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# Relationship vs. Correlation

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• Correlation

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data. In the broadest sense correlation is any statistical association, though in common usage it most often refers to how close two variables are to having 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 limited supply 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, in general, the presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e., correlation does not imply causation).

Formally, random variables are dependent if they do not satisfy a mathematical property of probabilistic independence. In informal parlance, correlation is synonymous with dependence. However, when used in a technical sense, correlation refers to any of several specific 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 be present even when one variable 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. Mutual information can also be applied to measure dependence between two variables.

Wikipedia
• Relationship (noun)

Connection or association; the condition of being related.

• Relationship (noun)

The links between the x-values and y-values of ordered pairs of numbers especially coordinates.

• Relationship (noun)

Kinship; being related by blood or marriage.

• Relationship (noun)

A romantic or sexual involvement.

"Why are they being mean to her just because she wants a relationship with him?"

• Relationship (noun)

A way in which two or more people behave and are involved with each other

"I have a good working relationship with my boss."

• Relationship (noun)

The level or degree of affinity between keys, chords and tones.

• Correlation (noun)

A reciprocal, parallel or complementary relationship between two or more comparable objects

• Correlation (noun)

One of the several measures of the linear statistical relationship between two random variables, indicating both the strength and direction of the relationship.

• Correlation (noun)

An isomorphism from a projective space to the dual of a projective space, often to the dual of itself.

Wiktionary
• Relationship (noun)

The state of being related by kindred, affinity, or other alliance.

• Correlation (noun)

Reciprocal relation; corresponding similarity or parallelism of relation or law; capacity of being converted into, or of giving place to, one another, under certain conditions; as, the correlation of forces, or of zymotic diseases.

Webster Dictionary
• Relationship (noun)

a relation between people; (`relationship' is often used where `relation' would serve, as in `the relationship between inflation and unemployment', but the preferred usage of `relationship' is for human relations or states of relatedness);

"the relationship between mothers and their children"

• Relationship (noun)

a state of connectedness between people (especially an emotional connection);

"he didn't want his wife to know of the relationship"

• Relationship (noun)

a state involving mutual dealings between people or parties or countries

• Relationship (noun)

state of relatedness or connection by blood or marriage or adoption

• Correlation (noun)

a reciprocal relation between two or more things

• Correlation (noun)

a statistic representing how closely two variables co-vary; it can vary from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation);

"what is the correlation between those two variables?"

• Correlation (noun)

a statistical relation between two or more variables such that systematic changes in the value of one variable are accompanied by systematic changes in the other

Princeton's WordNet