Chapter 6 Skills Practice 441

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Skills Practice Skills Practice for Lesson 6.1

Name _____________________________________________ Date _________________________

Mias 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 changeof 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 setclose 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 setunits 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 fitand 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.

Beagles Weight (female)

Age (weeks) Weight (kg)

6 1.0

12 3.0

16 4.5

24 6.5

30 8.0

Beagles 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)

Beagles Weight (Female)

Wei

gh

t (k

g)

Chapter 6 Skills Practice 443

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3. 4.

Chihuahuas Weight (male)

Age (weeks) Weight (oz)

6 15

12 30

16 39

24 46

30 51

Chihuahuas Weight (female)

Age (weeks) Weight (oz)

6 11

12 19

16 25

20 30

24 33

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5. 6.

Dalmatians Weight

Age (weeks) Weight (kg)

8 6.5

12 11.5

16 15.4

20 21.5

25 24.5

Pomeranians 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

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y

x2520

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5

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9. 10.

x2520

15

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10

10

150 5

5

y

x2520

15

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10

10

150 5

5

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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

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10

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5

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x2520

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5

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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

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x2520

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5

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Chapter 6 Skills Practice 447

Name _____________________________________________ Date _________________________

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Use the given equation to answer each question.

15. A grocery stores 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?

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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

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allo

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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

Name _____________________________________________ Date _________________________

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Estimate the equation of the line of best fit shown in each scatter plot.

5.

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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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8

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12 140 2 4 6

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8

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4

6

2

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8.

x2016 18

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8 10

8

10

12 140 2 4 6

4

6

2

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Chapter 6 Skills Practice 453

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9.

x2016 18

12

14

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20

8 10

8

10

12 140 2 4 6

4

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2

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10.

x2016 18

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20

8 10

8

10

12 140 2 4 6

4

6

2

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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 companys 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 artists 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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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 sisters 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

Name _____________________________________________ Date _________________________

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4. A fundraiser uses telemarketers to raise money. Every so often, they stop to determine how many phone calls theyve made and how much money theyve 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.

x2016 18

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20

8 10

8

10

12 140 4 62

4

6

2

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

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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4

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y

Chapter 6 Skills Practice 465

Name _____________________________________________ Date _________________________

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7.

x2016 18

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20

8 10

8

10

12 140 4 62

4

6

2

y

8.

x2016 18

12

14

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18

20

8 10

8

10

12 140 4 62

4

6

2

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 doesnt want to pay more than $60 a month for electricity. Should he rent this apartment?

11. Alice and Monique run a race. Alices distance in meters can be approximated using the equation a 6x and Moniques 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. Franciss distance in meters can be approximated by the equation f 9.09x and Marios 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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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.

x2016 18

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8 10

8

10

12 140 4 62

4

6

2

y 2.

x2520

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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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8 10

8

10

12 140 4 62

4

6

2

y 4.

x2016 18

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8

10

12 140 4 62

4

6

2

y

Chapter 6 Skills Practice 473

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5.

x2016 18

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14

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18

20

8 10

8

10

12 140 4 62

4

6

2

y 6.

x2016 18

12

14

16

18

20

8 10

8

10

12 140 4 62

4

6

2

y

7.

x2016 18

12

14

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18

20

8 10

8

10

12 140 4 62

4

6

2

y 8.

x2016 18

12

14

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18

20

8 10

8

10

12 140 4 62

4

6

2

y

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9.

x2016 18

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20

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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

Name _____________________________________________ Date _________________________

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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 gazelles 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 friends 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?

Chapter 6 Skills Practice 481

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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

Name _____________________________________________ Date _________________________

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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

Name _____________________________________________ Date _________________________

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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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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-interceptnumber 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 coefficientthe 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 friends 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 Linos 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

Name _____________________________________________ Date _________________________

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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 computers 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?

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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 patios 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

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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

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26.

Width Area

inches square inches

1 6

3 24

5 50

6 66

8 104

10 150