The formula in the image is the Pearson correlation coefficient, denoted as $R_{xy}$. Here's the equation as extracted from the image:

[ R_{xy} = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} ]

Where:

• $n$ is the number of data points.
• $\sum xy$ is the sum of the products of corresponding $x$ and $y$ values.
• $\sum x$ is the sum of the $x$-values.
• $\sum y$ is the sum of the $y$-values.
• $\sum x^2$ is the sum of the squares of the $x$-values.
• $\sum y^2$ is the sum of the squares of the $y$-values.

This formula calculates the correlation between two variables $x$ and $y$. The result will be a value between -1 and 1, where:

• $R_{xy} = 1$ means perfect positive correlation.
• $R_{xy} = -1$ means perfect negative correlation.
• $R_{xy} = 0$ means no correlation.

Would you like further details on how to apply this formula, or do you have any specific data you'd like to calculate it for?

Here are 5 relative questions to expand your understanding:

1. How do you interpret the Pearson correlation coefficient in terms of data relationships?
2. What are the differences between positive, negative, and zero correlation?
3. Can correlation imply causation between two variables?
4. What are the limitations of using Pearson's correlation coefficient?
5. How would you calculate each component (e.g., $\sum x^2$, $\sum xy$) in this formula?

Tip: Ensure the data you are using is linear for Pearson correlation, as it only measures linear relationships between variables.