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# Pearson correlation coefficient

The calculation of the correlation coefficient of two random variables

Here are a couple of definitions, if somebody forgot them

Almost all the definitions could be found at Wikipedia.

Correlation in mathematical statistics is a probability and statistical dependence without any strict functional nature. In contrast to the functional dependence, the correlation dependence occurs when one of the attributes is dependent not only of the given second attribute but also on a number of random factors, or when among the conditions, on which the attributes are depending on, there are common conditions for both of them.

The mathematical measure of the correlation of two random variables is correlation coefficient.

Some types of correlation coefficients may be positive or negative (there is also the possibility of the lack of statistical relationship - for example, for independent random variables). If it is assumed that the precedence relation is defined on the values of the variables then the negative correlation - the correlation, where the increase of one variable is associated with the decrease of the other variable, though the correlation coefficient can be negative.
The positive correlation in such conditions is a correlation, where an increase of one variable is associated with an increase of another variable and the correlation coefficient can be positive.

If the value modulus is closer to 1, it means that there is strong coupling, and if closer to 0 - the coupling is weak or nonexistent. When the correlation coefficient is equal to 1 by the value modulus people suggest a functional relationship, i.e. the changes of two quantities can be described by a mathematical function.

Pearson correlation coefficient is most commonly known (Karl Pearson, English mathematician, 1857-1936), characterizing the degree of linear dependence between the variables. It is defined as

$R_{X,Y}=\frac{M[XY]-M[X]M[Y]}{\sqrt{(M[X^2]-(M[X])^2)}\sqrt{(M[Y^2]-(M[Y])^2)}}$

where M - the mathematical expectation.

There is nothing left to say - enter the random variables in the chart (you can delete the default numbers) and the calculator will define the correlation coefficient by Pearson's formula.

### Pearson correlation coefficient

#### Changes of random variables

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Pearson correlation coefficient

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