Dr. Michael R. Hyman, NMSU

Correlation

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Correlation Coefficient

• Statistical measure of the co-variation or association between two variables

• The correlation coefficient for two variables, X and Y is:

• Sample question to test for statistical and managerial significance: Are dollar sales associated with advertising dollar expenditures?

xyr

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Correlation Does Not Mean Causation

• Rooster’s crow and the rising of the sun– Rooster does not cause the sun to rise.

• Teachers’ salaries and liquor consumption – Co-vary because both are influenced by

a third variable (e.g., state of economy)

Examples: High correlations without causation

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Possible Values for

• r ranges from +1 to -1• r = +1: a perfect positive linear relationship• r = -1: a perfect negative linear relationship• r = 0: no correlation

xyr

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Correlation Patterns

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22YYiXXi

YYXXrr iiyxxy

Simple Correlation Coefficient

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22yx

xyyxxy rr

Simple Correlation Coefficient

= Variance of X

= Variance of Y

= Covariance of X and Y

2x2y

xy

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Coefficient of Determination

Variance variance2

TotalExplainedr

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Correlation MatrixStandard form for reporting correlation results

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Correlation Matrix

Var1 Var2 Var3

Var1 1.0 0.45 0.31

Var2 0.45 1.0 0.10

Var3

0.31 0.10 1.0

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Correlation for Ordinal Data

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