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

Correlation

(Click icon for audio)

Dr. Michael R. Hyman, NMSU


Correlation coefficient

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

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

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

Correlation Patterns


Simple correlation coefficient

Simple Correlation Coefficient


Simple correlation coefficient1

= Variance of X

= Variance of Y

= Covariance of X and Y

Simple Correlation Coefficient


Coefficient of determination

Coefficient of Determination


Correlation matrix

Correlation Matrix

Standard form for reporting correlation results


Correlation matrix1

Correlation Matrix


Correlation for ordinal data

Correlation for Ordinal Data


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