# Pearson correlation coefficient

The Pearson correlation coefficient calculator is a tool that allows users to input sets of paired random variables and calculate the correlation between them.

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#### Maxim Tolstov

Erstellt: 2015-07-27 13:31:19, Letzte Aktualisierung: 2023-02-07 21:37:02

Correlation is a statistical measure that assesses the strength and direction of the relationship between two variables. The Pearson correlation coefficient was developed by British statistician and biologist, Karl Pearson. The Pearson correlation coefficient is a commonly used metric for determining the correlation between two variables and it is calculated using the Pearson formula.

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

The Pearson formula takes into account the means, standard deviations, and covariance of the two variables. The resulting value, the Pearson correlation coefficient, is a number between -1 and 1, where a value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation.

The Pearson correlation coefficient is commonly used in fields such as psychology, finance, and biology to assess the strength of the relationship between two variables.

The interpretation of the Pearson correlation coefficient is that it describes the strength of the relationship between the two variables and the direction of the relationship, with positive values indicating a positive relationship and negative values indicating a negative relationship. When interpreting the result of the Pearson correlation coefficient, it is important to consider the context and domain knowledge to fully understand the relationship between the variables.

#### Paired random variables

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Pearson correlation coefficient

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