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To calculate the correlation coefficient (often denoted as \( r \)) between two variables \( x \) and \( y \), we use the 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:
- \( n \) = number of data points
- \( \sum xy \) = sum of the products of \( x \) and \( y \)
- \( \sum x \) = sum of all \( x \) values
- \( \sum y \) = sum of all \( y \) values
- \( \sum x^2 \) = sum of squares of \( x \)
- \( \sum y^2 \) = sum of squares of \( y \)

Let's break this down:
1. Calculate the necessary sums: \( \sum x \), \( \sum y \), \( \sum x^2 \), \( \sum y^2 \), and \( \sum xy \).
2. Substitute into the formula to find \( r \).

I'll compute these steps for the given data.The correlation coefficient \( r \) for the given data is approximately \(-0.981\). This indicates a strong negative linear relationship between \( x \) and \( y \).

Would you like more details on how this calculation was done, or do you have any other questions?

Here are 5 related questions you might find helpful:
1. What does a correlation coefficient of \(-0.981\) signify?
2. How do you interpret the strength of a correlation?
3. What is the difference between correlation and causation?
4. How do you calculate a linear regression line using this data?
5. What are the limitations of using a correlation coefficient?

**Tip:** A correlation coefficient near -1 means that as one variable increases, the other tends to decrease linearly in a very predictable manner.

Based on the data shown, calculate the correlation coefficient (rounded to three decimal places).

Learn how to calculate the correlation coefficient for a given set of data points (x, y). This problem involves calculating key sums and applying the correlation coefficient formula. Suitable for high school statistics students.

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