Changes

==Origin==

==Origin==

Back-formation from co-rrelation

Back-formation from co-rrelation

*[http://en.wikipedia.org/wiki/17th_century 1643]

*[https://en.wikipedia.org/wiki/17th_century 1643]

==Definitions==

==Definitions==

*1: either of [[two]] [[things]] so [[related]] that one directly implies or is [[complementary]] to the other (as [[husband]] and [[wife]])

*1: either of [[two]] [[things]] so [[related]] that one directly implies or is [[complementary]] to the other (as [[husband]] and [[wife]])

*2: a [[phenomenon]] that accompanies another phenomenon, is usually [[parallel]] to it, and is related in some way to it <precise electrical correlates of [[conscious]] [[thinking]] in the human [[brain]]  

*2: a [[phenomenon]] that accompanies another phenomenon, is usually [[parallel]] to it, and is related in some way to it <precise electrical correlates of [[conscious]] [[thinking]] in the human [[brain]]  

==Description==

==Description==

In [[statistics]], dependence refers to any statistical [[relationship]] between [[two]] [http://en.wikipedia.org/wiki/Random_variable random variables] or two sets of [[data]]. Correlation refers to any of a broad class of statistical relationships involving dependence.

In [[statistics]], dependence refers to any statistical [[relationship]] between [[two]] [https://en.wikipedia.org/wiki/Random_variable random variables] or two sets of [[data]]. Correlation refers to any of a broad class of statistical relationships involving dependence.

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]]. In this example there is a [[causal]] relationship, because [[extreme]] [[weather]] causes people to use more [[electricity]] for heating or cooling; however, statistical dependence is not sufficient to [[demonstrate]] the presence of such a causal relationship.

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]]. In this example there is a [[causal]] relationship, because [[extreme]] [[weather]] causes people to use more [[electricity]] for heating or cooling; however, statistical dependence is not sufficient to [[demonstrate]] the presence of such a causal relationship.

[[Formally]], dependence refers to any situation in which [[random]] [[variables]] do not satisfy a [[mathematical]] condition of [[probabilistic]] independence. In loose usage, correlation can refer to any departure of [[two]] or more random variables from independence, but technically it refers to any of several more specialized [[types]] 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 [http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient Pearson correlation coefficient], which is [[sensitive]] only to a [[linear]] relationship between two [[variables]] (which may exist even if one is a nonlinear function of the other). Other correlation coefficients have been developed to be more robust than the Pearson correlation — that is, more sensitive to nonlinear relationships.[http://en.wikipedia.org/wiki/Correlate]

[[Formally]], dependence refers to any situation in which [[random]] [[variables]] do not satisfy a [[mathematical]] condition of [[probabilistic]] independence. In loose usage, correlation can refer to any departure of [[two]] or more random variables from independence, but technically it refers to any of several more specialized [[types]] 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 [https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient Pearson correlation coefficient], which is [[sensitive]] only to a [[linear]] relationship between two [[variables]] (which may exist even if one is a nonlinear function of the other). Other correlation coefficients have been developed to be more robust than the Pearson correlation — that is, more sensitive to nonlinear relationships.[https://en.wikipedia.org/wiki/Correlate]

[[Category: Statistics]]

[[Category: Statistics]]

[[Category: Mathematics]]

[[Category: Mathematics]]