Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Correlation ▷ Sample correlation coefficient

Definition: Let $x = \left\lbrace x_1, \ldots, x_n \right\rbrace$ and $y = \left\lbrace y_1, \ldots, y_n \right\rbrace$ be samples from random variables $X$ and $Y$. Then, the sample correlation coefficient of $x$ and $y$ is given by

\[\label{eq:corr-samp} r_{xy} = \frac{\sum_{i=1}^n (x_i-\bar{x}) (y_i-\bar{y})}{\sqrt{\sum_{i=1}^n (x_i-\bar{x})^2} \sqrt{\sum_{i=1}^n (y_i-\bar{y})^2}}\]

where $\bar{x}$ and $\bar{y}$ are the sample means.

 
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Metadata: ID: D168 | shortcut: corr-samp | author: JoramSoch | date: 2021-12-14, 07:23.