To compute Pearson's Product Moment Correlation Coefficient (often denoted as $r$), we can use the following formula:

[ r = \frac{n\sum{(XY)} - \sum{X}\sum{Y}}{\sqrt{[n\sum{X^2} - (\sum{X})^2] [n\sum{Y^2} - (\sum{Y})^2]}} ]

Where:

• $X$ and $Y$ are the two data sets.
• $n$ is the number of data points.
• $\sum{XY}$ is the sum of the product of corresponding data points.
• $\sum{X}$ and $\sum{Y}$ are the sums of the data sets $X$ and $Y$, respectively.
• $\sum{X^2}$ and $\sum{Y^2}$ are the sums of the squares of the data sets $X$ and $Y$, respectively.

Given the dataTo compute Pearson's Product Moment Correlation Coefficient (often denoted as $r$), we can use the following formula:

[ r = \frac{n\sum{(XY)} - \sum{X}\sum{Y}}{\sqrt{[n\sum{X^2} - (\sum{X})^2] [n\sum{Y^2} - (\sum{Y})^2]}} ]

Where:

• $X$ and $Y$ are the two data sets.
• $n$ is the number of data points.
• $\sum{XY}$ is the sum of the product of corresponding data points.
• $\sum{X}$ and $\sum{Y}$ are the sums of the data sets $X$ and $Y$, respectively.
• $\sum{X^2}$ and $\sum{Y^2}$ are the sums of the squares of the data sets $X$ and $Y$, respectively.

Given the

$\text{Data A} = [34, 22, 10, 11, 23, 20, 16, 18, 21, 15]$ $\text{Data B} = [12, 23, 21, 24, 10, 30, 28, 29, 32, 25]$

Let's calculate $r$ step by step.The Pearson's Product Moment Correlation Coefficient $r$ for the given data is approximately $-0.463$.

This negative value indicates an inverse relationship between Data A and Data B, meaning that as values in Data A increase, values in Data B tend to decrease, and vice versa.

Would you like more details on the calculation process or further explanation? Here are some related questions that might interest you:

1. How do you interpret the value of the Pearson correlation coefficient?
2. What is the significance of a negative Pearson correlation coefficient?
3. How does Pearson correlation differ from other types of correlation?
4. Can Pearson correlation be used for non-linear relationships?
5. What are the limitations of using Pearson's correlation coefficient?

Tip: Always plot your data when analyzing correlations to visually assess the relationship.