SCATTER PLOTS
How do we make a scatter plot?
What can we see in a scatter plot?
Review
• Guidelines for analyzing univariate data
• (Remember: Great Students Can
Succeed)
•G
•S
•C
•S
We will use the same guidelines for
Bivariate Data
• Graph 1st
• Look at the shape
• Are there any outliers?
• Describe the data with numerical
summaries
Using your preview
• Take out your list of main ideas and
concepts from chapter 3
• Take about 5 minutes to compare your list
with your team make any changes
• A person will post an item from your list
(one question and one main idea; no
repeats) on the board when directed by
Mrs. Brown
Explanatory variable
•X
• Independent variable
• Changes in a variable x are thought to
“explain” or even cause changes in a
second variable
Response Variable
•Y
• Dependent variable
• Measures the outcome of a study
• “What is predicted?”
Let’s Check
• Identify the explanatory and response
variables in each setting.
• How does drinking beer affect the level of
alcohol in our blood? The legal limit for
driving in all states is 0.08%. In a study,
adult volunteers drank different numbers of
cans of beer. Thirty minutes later, a police
officer measured their blood alcohol levels.
answer
• Explanatory – number of cans of beer
• Response – blood alcohol level
Identify the explanatory and response
variables in each setting.
• The National Student Loan Survey provides
data on the amount of debt for recent
college graduates, their current income,
and how stressed they feel about college
debt. A sociologist looks at the data with
the goal of using amount of debt and
income to explain the stress caused by
college debt.
answer
• Explanatory – debt and income score
• Response – stress level
Scatter Plots
• The most effective way to display the relationship
•
•
•
•
•
between two quantitative variables is a scatterplot.
A scatterplot is a plot of observations of quantitative
variables x and y as points in the plane.
The explanatory variable is always plotted on the
horizontal scale.
An explanatory –response relationship does not always
exist between the two variables.
Each point on the plot represents a single case (the same
individual or object)
Be sure your plot has a title, labels for both axes, and
appropriate scales for both axes.
Describing Scatter Plots
• Look for the overall pattern and any
striking deviations
• Describe the form, direction, and
strength
• An individual that falls outside the overall
pattern of the relationship is an outlier.
Linear Relationships
• Look like a line but can have some scatter
Positive
Negative
Non-linear relationships
Negative
Positive
Positive
No association
• A shapeless cloud of points
Associations
• Let’s look at some graphs and discuss their associations.
• 1st – ask yourself “Is this a linear association?”
• 2nd – ask yourself “What direction is the association?”
• Graphs from BVD p. 161
Problem 1
Non-linear
and negative
Problem 2
Linear and
positive
Problem 3
Linear and
negative
Problem 4
No
association
Problem 5
Linear and
positive
Problem 6
Non-linear
and
positive
Explanatory vs. Response
• Suppose you were to collect data for each pair of
variables. You want to make a scatterplot. Decide which
variable would be explanatory and which would be
response.
• A. Apples: weight in grams, weight in ounces
• B. Apples: circumference in inches, weight in
ounces
• C. College freshmen: shoe size, GPA
• D. Gasoline: number of miles you drove since
filling up, gallons remaining in your tank
• E. T-shirts at a store: price each, number sold
• F. Skin diving: depth, visibility
answers
• A. either
• B. x = circumference
• C. either
• D. x = number of miles you drove since filling up
• E. x = price
• F. x= depth
Making a scatterplot on the calculator
• STAT, EDIT, put data into L1 (x) and L2 (y)
• 2nd, Y=, #1
• ZOOM 9
Example:
Does how long children remain at the lunch table help
Calories
Time
predict how much they eat?
472
498
465
456
423
437
508
431
479
454
450
410
504
437
489
436
480
439
444
21.4
30.8
37.7
33.5
32.8
39.5
22.8
34.1
33.9
43.8
42.4
43.1
29.2
31.3
28.6
32.9
30.6
35.1
33.0