The formula for Pearson's correlation coefficient $r$ is:

$r = \frac{n \sum xy - \sum x \sum y}{\sqrt{\left( n \sum x^2 - (\sum x)^2 \right) \left( n \sum y^2 - (\sum y)^2 \right)}}$

Where:

• $n$ is the number of data points.
• $x$ and $y$ are the individual data points in two different datasets.
• $\sum xy$ is the sum of the products of paired values.
• $\sum x$ is the sum of the values in the $x$-dataset.
• $\sum y$ is the sum of the values in the $y$-dataset.
• $\sum x^2$ is the sum of the squares of the values in the $x$-dataset.
• $\sum y^2$ is the sum of the squares of the values in the $y$-dataset.

Would you like a breakdown of this formula with a sample dataset or more details on how it’s derived?

Related Questions:

1. How do you interpret the value of Pearson’s correlation coefficient?
2. What is the difference between Pearson's $r$ and Spearman’s rank correlation?
3. How can Pearson's correlation coefficient be affected by outliers?
4. What is the significance level for testing Pearson's correlation?
5. How do you calculate Pearson’s $r$ in Excel or other software?

Tip: Pearson's correlation assumes linearity and can be misleading if the relationship between variables is non-linear. Always check for linearity first!