AP Statistics
3.1 Scatterplots
Objectives: Explain the difference between an explanatory variable and a response variable.
Given a set of bivariate data, construct a scatterplot.
Explain what is meant by the direction, form, and strength of the overall pattern of a
scatterplot.
Explain how to recognize an outlier in a scatterplot.
Explain what it means for two variables to be positively or negatively associated.
Explain how to add categorical variables to a scatterplot
Use a TI-83/89 to construct a scatterplot.
The Relationship of Two Variables
 Remember that the relationship between two variables can be STRONGLY
influenced by other variables that are lurking in the background.
 Remember W5HW – Who, What, Why, When, Where, How, and by Whom.
Response Variables (y) measures an outcome of a study.
Explanatory Variables (x) helps explain or influence change.
REMEMBER that calling one variable explanatory and the other response DOES NOT
necessarily mean that changes in one causes changes in the other.
Exercise 3.1 (pg. 173)
a) Explanatory: Time spent studying, Response: Grade on the exam.
b) Explanatory: Height, Response: Weight
c) Explanatory: inches of rain, Response: yield of corn
d) Explore the relationship6y6
e) Explanatory: Family income, Response: years of education completed by eldest child.
Scatterplot: A scatterplot shows the relationship between two quantitative variables measured on
the SAME individual. The values of the eXplanatory variable appear on the horizontal
axis and the response appears on the vertical axis. Each individual in the data appears
as a point in the plot fixed by the values of both variables for the individual.
KEYS TO A SCATTERPLOT
 Title
 Label your axes
 Keep scale uniform
 Plot your points so you can read the pattern easy.
Interpreting Scatterplots
 Pattern: Look for an overall pattern and look for striking deviations.
o Direction, Form and Strength: Describe the pattern with the following terms:

Direction: How does the pattern move from left to right?
Form: Is the pattern curved, or a straight line?
Strength: Are the points close to the form?
YES  Strong
NO  Weak
Outliers: An important kind of deviation is an outlier – an individual value that falls outside of
the overall pattern.
Positive Association  A pattern that RISES from left to
right – starts in the lower left corner and rises to the upper
right corner.
D: Positive
F: linear
S: Strong
Negative Association  A pattern that FALLS from left to right – starts in the upper left corner and
falls to the lower right corner.
There is a moderately strong, negative, curved
relationship between the percent of students in a state
who take the SAT and the mean SAT math score.
Further, there are two distinct clusters of states and two
possible outliers that fall outside the overall pattern.
Categorical Variables in Scatterplots  To add a
categorical variable to a scatterplot, use a different color
Exercise 3.5 (pg. 179)
a) Number of powerboat registrations.
b) Positive, linear relationship between
these two variables.
c) Positively associated.
d) Yes, the relationship is linear.
e) The relationship is a strong, positive,
linear association. Yes, the number of
manatees killed can be predicted
accurately from powerboat
registrations.
SCATTERPLOT NOTES ON THE GRAPHING CALCULATOR
Using the data from page 177 from the blood alcohol content example, enter the beer consumption
into L1 and the BAC into L2.
Hit 2nd Y= (STAT PLOT), turn plot ON, and pick the FIRST graph (top left).
Hit Zoom – 9 (zoomstat)
NOTICE! There are no scales on the axes and they’re not labeled! If you copy a scatterplot from your
calculator onto your paper, make sure that your scale and label the axes. You can use TRACE to help
you.
Examples of Form and Direction for Scatterplots:
Linear
No
relationship
HW: pg. 173; 3.2 – 3.4 and pg.179; 3.6 – 3.8