Pearson

195. Pearson

Linear relationships

𝑟 = \frac{\sum_{𝑖 = 1}^{𝑛} (𝑥_{𝑖} - \bar{𝑥}) (𝑦_{𝑖} - \bar{𝑦})}{\sqrt{\sum_{𝑖 = 1}^{𝑛} {(𝑥_{𝑖} - \bar{𝑥})}^{2} \times {(𝑦_{𝑖} - \bar{𝑦})}^{2}}}

Interpretation:

Example

\begin{matrix} 𝑋 : [1, 2, 3, 4, 5] \\ 𝑌 : [2, 4, 6, 8, 10] \end{matrix}

Step 1: Calculate the Means of X and Y

\begin{matrix} \bar{𝑋} = 3 \\ \bar{𝑌} = 6 \end{matrix}

Step 2: Calculate the Differences from the Mean