Scatter Plots and
Correlations
Is there a relationship
between the amount of
gas put in a car and the
number of miles that can
be driven?
Positive Correlation
As one set of data values increases, so
does the other.
Positive Correlation
20
18
16
14
12
10
8
6
4
2
0
0
2
4
6
8
10
12
Is there a relationship between
the number of things you buy
at the mall and the amount of
money you have left?
Negative Correlation
As one set of data values increases, the
other decreases.
Negative Correlation
25
20
15
10
5
0
0
2
4
6
8
10
Is there a relationship between a
person’s age and the temperature
outside?
No Correlation
There is no relationship between the
two sets of data.
No Correlation
25
20
15
10
5
0
0
5
10
15
Would a scatter plot show a
positive,negative, or no
correlation?
Number of pages printed by a printer
and the amount of ink left in the
cartridge.
– Negative Correlation!
Would a scatter plot show a
positive,negative, or no
correlation?
Age of a child and the child’s shoe size
– Positive Correlation!
Would a scatter plot show a
positive,negative, or no
correlation?
Number of letters in a person’s first
name and the person’s height.
– No Correlation!
Would a scatter plot show a
positive,negative, or no
correlation?
Shots attempted and the number of
points made in a basketball game
– Positive Correlation!
Would a scatter plot show a
positive,negative, or no
correlation?
Length of a taxi ride and the amount of
the fare
– Positive Correlation!
Would a scatter plot show a
positive,negative, or no
correlation?
Outside temperature and the cost of air
conditioning.
– Positive Correlation!
Would a scatter plot show a
positive,negative, or no
correlation?
Miles ridden on a bicycle and the
thickness of the tire tread
– Negative Correlation!
Would a scatter plot show a
positive,negative, or no
correlation?
Temperature outside and the amount of
clothing a person wears
– Negative Correlation!
Think of some situations that
show a….
Positive Correlation:
Negative Correlation:
No Correlation:
Which graph to use…..?
Use bar graphs to make comparisons.
Use line graphs to show change over time.
Use circle graphs to show percentage of a
whole.
Use histograms when the data is arranged in
intervals.
Use scatter plots to show correlations
between two sets of numerical data.
Correlation Coefficient
Scatterplot displays the strength,
direction, and form of the relationship
between two quantitative variables.
A correlation coefficient measures the
strength of that relationship.
Correlation Coefficient Strength
Go to stat key and choose 1 Edit.
Enter the data into lists L1 and L2
on a graphing calculator. To clear
an existing list arrow up to L1 and
press clear and arrow down. The
list will be cleared. Use the linear
regression feature by pressing
STAT, choosing CALC, and
selecting 4:LinReg. The equation
of the line of best fit will appear.
Example 2: Anthropology Application
Anthropologists can
use the femur, or
thighbone, to estimate
the height of a human
being. The table shows
the results of a
randomly selected
sample.
Example 2 Continued
a. Make a scatter
plot of the data
with femur
length as the
independent
variable.
The scatter plot is
shown at right.
•
•• •
•
•• •
Example 2 Continued
b. Find the correlation coefficient r and the
line of best fit. Interpret the slope of the
line of best fit in the context of the problem.
Enter the data into lists L1
and L2 on a graphing
calculator. Use the linear
regression feature by
pressing STAT, choosing
CALC, and selecting
4:LinReg. The equation of
the line of best fit is
h ≈ 2.91l + 54.04.
Example 2 Continued
The slope is about 2.91, so for each 1 cm
increase in femur length, the predicted increase
in a human being’s height is 2.91 cm.
The correlation coefficient is r ≈ 0.986 which
indicates a strong positive correlation.
Example 2 Continued
c. A man’s femur is 41 cm long. Predict the
man’s height.
The equation of the line of best fit is
h ≈ 2.91l + 54.04. Use the equation to predict the
man’s height.
For a 41-cm-long femur,
h ≈ 2.91(41) + 54.04 Substitute 41 for l.
h ≈ 173.35
The height of a man with a 41-cm-long femur
would be about 173 cm.