The Pearson product-moment correlation coefficient is a measure of a linear correlation between two variables X and Y, giving a value between +1 and -1 inclusive. It is widely used in the science as a measure of the strength of linear dependence between two variables. Pearsonâ€™s correlation coefficient between two variables is defined as the covariance of the two variables divided by the product of their standard deviation. The form involves a product moment that is the mean of the product of the mean-adjusted random variables; hence the modifier product moment in the name.

The absolute value of both the sample and population Pearson correlation coefficients are less than or equal to 1. Correlations equal to 1 or -1 correspond to data points lying exactly on a line, or to a bivariate distribution entirely supported on a line. A key mathematical property of the Pearson correlation coefficient is that it is invariant to separate changes in location and scale in the two variables.

The correlation coefficient ranges from -1 to 1. A value of 1 implies that a linear equation describes the relationship between X and Y perfectly with all data points lying on a line for which Y increases as X increases. A value of -1 implies that all data points lie on a line for which Y decreases as X increases. A value of 0 implies that there is o linear correlation between the variables.

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