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Notes 4
1
BIVARIATE DATA
Bivariate data is data for which there are two variables for each observation
.
Example:
The following bivariate data show the High school and college GPAs for 10 college sophmores.
High School 3.3 4.0 2.9 3.5 3.8 3.7 3.7 2.8 3.2 3.6
College
3.5 3.9 3.3 3.6 3.9 3.8 3.4 3.0 3.2 3.8
Response/Dependent variable
: measures the outcome of the study, i.e. the quantity that we are
interested in.
Explanatory/Independent variable
: An explanatory variable is one that influences the values
of the response variable, either directly or indirectly.
As mentioned previously, we must always be wary of lurking variables and confounding. The
“hidden” effect may cause us to misinterpret the relationship between the explanatory and
response variables.
Scatterplots
A scatter plot displays any relationship between bivariate data in a graphical manner.
Each point on a scatterplot marks a pair of observations taken from one individual
in the sample.
Typically, the independent variable (X)
is plotted on the horizontal axis
and the dependent
variable (Y)
is plotted on the vertical axis
.
Example:
The table below gives the weights (in hundreds of pounds) and highway fuel usage
rates (in miles per gallon) for a sample of new domestic cars.
Weight
29
35
28
44
25
34
30
33
28
24
Fuel Usage
31
27
30
25
31
29
28
28
28
33
Which variable do you think is the response, Y?
(Hint: Y depends on X)
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2
Fuel Usage vs Weight
24
25
26
27
28
29
30
31
32
33
34
23
25
27
29
31
33
35
37
39
41
43
45
Weight
Fuel Usage
Based on the data, can you expect to use more gas if you buy a heavier car?
What might the fuel usage be for a car that weighs 40 hundred pounds?
Interpreting scatterplots
After plotting two variables on a scatterplot, we describe the relationship by examining the
form
,
direction
and
strength
of the association. We also look for an overall pattern and deviations
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 Spring '08
 BATEH
 Statistics

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