Correlation, r, measures the direction and strength of the linear relationship between two quantitat

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Correlation, r, measures the direction and
strength of the linear relationship between two
quantitative variables. We have (x, y) data on
n individuals. r
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Note that r is calculated by
multiplying the z-scores for each individuals
x- and y-values, adding the products, and
dividing by n-1.
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Properties of Correlationr makes no
distinction between explanatory and response
variables.
Correlation requires that both variables be
quantitative.
r does not change if we change the units of
measurement. r has no unit of measurement it
is just a number.
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r gt 0 indicates a positive association
r lt 0 indicates a negative association.
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1 r 1
Values near 0 indicate a very weak linear
relationship. The strength of the linear
relationship increases as r moves away from zero
and toward 1 or 1.
r 1 or 1 only if all the data points are
collinear.
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Correlation measures only the strength of a
linear relationship between two quantitative
variables.
Correlation does not describe curved
relationships, no matter how strong they may be.
ALWAYS visually examine your data!!
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r is not a resistant measure.
Use r with caution when the scatter-plot shows
outliers.
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Correlation is not a complete description of
two-variable data.When describing 2-variable
data, give the values of , sx, and sy
in addition to r.
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Note that the correlation coefficient only
measures the strength of a linear relationship
between your variables.  It cannot determine
causation.  A strong linear relationship between
two quantities (life expectancy and people per
TV for example) does not guarantee a cause/effect
relationship! 
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Generally, you can NOT conclude that there is a
cause/effect relationship until you have run a
carefully designed experiment (discussed in
chapter 3).   This idea is usually written 
ASSOCIATION ? CAUSATION.