Definition:Sample Correlation Coefficient
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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.