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Section 4.1 – Scatter Diagrams and Correlation
Correlation
– There is a correlation between two variables when one of them is related to the other in
some way.
The
response variable
is the variable whose value can be explained by the value of the
predictor
(explanatory) variable
.
Scatter Diagram
– A graph in which the (biviariate) paired (
x
,
y
) sample data are plotted as single
points.
Each individual in the data set is represented by a single point.
The explanatory variable is
plotted on the horizontal axis and the response variable is plotted on the vertical axis.
Example
:
Create a scatterplot of the following data:
Looking at a scatter diagram can help you determine if the variables have a linear relationship.
(See the graphs on pg. 194)
The
linear correlation coefficient
(
r
)
measures the strength and direction of the linear relationship
between the two variables.
It is also called the Pearson product moment correlation coefficient.
∑
∑
∑
∑
∑
∑
∑



=
2
2
2
2
)
(
)
(
)
(
)
(
)
)(
(
y
y
n
x
x
n
y
x
xy
n
r
(
ALWAYS
ROUND
TO
3
DECIMAL
PLACES
)
x
y
3
3
4
2
3
4
1
5
5
2
2
5
5
1
1
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View Full Document Properties of
r
:
1.
–1 ≤
r
≤ 1
2.
The closer
r
is to +1, the stronger is the evidence of positive association.
3.
The closer
r
is to –1, the stronger is the evidence of negative association.
4.
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This note was uploaded on 01/06/2012 for the course MATH 1342 taught by Professor Lisajuliano during the Spring '12 term at Collins.
 Spring '12
 LisaJuliano
 Correlation

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