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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