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Correlation

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Dr. Michael R. Hyman, NMSU

- 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?

- 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

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

= Variance of X

= Variance of Y

= Covariance of X and Y

Standard form for reporting correlation results