# What is correlation?

## What Does correlation Mean

Correlation is called the reciprocal or corresponding link that exists between two or more elements. The concept is used in different ways depending on the context.

In the field of mathematics and statistics , correlation refers to the proportionality and the linear relationship that exists between different variables. If the values ​​of one variable are systematically modified with respect to the values ​​of another, both variables are said to be correlated.
Suppose we have a variable R and a variable S . A the increasing values of R , values increase S . Similarly, as the values ​​of S increase, the values ​​of R increase . Therefore there is a correlation between the variables R and S .

We can present this same example graphically if we think of the accounting of a company, specifically in two variables that record "the expenses for the purchase of products" and the "total stock in the warehouse"; it is correct to say that as the first increases, so does the second, and that this correlation cannot be avoided.
It can be noted that correlation is the measure that is recorded of the dependence between different variables. The degree of correlation can be measured by so-called correlation coefficients , such as the intraclass correlation coefficient , Spearman's correlation coefficient, and Jaspen's coefficient .
It is important to note that the existence of a statistical correlation between two events does not imply that there is a causal connection between them. This fallacious belief is summarized with the Latin expression Cum hoc ergo propter hoc , which is usually summarized as “correlation does not imply causality” . The presumed causality in the correlation may be due to a coincidence or the existence of some unknown factor, for example .
The idea of electronic correlation , on the other hand, refers to the interaction that electrons maintain in a quantum-type system. This concept is framed in the field of quantum mechanics , a discipline that physics uses to fundamentally describe nature, taking small spatial scales as a reference.
Physics took this term from statistics, where it is used to define the case in which two distribution functions do not have independence from each other. By distribution function we understand the one that serves to describe the probability that the variable to which it is associated is less than or equal to another, around which it is applied.

Take, for example, two electrons, a and b ; If we defined the distribution function p (ra, rb) to establish the joint probability that the first is in ra and the second, in rb , we would be talking about a correlation between them as long as it is not equal to the product of p ( ra) by p (rb) , that is, of the individual probabilities of each variable.
The quantum chemistry , on the other hand, is a branch of chemistry that can be applied to quantum field theory and quantum mechanics; it is the description by mathematical means of the fundamental behavior of matter , on a scale that is measured in molecules. In the so - called Hartree-Fock method , an approximation of the quantum mechanical equations for elementary particles called fermions , there is an asymmetric wave function that describes a group of electrons that is only approximated by a particular technique, known as Slater's determinant. .
On the other hand, exact wave functions cannot always be represented as unique determinants, since this leaves aside the correlation between electrons whose spin is opposite (spin is a property of elementary particles that describes an intrinsic angular momentum whose value does not change).

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