To calculate the correlation coefficient $r$ for a set of data points, we can 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:

• $n$ is the number of data points,
• $x$ and $y$ are the individual values of the variables.

Let’s calculate this step-by-step.

We have the following data points: $(5, 78.2), (6, 86.2), (7, 85.2), (8, 88.4), (9, 90), (10, 99.8)$

First, I will calculate the required sums for $x$, $y$, $xy$, $x^2$, and $y^2$. Let me handle that.The correlation coefficient $r$ is approximately $0.926$ (rounded to three decimal places).

Would you like further details or clarification?

Here are some related questions to consider:

1. What does a correlation coefficient of 0.926 indicate?
2. How does the value of $r$ relate to the strength of the relationship between $x$ and $y$?
3. What is the interpretation of $r = 1$ or $r = -1$?
4. How can we visualize the relationship between $x$ and $y$?
5. What are the limitations of using the correlation coefficient?

Tip: A correlation coefficient close to 1 indicates a strong positive linear relationship between the two variables.