Download Examining Relationships

Examining Relationships
• So far we have primarily focused on a
single variable.
• It is often more interesting to examine the
relationship between variables.
• For now, we will focus on relationships
between two quantitative variables.
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Roles for Variables
• Response Variable
– Often the variable we are most interested in
• Explanatory Variable (Predictor)
– Used to explain the variation in the response
variable
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Scatterplots
• Scatterplots are a common and effective
way to visualize the relationship between
two quantitative variables
• When describing the association, or
relationship, between two variables,
always look at the overall pattern and
deviations from the pattern.
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1
Teenage Drug Use
• Is there a relationship between the use of
marijuana and the use of other drugs?
• A survey was conducted in the U.S. and in
10 countries of Western Europe to
determine the percentage of teenagers
who had used marijuana and other drugs.
• A scatterplot of the data follows.
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Teenage Drug Use
Bivariate Fit of Other Drugs (%) By Marijuana (%)
Other Drugs (%)
40
30
20
10
0
0
10
20
30
40
50
60
Marijuana (%)
5
Positive Association
• Above average values of marijuana usage
are associated with above average values
of the usage of other illegal drugs.
• Below average values of marijuana usage
are associated with below average values
of the usage of other illegal drugs.
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2
Price of Used Cars
• Is there a relationship between the age of
a car and its price?
• A scatterplot of the ages and prices of 17
used Toyota Corollas follows.
7
Price of Used Cars
Bivariate Fit of Prices Advertised ($) By Age (yr)
15000
Prices
Advertised ($)
12500
10000
7500
5000
2500
0
0
2.5
5
7.5
10
12.5
15
Age (yr)
8
Negative Association
• Above average values of car age are
associated with below average values of
car price.
• Below average values of car age are
associated with above average values of
car price.
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