# Correlational Relationship

A Correlational Relationship is a mathematical relationship between an event and another event that occur together more frequently than a Random Relationship.

**AKA:**Correlation, Linear Correlation.**Example(s):****Counter-Example(s):****See:**Correlation Function, Correlation Coefficient, Linear Relationship, Correlation Does Not Imply Causation, Conditional Expectation.

## References

### 2016

- https://en.wiktionary.org/wiki/correlation#Noun
- A reciprocal, parallel or complementary relationship between two or more comparable objects
- Template:Label One of the several measures of the linear statistical relationship between two random variables, indicating both the strength and direction of the relationship.
- Template:Lb An isomorphism from a projective space to the dual of a projective space, often to the dual of itself.

### 2016

- (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/Correlation_and_dependence Retrieved:2016-6-5.
- In statistics,
**dependence**is any statistical relationship between two random variables or two sets of data.**Correlation**refers to any of a broad class of statistical relationships involving dependence, though in common usage it most often refers to the extent to which two variables have a linear relationship with each other.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 (i.e., correlation does not imply causation).

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 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.^{[1]}^{[2]}^{[3]}Mutual information can also be applied to measure dependence between two variables.

- In statistics,

- ↑ Croxton, Frederick Emory; Cowden, Dudley Johnstone; Klein, Sidney (1968)
*Applied General Statistics*, Pitman. ISBN 9780273403159 (page 625) - ↑ Dietrich, Cornelius Frank (1991)
*Uncertainty, Calibration and Probability: The Statistics of Scientific and Industrial Measurement*2nd Edition, A. Higler. ISBN 9780750300605 (Page 331) - ↑ Aitken, Alexander Craig (1957)
*Statistical Mathematics*8th Edition. Oliver & Boyd. ISBN 9780050013007 (Page 95)