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Correlation
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positive relationship
when one variable increases, the other variable increases
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negative relationship
when one variable increases, the other variable decreases
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 goal of correlations is to figure out the relationship between 2 variables
•
what is the mean?
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What is the variation from the mean?
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Covariance
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 measure of average relationship between variables
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cov(x,y) = SUM(x
i
– mean of x)(y
i
– mean of y)
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(N – 1)
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example:
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(55.4)(811)+(45.4)(911)+(45.4)(1011)+(65.4)(1311)+(85.4)(1511)
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4
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= .4(3)+(1.4)(2)+(1.4)(1)+(.6)(2)+(2.6)(4)
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4
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= 1.2+2.8+1.4+1.2+9.6
= 16.2
= 4.25
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4
4
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Pearson Correlation Coefficent
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 used to compare covariances
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r = cov(x,y)
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s
x
s
y
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example:
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4.25
=
4.25
= .87
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1.67(2.92)
4.88
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 correlation varies between 1 and +1
•
0 = no relationship
•
negative correlation = negative relationship
•
positive correlation = positive relationship
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 Spring '08
 Hoffman

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