To calculate the correlation coefficient $r$ using the given data, we use the formula:

$r = \frac{N \sum XY - \sum X \sum Y}{\sqrt{(N \sum X^2 - (\sum X)^2)(N \sum Y^2 - (\sum Y)^2)}}$

Given: $\sum X = 162, \quad \sum Y = 675, \quad \sum X^2 = 2652, \quad \sum Y^2 = 46459, \quad \sum XY = 10967, \quad N = 10$

Let's calculate it step by step.

Step 1: Calculate the numerator

$N \sum XY - \sum X \sum Y = 10 \times 10967 - 162 \times 675$

Step 2: Calculate the denominator

= \sqrt{(10 \times 2652 - 162^2) \times (10 \times 46459 - 675^2)}$$ ### Step 3: Compute the correlation coefficient $$r$$. I'll calculate it now.The correlation coefficient $$r$$ is approximately **0.203**. Would you like more details, or do you have any questions? Here are five related questions to expand your understanding: 1. How does the value of $$r$$ indicate the strength of the correlation? 2. What does a correlation coefficient close to 0 imply about the relationship between the variables? 3. How would the calculation differ if the sample size $$N$$ increased? 4. Can the correlation coefficient $$r$$ be negative? If so, what would that indicate? 5. How can you calculate the coefficient of determination ($$r^2$$) from the correlation coefficient? **Tip:** The correlation coefficient only measures the strength of a linear relationship. For non-linear relationships, other statistical methods might be more appropriate.