NAME DATE PERIOD 4-5 Study Guide and Intervention

NAME

DATE

PERIOD

4-5 Study Guide and Intervention

Scatter Plots and Lines of Fit

Investigate Relationships Using Scatter Plots A scatter plot is a graph in

which two sets of data are plotted as ordered pairs in a coordinate plane. If y increases as x increases, there is a positive correlation between x and y. If y decreases as x increases, there is a negative correlation between x and y. If x and y are not related, there is no correlation.

Example EARNINGS The graph at the right shows the amount of money Carmen earned each week and the amount she deposited in her savings account that same week. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

The graph shows a positive correlation. The more Carmen earns, the more she saves.

Dollars Saved

Carmen's Earnings and Savings

35 30 25 20 15 10 5

0

40 80 120

Dollars Earned

Exercises

Determine whether each graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

1. Average Weekly Work Hours in U.S.

34.6 34.4 34.2 34.0 33.8 33.6

Hours

0 1 23 4 5 67 8 9 Years Since 1995

Source: The World Almanac

no correlation

Hourly Earnings ($)

3. Average U.S. Hourly Earnings

19 18 17 16 15 0

12345

Years Since 2003 Source: U.S. Dept. of Labor

Positive correlation; as years increase, the average weekly work hours also increase.

Miles per Hour

2. Average Jogging Speed

10 5

0 5 10 15 20 25 Minutes

Negative correlation; as time increases, speed decreases.

4. U.S. Imports from Mexico Positive

Imports ($ billions)

220

correlation;

190

as years

160 130

0 12345

increase, the amount of imports

Years Since 2003

also

Source: U.S. Census Bureau

increase.

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 4

30

Glencoe Algebra 1

NAME

DATE

PERIOD

4-5 Study Guide and Intervention (continued)

Scatter Plots and Lines of Fit

Use Lines of Fit

Example The table shows the number of students per computer in Easton High School for certain school years from 1996 to 2008.

Year

1996 1998 2000 2002 2004 2006 2008

Students per Computer 22

18

14

10

6.1

5.4

4.9

Students per Computer

a. Draw a scatter plot and determine what relationship exists, if any.

Since y decreases as x increases, the

24

correlation is negative.

20

b. Draw a line of fit for the scatter plot.

16

12

Draw a line that passes close to most of the points.

8

A line of fit is shown.

4

Students per Computer in Easton High School

c. Write the slope-intercept form of an equation for the line of fit.

0 1996 1998 2000 2002 2004 2006 2008 Year

The line of fit shown passes through (1999, 16) and (2005, 5.7). Find the slope.

m = - 2050.75 -- 116999

m = -1.7

Find b in y = -1.7x + b.

16 = -1.7 ? 1993 + b

3404 = b

Therefore, an equation of a line of fit is y = -1.7x + 3404.

Exercises

Refer to the table for Exercises 1?3.

1. Draw a scatter plot.

2. Draw a line of fit for the data.

3. Write the slope-intercept form of an equation for the line of fit.

The points (0, 5.08) and (3, 5.81) give y = 0.243x + 5.08 as a line of fit.

Movie Admission Prices

6.2 6

5.8 5.6 5.4 5.2

5

0 12345 Years Since 1999

Source: U.S. Census Bureau

Years

Admission

Since 1999 (dollars)

0

$5.08

1

$5.39

2

$5.66

3

$5.81

4

$6.03

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Admission ($)

Lesson 4-5

Chapter 4

31

Glencoe Algebra 1

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