2.6
Draw Scatter Plots and
Best Fitting Lines
p Fit lines to data in scatter plots.
Goal
Your Notes
VOCABULARY
Scatter plot
Positive correlation
Negative correlation
Correlation coefficient
Best-fitting line
Example 1
Estimate correlation coefficients
For each scatter plot, describe the correlation shown
and tell whether the correlation coefficient is closest to
21, 20.5, 0, 0.5, or 1.
a.
b.
y
1
y
1
1
x
x
1
Solution
a. The scatter plot shows a
So, the best estimate given is r 5
correlation.
.
correlation.
b. The scatter plot shows a
So, r is between
and
but not too close to either
one. The best estimate given is r 5
.
Copyright © Holt McDougal. All rights reserved.
Lesson 2.6 • Algebra 2 Notetaking Guide
47
2.6
Draw Scatter Plots and
Best Fitting Lines
p Fit lines to data in scatter plots.
Goal
Your Notes
VOCABULARY
Scatter plot A graph of a set of data pairs (x, y)
Positive correlation The relationship between paired
data when y tend to increase as x increases
Negative correlation The relationship between paired
data when y tends to decrease as x increases
Correlation coefficient A number, denoted by r, from
21 to 1 that measures how well a line fits a set of
data pairs (x, y)
Best-fitting line The line that lies as close as
possible to all the data points
Example 1
Estimate correlation coefficients
For each scatter plot, describe the correlation shown
and tell whether the correlation coefficient is closest to
21, 20.5, 0, 0.5, or 1.
a.
b.
y
1
y
1
1
x
1
x
Solution
a. The scatter plot shows a strong negative correlation.
So, the best estimate given is r 5 21 .
b. The scatter plot shows a weak positive correlation.
So, r is between 0 and 1 but not too close to either
one. The best estimate given is r 5 0.5 .
Copyright © Holt McDougal. All rights reserved.
Lesson 2.6 • Algebra 2 Notetaking Guide
47
Your Notes
APPROXIMATING A BEST-FITTING LINE
of the data.
Step 1 Draw a
that appears to follow most
Step 2 Sketch the
closely the trend given by the data points. There
the
should be about as many points
line as
it.
on the line, and estimate
Step 3 Choose
the coordinates of each point.
of the line that passes
Step 4 Write an
through the two points from Step 3.
Approximating a best-fitting line
Example 2
The table below gives the number of people y who
atended each of the first seven football games x of the
season. Approximate the best-fitting line for the data.
1
2
3
4
5
6
7
y
722
763
772
826
815
857
897
1. Draw a
.
2. Sketch the best-fit line.
3. Choose two points on the
line. For the scatter plot
shown, you might choose
) and (2,
).
(1,
Number of people
Be sure that about
the same number
of points lie above
your line of fit as
below it.
x
y
900
850
800
750
700
650
0
0 1 2 3 4 5 6 7 x
Football game
4. Write an equation of the line. The line that passes
through the two points has a slope of:
m5
5
Use the point-slope form to write the equation.
y 2 y1 5 m(x 2 x1)
5
y2
y5
Point-slope form
Substitute for m, x1, and y1.
Simplify.
An approximation of the best-fitting line is
y5
.
48
Lesson 2.6 • Algebra 2 Notetaking Guide
Copyright © Holt McDougal. All rights reserved.
Your Notes
APPROXIMATING A BEST-FITTING LINE
Step 1 Draw a scatter plot of the data.
Step 2 Sketch the line that appears to follow most
closely the trend given by the data points. There
should be about as many points above the
line as below it.
Step 3 Choose two points on the line, and estimate
the coordinates of each point.
Step 4 Write an equation of the line that passes
through the two points from Step 3.
Approximating a best-fitting line
Example 2
The table below gives the number of people y who
atended each of the first seven football games x of the
season. Approximate the best-fitting line for the data.
1
2
3
4
5
6
7
y
722
763
772
826
815
857
897
1. Draw a scatter plot .
2. Sketch the best-fit line.
3. Choose two points on the
line. For the scatter plot
shown, you might choose
(1, 722 ) and (2, 750 ).
Number of people
Be sure that about
the same number
of points lie above
your line of fit as
below it.
x
y
900
850
800
750
700
650
0
0 1 2 3 4 5 6 7 x
Football game
4. Write an equation of the line. The line that passes
through the two points has a slope of:
m5
750 2 722
221
5 28
Use the point-slope form to write the equation.
y 2 y1 5 m(x 2 x1)
Point-slope form
y 2 722 5 28(x 2 1)
y 5 28x 1 694
Substitute for m, x1, and y1.
Simplify.
An approximation of the best-fitting line is
y 5 28x 1 694 .
48
Lesson 2.6 • Algebra 2 Notetaking Guide
Copyright © Holt McDougal. All rights reserved.
Your Notes
Use a line of fit to make predictions
Example 3
Use the equation of the line of best fit from Example
2 to predict the number of people that will attend the
tenth football game.
Because you are predicting the tenth game, substitute
for x in the equation from Example 2.
5
y5
5
people will attend the tenth
You can predict that
football game.
Checkpoint Complete the following exercises.
For each scatter plot (a) tell whether the data
has positive correlation, negative correlation, or
no correlation, and (b) tell whether the correlation
coefficient is closest to 21, 20.5, 0, 0.5, or 1.
1.
2.
y
1
y
1
x
1
x
1
3. The table gives the average class score y on each
chapter test for the first six chapters x of the
textbook.
x
1
2
3
4
5
6
y
84
83
86
88
87
90
Homework
b. Use your equation from part
(a) to predict the test score
for the 9th test that the
class will take.
Average class score
a. Approximate the best-fitting line for the data.
y
90
88
86
84
82
0
0 1 2 3 4 5 6 x
Test
Copyright © Holt McDougal. All rights reserved.
Lesson 2.6 • Algebra 2 Notetaking Guide
49
Your Notes
Use a line of fit to make predictions
Example 3
Use the equation of the line of best fit from Example
2 to predict the number of people that will attend the
tenth football game.
Because you are predicting the tenth game, substitute
10 for x in the equation from Example 2.
y 5 28x 1 694 5 28(10) 1 694 5 974
You can predict that 974 people will attend the tenth
football game.
Checkpoint Complete the following exercises.
For each scatter plot (a) tell whether the data
has positive correlation, negative correlation, or
no correlation, and (b) tell whether the correlation
coefficient is closest to 21, 20.5, 0, 0.5, or 1.
1.
2.
y
1
y
1
x
1
x
1
a. positive correlation
b. 1
a. no correlation
b. 0
3. The table gives the average class score y on each
chapter test for the first six chapters x of the
textbook.
x
1
2
3
4
5
6
y
84
83
86
88
87
90
Homework
b. Use your equation from part
(a) to predict the test score
for the 9th test that the
class will take.
a. y 5 1.3x 1 82.1
b. about 94
Copyright © Holt McDougal. All rights reserved.
Average class score
a. Approximate the best-fitting line for the data.
y
90
88
86
84
82
0
0 1 2 3 4 5 6 x
Test
Lesson 2.6 • Algebra 2 Notetaking Guide
49