Two random variables are positively correlated if high values of one are likely to be associated with high values of the other. They are negatively correlated if high values of one are likely to be associated with low values of the other.

Formally, a correlation coefficient is defined between the two random variables (x and y, here). Let s_{x} and x_{y} denote the standard deviation of x and y. Let s_{xy} denote the covariance of x and y.

The correlation coefficent between x and y, denoted sometimes r_{xy}, is defined by:

r_{xy} = s_{xy} / s_{x}s_{y}

Correlation coefficients are between -1 and 1, inclusive, by definition. They are greater than zero for positive correlation and less than zero for negative correlations.

### Terms related to Correlation:

- Standard deviations
- Durbin-Watson Statistic

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### Books on Correlation:

- Volatility and Correlation: The Perfect Hedger and the Fox
- Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences
- Volatility and Correlation: In the Pricing of Equity, FX and Interest-Rate Options

### Journal Articles on Correlation:

- Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics
- Subjectivity and correlation in randomized strategies