A Correlation Coefficient is a Statistic (between -1 and 1) that measures the degree to which two Continuous Random Variables are related (Correlation Function).
References
2009
- http://en.wikipedia.org/wiki/Correlation_and_dependence
- In statistics, correlation and dependence are any of a broad class of statistical relationships between two or more random variables or observed data values. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a product and its price. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. Correlations can also suggest possible causal, or mechanistic relationships; however statistical dependence is not sufficient to demonstrate the presence of such a relationship.
- Formally, dependence refers to any situation in which random variables do not satisfy a mathematical condition of probabilistic independence. In general statistical usage, correlation or co-relation can refer to any departure of two or more random variables from independence, but most commonly refers to a more specialized type of relationship between mean values. There are several correlation coefficients, often denoted ρ or r, measuring the degree of correlation. The most common of these is the Pearson correlation coefficient, which is mainly sensitive to a linear relationship between two variables. Other correlation coefficients have been developed to be more robust than the Pearson correlation, or more sensitive to nonlinear relationships.
2006
- (Dubnicka, 2006e) => Suzanne R. Dubnicka. (2006). "Random Vectors and Multivariate Distributions - Handout 5. Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
- TERMINOLOGY : Suppose that X and Y are random variables with variances 2 X and 2 Y , respectively. The correlation between X and Y is given by Corr(X, Y ) = X,Y = Cov(X, Y ) X Y . The quantity X,Y is also called the correlation coefficient between X and Y .