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Pearson correlation coefficient

The calculation of the correlation coefficient of two random variables

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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 functional dependence, the correlation dependence occurs when one of the attributes depends not only on the given second attribute but also on many random factors, or when among the conditions on which the attributes are depending, 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 variables' values, 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, 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 mathematical function can describe a functional relationship, i.e., the changes of two quantities.

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.

PLANETCALC, Pearson correlation coefficient

Pearson correlation coefficient

Changes of random variables

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Pearson correlation coefficient
 

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