Population correlation coefficient
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
Pearson's correlation coefficient when applied to a population is commonly represented by the Greek letter ρ (rho) and may be referred to as the population correlation coefficient or the population Pearson correlation coefficient.
Population correlation coefficient.:
The correlation ρ between two variables is:
\[\rho = \frac{1}{N}\sum\left [ \frac{X_{i}-\mu _{x}}{\sigma _{x}} \times \frac{Y_{i}-\mu _{y}}{\sigma _{y}} \right ] \]
where N is the number of observations in the population, Σ is the summation symbol, Xi is the X value for observation i, μX is the population mean for variable X, Yi is the Y value for observation i, μY is the population mean for variable Y, σx is the population standard deviation of X, and σy is the population standard deviation of Y.
