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Correlation Coefficient

Main Concept

Pearson Product-Moment Correlation Coefficient

The Pearson Product-Moment Correlation Coefficient (also known as r) is a value that measures the correlation between two variables X and Y.

The coefficient value ranges from 1 to 1, where a positive value represents a positive correlation, a value of 0 represents no correlation and a negative value represents a negative correlation.

Values of ±1 are considered total correlations and only occur when all of the data points lie on a straight line.

Data sets with values of r near 0 are considered to have weak correlations, while data sets with values of r near +1 or 1 are considered to have strong correlations.



Calculating r

The formula used to calculate the Pearson Product-Moment Correlation Coefficient (r) on a given sample is

r = nxi yixiyinxi2xi2n yi2yi2

where n represents the amount of data points and xi,yi are the samples indexed with i.

Coefficient of Determination

The coefficient of determination measures how much of the variation in the value of y can be explained by the relationship between x and y.

This value, as a percent, can be calculated with  r2:

Example: if r = 0.5 then the coefficient of determination of the data set is  0.52  which is  0.25.

This means that 25% of the variation in the value of y can be explained by the relationship between x and y. The other 75% remains unexplained.


Click on the plot to make data point or press Randomly Generate Some Data Points to randomly plot a random amount of data points. At least three data points are needed to show the correlation coefficient.


Formula for correlation coefficient ( r )

nxi yixiyinxi2xi2n yi2yi2













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