Definition:Sample Correlation Coefficient

Definition

Let $S = \sequence {x_i, y_i}$ be a sequence of paired observations from a population.

The sample correlation coefficient of $S$ is given by:

$r = \dfrac {s_{x y} } {\sqrt {s_{x x} s_{y y} } }$

where:

$s_{x y}$ denotes the sum of the products of deviations of $x_i$ and $y_i$ from their means

$s_{x x}$ and $s_{y y}$ are the sums of the squares of the deviations of $x_i$ and $y_i$ from their respective means.

Also see

• Results about sample correlation coefficients can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): correlation coefficient: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): correlation coefficient: 1.