formula for Pearson's correlation coefficient r*r* is

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!

Understand the formula for Pearson's correlation coefficient r with step-by-step breakdowns. Learn how to calculate correlation between two datasets, interpret results, and apply the formula to data analysis. Suitable for students in Grades 10-12 and undergraduate statistics courses.

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