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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: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 4.33 21.65United
Kingdom 3 22.9
United States 7.97 39.15
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.
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 associationb) 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
1
yx s
yy
s
xx
nr
Height Weight
Jim 68 145
Jill 65 130
Frank 71 173
Mark 73 205
Eric 66 143
Zach 70 166
Remember the TV thing: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 4.33 21.65United
Kingdom 3 22.9
United States 7.97 39.15r = 0.5378
Remember the TV thing: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 4.33 21.65United
Kingdom 3 22.9
United States 7.97 39.15r = 0.0884
Questions
