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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 it most in common usage 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).

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Correlation_and_dependence

**Correlation** is a measure of relationship between two mathematical variables or measured data values, which includes the Pearson correlation coefficient as a special case.

**Correlation** may also refer to:

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Correlation_(disambiguation)

In projective geometry, a **correlation** is a transformation of a *d*-dimensional projective space that transforms objects of dimension *k* into objects of dimension *d* − *k* − 1, preserving incidence. Correlations are also called **reciprocities** or **reciprocal transformations**.

For example, in the real projective plane points and lines are dual to each other. As expressed by Coxeter,

Given a line *m* and *P* a point not on *m*, an elementary correlation is obtained as follows: for every *Q* on *m* form the line *PQ*. The inverse correlation starts with the pencil on *P*: for any line *q* in this pencil take the point *m* ∩ *q*. The composition of two correlations that share the same pencil is a perspectivity.

In a 3-dimensional projective space a correlation maps a point to a plane. As stated in one textbook:

Three-dimensional correlations also transform lines into lines, so they may be considered to be collineations of the two spaces.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Correlation_(projective_geometry)

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