Scatterplots
Chapter 7
Definition and components
Describing
Correlation
Correlation vs. Association
I. Scatterplots
• A graph that plots the
relationship between
two quantitative
variables.
• Used to see if a
relationship exists
between the two
variables.
I. Scatterplots
• Explanatory Variable
– x- value
– Predictor
– Input
– Independent
• Response Variable
– Y-value
– Output
– Dependent
II. Creating a Scatterplot
• Enter all x-variables in
L1, and all y-variables
in L2.
• Turn on Statplot and
go to
• Use ZoomStat to
obtain graph.
• Use Trace to get
specific points
• Scale and label axes.
• I:\Math
Department\TI-84Emulator\Wabbitemu.
exe
Does fast driving waste fuel?
Speed
(km/h)
Fuel used
(L/100km)
Speed
(km/h)
Fuel used
(L/100km)
10
21.00
90
7.57
20
13.00
100
8.27
30
10.00
110
9.03
40
8.00
120
9.87
50
7.00
130
10.79
60
5.90
140
11.77
70
6.30
150
12.83
80
6.95
• Make scatterplot in calculator.
• Transfer information onto your paper, make
sure to add labels and scale for x & y-axis.
Now try on your own.
Either by hand or in the calculator,
create a scatterplot of the data on Age
at First Word vs. Gesell Score.
A score of 100 is considered to be
average.
III. Describing Scatterplots
• Direction
– Positive
– Negative
• Form
–
–
–
–
Linear
Exp. Curve
Quadratic curve
none
III. Describing Scatterplots
• Strength
– Strong
– Weak
• Unusual Features
– Outliers
– Change in form or
strength.
Example 2
• Describe the following Scatterplots
(direction, form, strength, unusual features)
Describe the scatterplot you made in the fuel
efficiency example.
Now try on your own.
Now describe the relationship
between Age at First Word vs. Gesell
Score on your worksheet.
IV. Correlation coefficient
• Measures the strength of the linear
association between two quantitative
variables.
• In order to use this number, the data must
meet the following conditions.
– Quantitative Variables Condition
– Straight Enough Condition
– Outlier Condition (calculate with & without
outlier)
IV. Correlation Coefficient
• To calculate correlation:
– Enter data into L1 & L2
– Go to Catalog (2nd ,0) and choose
DiagnosticsON.
– STAT, CALC, LinReg(ax+b).
– The correlation number is the last entry r=
• Calculate to correlation coefficient of
your speed vs fuel example.
• Is it appropriate to use correlation for
this example? Why or Why not?
IV. Correlation Coefficient
• Correlation gives strength and direction.
– Closer to -1 indicates perfect Negative linear
association.
– Closer to +1 indicates perfect Positive linear
association.
– Closer to 0 indicates NO Linear association.
Now try on your own.
Calculate the correlation coefficient
for the relationship between Age at
First Word vs. Gesell Score on your
worksheet.
Then answer question # 4 on the
worksheet.
Now try on your own.
Calculate the correlation coefficient
for the relationship between Age at
First Word vs. Gesell Score on your
worksheet.
Pick up SEC Football
Worksheet.
This is due at the end of the class.
What do you think the correlation
coefficients are for the
following?
IV. Correlation Coefficient
• Has no units, based on z-scores
• Are unaffected by changes in center or
scale.
• Can be greatly affected by outliers.
V. Correlation vs Association
Association
Correlation
• Indicates that there is a
relationship between the two
variables (any form).
• Measures the strength
of a LINEAR
association.
Examples
• Sketch what you think the scatterplot would
look like, then describe the association.
–
–
–
–
–
Drug dose vs. degree of pain relief.
Calories consumed and weight loss.
Hours of sleep and score on a test.
Shoe size and grade point average
Age of car and money spent on repairs