Correlation | Linear Regression | Variance and Standard Deviation

# Calculator Correlation and Significance

Calculates the correlation coefficient for two characteristics and the significance of the data. Correlation is the statistical relationship. It tells how much two quantifiable characteristics have to do with each other. The correlation coefficient indicates the degree of this relationship, it is between -1 and 1. 1 means perfect relationship, -1 means perfect inverse relationship and 0 is no relationship. Correlation says nothing about causality. If two things are related, it does not necessarily mean that one thing causes the other.

Significance tells how certain a measured relationship actually is. There can always be errors and coincidences with measured values. This can only be ruled out with a certain probability, 95% and 99% are common as significance levels. A t-test determines the significance.

Please enter the values of the two characteristics separately. For each characteristic, the values must be separated from one another with a blank or a line break. The number of values per characteristic must be the same. The n-th value of the first feature belongs to the n-th value of the second feature.
*Example* calculates with the size (in 1000 km²) and population (in millions) of some European countries.

## The formulas are:

n: number of value pairs, Σ: sum i=1 to n

x

_{m}: mean of all x

_{i}, y

_{m}: mean of all y

_{i}

Covariance x und y: s

_{xy}= 1/n * Σ (x

_{i}−x

_{m})(y

_{i}−y

_{m})

Standard deviation x: s

_{x}= √ 1/n * Σ (x

_{i}−x

_{m})²

Standard deviation y: s

_{y}= √ 1/n * Σ (y

_{i}−y

_{m})²

Correlation coefficient: r

_{xy}= s

_{xy}/ (s

_{x}*s

_{y})

Test variable: t=√(n−2)/(1−r

_{xy}²)

Degrees of freedom: df=n-2

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