Correlation
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Correlation. (Click icon for audio). Correlation Coefficient. Statistical measure of the co-variation or association between two variables The correlation coefficient for two variables, X and Y is:

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Correlation

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Correlation

(Click icon for audio)

Dr. Michael R. Hyman, NMSU


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?


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


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


Correlation Patterns


Simple Correlation Coefficient


= Variance of X

= Variance of Y

= Covariance of X and Y

Simple Correlation Coefficient


Coefficient of Determination


Correlation Matrix

Standard form for reporting correlation results


Correlation Matrix


Correlation for Ordinal Data


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