EVALUATE

Evaluate: Homework and Practice

EVALUATE

Estimate the value of r. Indicate whether r is closest to -1, -0.5, 0, 0.5 or 1 for the following data sets.

1.

1

8

1.

2

4.037522

1.

3

7.200593

1.

4

4.180245

1.

5

Explore Describing How Variables are Related in Scatter Plots

Exercises 21–22

4.763788

1.

6

1

0

7

1.047031

Example 1 Estimating the Correlation Coefficient of a Linear Fit

Exercises 1–4, 25

8

2.436249

9

1.844607

Example 2 Fitting Linear Functions to Data

Exercises 5–8, 20, 24

Example 3 Using Linear Functions Fitted to Data to Solve Problems

Exercises 9–12, 19

Example 4 Distinguishing Between Correlation and Causation

Exercises 13–18, 23

AVOID COMMON ERRORS Students may think that a positive r-value indicates a stronger correlation than a negative r-value. Explain that the strength of a correlation is determined by the absolute value of r. For example, r-values of -0.8 and 0.8 indicate correlations of equal strength.

2.

The table below presents exam scores earned by six students and how long they each studied.

Hours of Study

Exam Score

2

63

2

71

2.5

75

3

67

4.5

82

5

95

x

1 2 3 4 5 Studying time (hours)

The value of r for this data is closest to 1. 3.

y

95 90 85 80 75 70 65 60 55 50 0

Raymond opens a car wash and keeps track of his weekly earnings, as shown in the table

Weeks after Opening

Earnings ($)

0

1050

1

1700

2

2400

3

2000

4

3500

5

3600

Module 10

Exercise

A1_MNLESE368170_U4M10L1.indd 443

Lesson 10.1

x 1 2 3 4 5 6 7 8 9

The value of r for this data is closest to -0.5.

3500 3000 2500 2000 1500 1000 0

y

x 1 2 3 4 5

Weeks after opening

The value of r for this data is closest to 1.

443

y

Test score (%)

Practice

© Houghton Mifflin Harcourt Publishing Company

Concepts and Skills

y

Weekly revenue (dollars)

ASSIGNMENT GUIDE

x

9 8 7 6 5 4 3 2 1

1.

• Online Homework • Hints and Help • Extra Practice

443

Lesson 1

Depth of Knowledge (D.O.K.)

Mathematical Practices

1

1 Recall of Information

MP.6 Precision

2–4

1 Recall of Information

MP.4 Modeling

5

1 Recall of Information

MP.6 Precision

6–8

1 Recall of Information

MP.4 Modeling

9

1 Recall of Information

MP.6 Precision

6/8/15 6:07 PM

Rafael is training for a race by running a mile each day. He tracks his progress by timing each trial run.

Trial

Run Time (min)

1

8.2

2

8.1

3

7.5

4

7.8

5

7.4

6

7.5

7

7.1

8

7.1

Run time (min)

4.

8.2 8.0 7.8 7.6 7.4 7.2 7.0 0

y

x 1 2 3 4 5 6 7 Training run

The value of r for this data is closest to -1.

Determine a line of fit for the data, and write the equation of your line. y

1

7.15

2

8.00

3

4.81

4

7.14

5

3.56

9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00

6

2.12

0

7

1.00

8

3.76

9

1.42

_ _ _ _

Test Score (%)

2

63

1.

2

71

1.

2.5

75

1.

3

67

1.

4.5

82

1.

5

95

Possible answer: 90 - 50 m= =8 5-0

_

Exercise

95 90 85 80 75 70 65 60 55 50 0

y

x 1 2 3 4 5

Studying time (hours)

y = 8x + 50

Module 10

A1_MNLESE368170_U4M10L1.indd 444

x 1 2 3 4 5 6 7 8 9

Possible answer: 2-6 -4 = m= 5 8-3 42 4 y= - x+ or y = -0.8x + 8.4 5 5

Studying Time (Hours)

1.

y

© Houghton Mifflin Harcourt Publishing Company

6.

x

Test score (%)

5.

Lesson 1

444

Depth of Knowledge (D.O.K.)

Mathematical Practices

10–12

1 Recall of Information

MP.4 Modeling

13–19

2 Skills/Concepts

MP.3 Logic

20–21

2 Skills/Concepts

MP.6 Precision

22

2 Skills/Concepts

MP.4 Modeling

23–25

2 Skills/Concepts

MP.3 Logic

6/8/15 6:07 PM

Scatter Plots and Trend Lines

444