Dr. Michael R. Hyman, NMSU Correlation (Click icon for audio)

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3 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?

4 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

5 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

6 Correlation Patterns

7 Simple Correlation Coefficient

8 = Variance of X = Variance of Y = Covariance of X and Y

9 Coefficient of Determination

10 Correlation Matrix Standard form for reporting correlation results

11 Correlation Matrix

12 Correlation for Ordinal Data

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