Section 4.1
Exploring Associations between Two
Quantitative Variables?
Example:
 Is there, on a national scale, an association
between TV watching and obesity?

What do you think?

What does the data Show?
Data:
The average hours of TV watched by adults in 18
industrialized countries and the Obesity rate of
adults in those countries.
Does there seem to be a associated?
Lets look at a bar graph and see if that helps.
Country
TV Viewing
Hours
Obesity
Rate
Australia
3.25
24.35
Austria
2.72
20.75
Belgium
3.68
11.35
Canada
3.09
23.45
Denmark
2.87
8.85
Finland
2.87
18.35
Ireland
2.58
9.7
Italy
3.98
12.75
Japan
3.73
1.65
Korea
3.19
7.1
New Zealand
2.82
27.3
Portugal
3.41
14.95
Spain
3.82
15.7
Sweden
2.47
11.4
Switzerland
2.47
15.55
Turkey
United
Kingdom
4.33
21.65
3
22.9
United States
7.97
39.15
Data:
TV vs. Obesity
TV Viewing Hours
Obesity Rate
New Tool: Scatter Plot:
 To build a scatter plot treat your explanatory
variable as x, and your response variable as
y, and plot your data on an (x , y) plane.
Height
Weight
Jim
68
145
Jill
65
130
Frank
71
173
Mark
73
205
Eric
66
143
Zach
70
166
New Tool: Scatter Plot:
 We look at three things on a scatter Plot:
 Is there a linear association?
 What is the direction?
 How strong is the
association?
Correlation.
 Correlation is a numerical value that summarizes the direction and
strength of the association between two quantitative variables.
 Properties:

Denoted r.

Positive r indicated a positive association

Negative r indicated a negative association

Values fall within the interval [-1, 1]

The closer to r = zero the weaker the association.
Correlation
Would you expect a positive association, a
negative association or no association between
the age of the car and the mileage on the
odometer?
a) Positive association
b) Negative association
c) No association
New Tool: Scatter Plot:
 What would we expect as the r value for the scatter plot below?
Questions
Calculating Correlation.
1
xx y y
r
(
)(
)

n 1
sx
sy
Height
Weight
Jim
68
145
Jill
65
130
Frank
71
173
Mark
73
205
Eric
66
143
Zach
70
166
Remember the TV thing:
r = 0.5378
Country
TV Viewing
Hours
Obesity
Rate
Australia
3.25
24.35
Austria
2.72
20.75
Belgium
3.68
11.35
Canada
3.09
23.45
Denmark
2.87
8.85
Finland
2.87
18.35
Ireland
2.58
9.7
Italy
3.98
12.75
Japan
3.73
1.65
Korea
3.19
7.1
New Zealand
2.82
27.3
Portugal
3.41
14.95
Spain
3.82
15.7
Sweden
2.47
11.4
Switzerland
2.47
15.55
Turkey
United
Kingdom
4.33
21.65
3
22.9
United States
7.97
39.15
Remember the TV thing:
r = 0.0884
Country
TV Viewing
Hours
Obesity
Rate
Australia
3.25
24.35
Austria
2.72
20.75
Belgium
3.68
11.35
Canada
3.09
23.45
Denmark
2.87
8.85
Finland
2.87
18.35
Ireland
2.58
9.7
Italy
3.98
12.75
Japan
3.73
1.65
Korea
3.19
7.1
New Zealand
2.82
27.3
Portugal
3.41
14.95
Spain
3.82
15.7
Sweden
2.47
11.4
Switzerland
2.47
15.55
Turkey
United
Kingdom
4.33
21.65
3
22.9
United States
7.97
39.15
Questions