Lesson 9.1 Assignment - d3jc3ahdjad7x7.cloudfront.net · Chapter 9 Assignments 121 9 Lesson 9.2...

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Chapter 9 Assignments 115

9

Lesson 9.1 Assignment

Name Date

Like a GloveLeast Squares Regression

Mr. Li is a math teacher at Pinkston High School and is preparing his students to take the SAT test. He collected data from 10 students who took the test last year and presented this information to the students in a table. The highest math SAT score a student can achieve is 800.

Time Spent Studying (hours)

Math SAT Score

1 350

22 780

12 600

14 700

4 380

10 650

9 580

3 400

7 530

4 410

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116 Chapter 9 Assignments

9

1. Analyze the data.

a. Construct a scatter plot of the data and describe any patterns you see in the data.

0 4 8 12 16 20 24 28 32 36x

y

400

500

200

300

100

600

700

800

900

b. Determine the equation of a line passing through (14, 700) and (7, 530). Then determine the equation of a line passing through (22, 780) and (4, 380). Graph both lines on the same graph as the scatter plot.

c. Which line seems to best fit the data? Would you use either one of these lines to make predictions about a student’s math SAT score based on the amount of studying they do? Why or why not?

Lesson 9.1 Assignment page 2

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9d. Calculate the regression line for this problem situation. Complete the table below to help with the

calculations.

x y xy x2

1 350

22 780

12 600

14 700

4 380

10 650

9 580

3 400

7 530

4 410

Sx 5 86 Sy 5 5380 Sxy 5 Sx 25

e. Interpret the least squares regression equation in terms of the problem situation.


Name Date

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f. Use the regression line to predict the math SAT score for a student who studies for 17 hours. Did you use interpolation or extrapolation to make this prediction? Is this prediction reasonable for this problem situation? Explain your reasoning.

g. Use the line of best fit to predict the math SAT score for a student who studies for 40 hours. Did you use interpolation or extrapolation to make this prediction? Is this prediction reasonable for this problem situation? Explain your reasoning.

h. One of Mr. Li’s students comes back to him the following year and says that he studied for 15 hours for the math SAT and got a score of 610. He argues that the equation predicted that he would have scored a 682. What do you think explains the discrepancy?


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9Gotta Keep It Correlatin’Correlation

1. The table shows the percent of the United States population who did not receive needed dental care services due to cost.

Year 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Percent 7.9 8.1 8.7 8.6 9.2 10.7 10.7 10.8 10.5 12.6 13.3

a. Do you think a linear regression equation would best describe this situation? Explain your reasoning.

b. Determine the linear regression equation for these data. Interpret the equation in terms of this problem situation.

c. Determine and interpret the correlation coefficient of this data set. Does it seem appropriate to use a line of best fit? Explain your reasoning.


Name Date

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d. Sketch a scatter plot of the data. Then, plot the equation of the regression line on the same grid. Do you still think a linear regression is appropriate? Explain your answer.

0 1 2 3 4 5 6 7 8 9x

y

8

10

4

6

2

12

14

16

18

2. The table shows the percent of adults (18-64 years of age) in the United States who delayed or did not receive needed medical care due to cost.

Year 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Percent 9.2 9.2 9.5 9.7 10.6 11.4 11.0 11.7 11.8 13.6 15.1

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Name Date

a. Sketch the scatter plot for this data. Do you think a linear regression equation would best describe this situation? Explain your reasoning.

0 1 2 3 4 5 6 7 8 9x

y

8

10

4

6

2

12

14

16

18

b. Determine the least squares regression equation and the correlation coefficient r. Interpret both in terms of the problem situation.

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c. Graph the linear regression equation on the same grid as the scatter plot. Would you use this linear regression equation to make a prediction about the percent of adults that will delay or not receive needed medical care in 2010? Explain your reasoning.

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9The Residual EffectCreating Residual Plots

1. A manager of a telemarketing firm is trying to increase his employees’ productivity. The table shown indicates the number of months the employees have been working and the number of calls they successfully complete with customers per day.

EmployeeNumber of Months

of EmploymentObserved Number of

Successful Calls

A 10 18

B 10 19

C 11 22

D 14 23

E 15 25

F 17 27

G 18 28

H 20 28

I 20 31

J 21 31

K 22 32

L 22 33

M 24 31

N 25 31

O 25 32

P 25 33

Q 28 33

R 29 33

S 30 34


Name Date

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a. Construct a scatter plot of the data.

0 4 8 12 16 20 24 28 32 36x

y

16

20

8

12

4

24

28

32

36

b. Based on the shape of the scatter plot, is linear regression appropriate? What type of correlation appears to be present?

c. Write a function c(m) to represent the line of best fit. Then interpret the function in terms of the problem situation.

d. Determine and interpret the correlation coefficient.

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Name Date

e. Complete the table to determine the residuals for the employee data.

Number of Months of

Employment

Observed Number of Successful Calls

Predicted Number of Successful Calls

Residual Value

10 18

10 19

11 22

14 23

15 25

17 27

18 28

20 28

20 31

21 31

22 32

22 33

24 31

25 31

25 32

25 33

28 33

29 33

30 34

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f. Create a scatter plot of the months employed versus the residual value.

4 8 12 16 20 24 28 32 36x

y

–0.8

0

–2.4

–1.6

–3.2

0.8

1.6

2.4

3.2

g. Based on the residual plot, is a linear model appropriate for the data? Explain your reasoning.

h. Should the manager use a linear regression equation to predict how many successful calls an employee will make if they have been employed for 36 months? Explain your reasoning.

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9To Fit or Not To Fit? That Is The Question!Using Residual Plots

1. The value of a new car starts to depreciate the minute a new owner drives it off the lot. The table shows the values of 15 used cars and their ages.

Age of Car (years) Price (dollars)

1 11,500

1 13,000

2 10,500

3 9500

3 9100

4 8000

4 7000

5 7500

6 6000

6 5100

9 3000

9 2200

11 3000

11 2900

13 2500


Name Date

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a. Construct a scatter plot of the data.

0 2 4 6 8 10 12 14 16 18x

y

6000

7500

3000

4500

1500

9000

10,500

12,000

13,500

b. Write a function P(x) to represent the line of best fit for the data. Graph and then interpret the line of best fit in terms of the problem situation.

c. Does the line of best fit appear to be a good model for this data set? Explain your reasoning.


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Name Date

d. Calculate the residuals for the data. Round to the nearest whole number.

Age of Car (years) Observed Value (dollars) Predicted Value Residual

1 11,500

1 13,000

2 10,500

3 9500

3 9100

4 8000

4 7000

5 7500

6 6000

6 5100

9 3000

9 2200

11 3000

11 2900

13 2500

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e. Create a residual plot of the data.

2 4 6 8 10 12 14 16 18x

y

–500

0

–1500

–1000

–2000

500

1000

1500

2000

f. Based on the residual plot, do you think a linear model is a good fit for the data? Why or why not?

g. The quadratic function f(x) 5 79.3x 2 2 1927.9x 1 14,192.1 also represents this data set. Graph this function on the same graph as the scatter plot and line of best fit. Does it appear to fit the data better than the line of best fit?


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Name Date

h. Complete the table of residuals for the quadratic function f(x).

Age of Car (years) Observed Price (dollars) Predicted Value Residual

1 11,500

1 13,000

2 10,500

3 9500

3 9100

4 8000

4 7000

5 7500

6 6000

6 5100

9 3000

9 2200

11 3000

11 2900

13 2500

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i. Then create a residual plot of the data. What does the residual plot tell you about the quadratic model used for the data?

2 4 6 8 10 12 14 16 18x

y

–250

0

–750

–500

–1000

250

500

750

1000


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9Who Are You? Who? Who?Causation vs. Correlation

1. A teacher claims that students who study will receive good grades.

a. Do you think that studying is a necessary condition for a student to receive good grades?

b. Do you think that studying is a sufficient condition for a student to receive good grades?

c. Do you think that there is a correlation between students who study and students who receive good grades?

d. Do you think that it is true that studying will cause a student to receive good grades?

e. List two or more confounding variables that could have an effect on this claim.

2. It has been said that watching TV causes brain damage.

a. Do you think that watching TV is a necessary condition for a person to become brain damaged?

b. Do you think that watching TV is a sufficient condition for a person to become brain damaged?

c. Do you think that there is a correlation between watching TV and becoming brain damaged?


Name Date

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d. Do you think that it is true that watching TV will cause a person to become brain damaged?

e. List two or more common responses that may also cause the result of brain damage.

3. For each of the following situations, decide whether the correlation implies causation. List reasons why or why not.

a. The number of violent video games sold in the U.S. is highly correlated to crime rates in real life.

b. The number of newspapers sold in a city is highly correlated to the number of runs scored by the city’s professional baseball team.

c. The number of mouse traps found in a person’s house is highly correlated to the number of mice found in their house.


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Lesson 9.1 Assignment - d3jc3ahdjad7x7.cloudfront.net · Chapter 9 Assignments 121 9 Lesson 9.2...

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