.98
If a student studied for 5 hours in one week, what would you expect their average test grade
to be for that week?
y � 2.21x � 66.7
y � 2.21(5) � 66.7 � 11.05 � 66.7 � 77.75
Their average test grade for that week would be approximately 77.75.
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20. A pet store collects data to study the number of fancy goldfish per tank, x, and the size of
each tank in gallons, y. The screenshot below shows the graphing calculator output when
determining the linear regression equation for these data.
If you buy 4 fancy goldfish, what is a good estimate for the size of tank that you should
buy? Round to the nearest gallon.
y � ax � b
a � 7.77
b � 0.89
r2 � 0.998
r � 0.999
21. You record the number of hours that you sleep per night, x, and your average test grade
(out of 100), y, on the next school day. The screenshot below shows the graphing calculator
output when determining the linear regression equation for these data.
y � ax � b
a � 5
b � 57.86
r2 � 0.99
r � 0.995
If you need to average at least 85 on a test tomorrow, how much sleep should you get
tonight? Round to the nearest half hour.
Chapter 6 ● Skills Practice 491
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22. A company surveyed its employees and asked them the number of vacation days they used
per year, x, and the number of places they visited that year, y. The screenshot below shows
the graphing calculator output when determining the linear regression equation for these data.
y � ax � b
a � 0.421
b � �0.34
r2 � 0.913
r � 0.955
If you want to visit at least 3 different places next year, how many vacation days should you
plan on using, according to the data in the survey? Round to the nearest number of whole days.
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Chapter 6 ● Skills Practice 493
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Skills Practice Skills Practice for Lesson 6.6
Name _____________________________________________ Date _________________________
Human Chain: Shoulder ExperimentUsing Technology to Find a Linear Regression, Part 2
Vocabulary
Match each definition to its corresponding term.
1. indicates how close the data are to forming a
straight line a. linear regression equation
2. the sum of all the values of a data set divided by the b. y-intercept
number of values in the data set
3. the equation of the line of best fit c. mean
4. the y-coordinate of the point where a graph crosses d. correlation coefficient
the y-axis
Problem Set
For each value of the correlation coefficient r, indicate how close the data are to being a straight line. Use a complete sentence in your explanation.
1. r � 0.2
The data are not close to being a straight line because the value of r is closer to 0 than to 1.
2. r � �0.2
3. r � �1.0
4. r � 1.0
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5. r � �0.75
6. r � 0.75
What does the slope of each linear regression equation mean in terms of the given problem situation?
7. Lino sometimes walks to school from his friend’s house. He determined that his distance
from home when walking for x hours can be modeled by the equation y � 0.33x � 3.4.
Identify the slope and explain how it is related to Lino’s walk to school.
The slope is 0.33.
In this situation, the slope is the rate at which Lino walks in miles per hour.
8. Alberto borrows some money from his sister, and then he keeps borrowing more from her
each day. The equation y � �0.25x � 7.5 shows the amount of money in dollars he has
borrowed x days after borrowing the initial amount of money. Identify the slope and explain
how it is related to the total amount of money he has borrowed.
9. A city sanitation committee tracks the amount of trash it collects, in pounds, for a certain
number of residents. The city determined that the equation y � 1 __ 2 x � 3 models the amount
of trash in pounds created by x residents. Identify the slope and explain what it means in
this situation.
10. A concert hall records the number of seats available after a certain number of tickets are
purchased. The number of seats remaining after x tickets have been purchased is given by
the equation y � �x � 352. Identify the slope and explain what it means in this situation.
Chapter 6 ● Skills Practice 495
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Use your graphing calculator to determine the linear regression equation for the given data values. Write the values for a, b, r2, and r that are provided by your calculator. Explain your results.
11. (15, 4.33), (10, 2.41), (5, 1.29), and (10, 2.18)
y � ax � b
a � 0.304
b � �0.4875
r 2 � 0.940625652
r � 0.9698585732
The linear regression equation is y � 0.304x � 0.4875. The values of r 2 and r show that the data are almost a straight line and the line of best fit has a positive slope.
12. (30, 6.77), (45, 11.08), (8, 2.17), and (20, 4.63)
13. (1, 4.5), (3, 20), (5, 15), and (7, 11)
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14. (10, 3), (8, 6), (5, 6), and (1, 2)
Use your graphing calculator and the data from each table to calculate the linear regression equation. Round to the nearest hundredth, if necessary.
15.
x y
3 7
4 6
5 6
8 2
9 3
Answers will vary but should be close to the equation y � �0.79x � 9.39.
16.
x y
5 0
4 2
3 3
2 5
9 3
Chapter 6 ● Skills Practice 497
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17.
x y
6 30
5 40
4 80
3 80
2 90
18.
x y
10 100
8 75
9 110
5 200
3 400
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Use the graphing calculator screenshot to write the corresponding linear regression equation. Then use the linear regression equation to answer each question.
19. You collect information from college freshmen asking them the number of classes they
miss per week, x, and their grade point average, y, on a scale from 0 to 4.0. The screenshot
below shows the graphing calculator output when determining the linear regression
equation for these data.
y � ax � b
a � �0.211
b � 3.78
r2 � 0.963
r � �0.981
If a freshman maintains a 3.5 GPA in college, what is the expected maximum number of
classes that he or she could miss per week?
y � �0.211x � 3.78
3.5 � �0.211x � 3.78
�0.28 � �0.211x
x � 1.33
He or she could miss at most 1 class per week, because missing more than 1.33 classes would bring his or her GPA down below 3.5.
Chapter 6 ● Skills Practice 499
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20. A deli owner records the number of sandwiches they made, x, and the number of pounds
of meat used, y. The screenshot below shows the graphing calculator output when
determining the linear regression equation for these data.
y � ax � b
a � 0.126
b � �0.106
r2 � 0.995
r � 0.997
If the deli has 40 sandwich orders to fill, how many pounds of meat should they buy, if they
buy meat in tenth-of-a-pound increments?
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21. A magazine editor records the number of pages of advertising the firm sells per issue, y,
and the number of celebrities featured in that issue, x. The screenshot below shows the
graphing calculator output when determining the linear regression equation for these data.
y � ax � b
a � 29.86
b � 25.59
r2 � 0.995
r � 0.998
If the magazine features 7 celebrities in one issue, at least how many pages of advertising
can they expect to sell?
22. A photographer records the number of megabytes used on his computer’s hard drive, y,
and the number of photos stored, x. The screenshot below shows the graphing calculator
output when determining the linear regression equation for these data.
y � ax � b
a � 6.102
b � �74.31
r2 � 0.973
r � 0.987
If the photographer wants to limit the total photo files on his computer to 8000 megabytes,
what is the greatest number of photos he should store on his computer?
Chapter 6 ● Skills Practice 501
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Skills Practice Skills Practice for Lesson 6.7
Name _____________________________________________ Date _________________________
Making a QuiltScatter Plots and Non-Linear Data
Vocabulary Write the term that best completes each statement.
1. A(n) is a graph that shows ordered pairs.
2. The of a rectangle is equal to the product of its length and width.
3. The of a set of data shows how close the data are to forming a
straight line.
4. A(n) is used to approximate data as close to as many points as
possible.
5. The of a rectangle is equal to the sum of twice its width and twice
its length.
Problem Set Write the set of ordered pairs from each table.
1. 2.
x y x y
1 3 0 5
2 6 2 7
3 9 4 9
(1, 3), (2, 6), (3, 9)
3. 4.
x y x y
1 9 2 1
3 13 3 4
7 21 6 13
12 31 11 28
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5. 6.
x y x y
21 145 10 200
33 99 9 125
45 62 8 70
57 50 7 0
Create a scatter plot of the ordered pairs in each table.
7. Create a scatter plot that shows the length of the patio as a function of the patio’s width.
Width of Patio Length of Patio
feet feet
6 12
8 16
10 20
12 24
0 2 4 6 8 10 12 14 16 18 20
3
6
9
12
15
18
21
24
27
30
Width of Patio (feet)
Len
gth
of
Pat
io (
feet
)
x
y
8. Create a scatter plot that shows the perimeter of the door as a function of its length.
Length of Door Perimeter of Door
inches inches
76 204
80 220
84 236
88 252
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9. Create a scatter plot that shows the amount of money earned as a function of the time
worked.
Time Worked Money Earned
hours dollars
10 85
15 127.5
25 212.5
40 340
10. Create a scatter plot that shows the profit as a function of the number of T-shirts sold .
T-shirts Sold Profi t
T-shirts dollars
100 500
200 2000
350 4250
650 8750
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11. Create a scatter plot that shows the area of the picture frame as a function of its width.
Width of Picture Frame
Area of Picture Frame
inches square inches
5 35
8 89.6
10 140
15 315
12. Create a scatter plot that shows the area of the floor as a function of its length.
Length of Floor Area of Floor
feet square feet
10 80
12 120
14 168
16 224
13. Create a scatter plot that shows the area inside of the fence as a function of its perimeter.
Perimeter of Fence
Area Inside of Fence
meters square meters
10 100
15 225
20 400
25 625
Chapter 6 ● Skills Practice 505
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14. Create a scatter plot that shows the area of the poster as a function of its perimeter.
Perimeter of Poster Area of Poster
inches square inches
10 200
12 288
16 512
20 800
Use a ruler to draw a line of best fit on each graph.
15.
2 4 6 8 10 12 14 16 18 20
1
2
3
4
5
6
7
8
9
10
Length (meters)
Wid
th (
met
ers)
y
x0
16.
1 2 3 4 5 6 7 8 9 10
3
6
9
12
15
18
21
24
27
30
Width (inches)
Leng
th (
inch
es)
y
x0
17.
1 2 3 4 5 6 7 8 9 10
2000
4000
6000
8000
10,000
12,000
14,000
16,000
18,000
20,000
Time (years)
Sal
es (
dolla
rs)
y
x0
18.
2 4 6 8 10 12 14 16 18 20
100
200
300
400
500
600
700
800
900
1000
Time (months)
Pro
fit (
dolla
rs)
y
x0
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A scatter plot and its line of best fit are shown on each graph. Write the equation of the line of best fit.
19.
5 10 15 20 25 30 35 40 45 50
200
400
600
800
1000
1200
1400
1600
1800
2000
Ticket Price (dollars)
Atte
ndan
ce
x
y
0
20.
200 400 600 800 1000
200
400
600
800
1000
1200
1400
1600
1800
2000
Number of Units ProducedO
pera
ting
Cos
ts (
dolla
rs)
x
y
0
Line of best fit should be close to y � �43x � 2329.
21.
0 500 1000 1500 2000 2500
2000
4000
6000
8000
10,000
12,000
14,000
16,000
18,000
20,000
Number of Units Sold
Rev
enue
(do
llars
)
x
y 22.
0 1 2 3 4 5 6 7 8 9 10
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Time (years)
Pop
ulat
ion
y
x
Chapter 6 ● Skills Practice 507
Name _____________________________________________ Date _________________________
6
© 2
010 C
arn
eg
ie L
earn
ing
, In
c.
Create a scatter plot of the ordered pairs in each table and draw a smooth curve through the points.
23.
Width Area
centimeters square centimeters
1 3
2 12
4 48
6 108
7 147
8 192
1 2 3 4 5 6 7 8 9 10
20
40
60
80
100
120
140
160
180
200
Width (centimeters)
Are
a (s
qu
are
cen
tim
eter
s)
y
x0
24.
Length Area
feet square feet
0 0
5 20
10 80
15 180
20 320
25 500
25.
Length Area
meters square meters
2 4
3 9
4 16
5 25
6 36
7 49
508 Chapter 6 ● Skills Practice
6©
2010 C
arn
eg
ie L
earn
ing
, In
c.
26.
Width Area
inches square inches
1 6
3 24
5 50
6 66
8 104
10 150
