Scatterplots &
Correlation
Section 3.1A
Relationships between two
Variables
O A study found that short women are more
likely to have heart attacks than tall
women….
O Smokers on average die younger than
nonsmokers….
O But – to make these conclusions we must
first eliminate the effect of other variables.
Lurking Variables
O Can strongly influence the relationship
between two variables.
Case of the Missing
Cookies
Variables
O Response Variable
O Measures the outcome of a study.
O It’s the dependent variable.
O Explanatory Variable
O May help explain or influence changes in
a response variable.
O It’s the independent variable.
Identify the explanatory
and response variable.
O 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.
Identify the explanatory
and response variable.
O 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 be college debt.
Scatterplot
O Used to show the relationship between
two quantitative variables measured on
the same individuals. Each individual in
the data appears as a point in the graph.
O Explanatory variable goes on the horizontal
axis.
O If there is no explanatory variable then either
variable can go on the horizontal axis.
The following data represents 9th grade
students who go on a backpacking trip.
Body wt
(lb)
120 187 109 103 131 165 158 116
Backpa
ck (lb) 26 30 26 24 29 35 31 28
Has the increase been constant?
% Responding Yes
Would Vote for a woman
100
80
60
Series1
40
20
0
0
50
100
Years (since 1900)
150
Interpreting Scatterplots
O Look for direction (positive, negative, none)
O Look at the form of the relationship
O Straight or curved
O Any clusters
O Look at the Strength
O How closely does it follow the form
O Look for outliers
O Individual value hat falls outside the overall pattern of the
relationship
Interpret: Backpack
Backpack (lb)
40
35
30
25
20
Backpack (lb)
15
10
5
0
0
50
100
150
200
Types of Correlation
90
100
80
90
80
70
60
70
60
50
50
40
40
30
30
20
20
10
10
0
0
0
10
20
30
40
50
0
20
120
100
80
60
40
20
0
0
20
40
60
80
100
40
60
80
Caution…..
Association does not
imply causation!
Graph Using a calculator:
Sprint Time (sec)
5.41
5.05
9.49
8.09
7.01
7.17
6.83
6.73
8.01
5.68
5.78
6.31
6.04
Long Jump (in)
1.71
184
48
151
90
65
94
78
71
130
173
143
141
Interpret….
1. Direction
2. Form
3. Strength
4. Outliers
Homework
O Page 159 (1-13) odd