To solve for the correlation coefficient $r$ between the two variables $X$ (year) and $Y$ (temperature) based on the data provided, I will first extract the $X$ and $Y$ values from the table. After that, I'll use the formula for the Pearson correlation coefficient, which is:

[ 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:

• $X$ represents the year,
• $Y$ represents the high temperature,
• $n$ is the number of data points (13 in this case).

Let me calculate this for you.The correlation coefficient $r$ between $X$ (the year) and $Y$ (the high temperature) is approximately:

$r = 0.974$

This indicates a strong positive linear relationship between the two variables.

Would you like any further details or have questions about this calculation?

Here are 5 questions that might help expand your understanding:

1. What does a correlation coefficient close to 1 imply about the relationship between two variables?
2. How would the interpretation of the correlation coefficient change if the result were negative?
3. Can correlation coefficients ever exceed 1 or fall below -1?
4. What assumptions are involved in calculating Pearson's correlation coefficient?
5. How does the correlation coefficient differ from covariance?

Tip: While correlation shows the strength of a relationship between two variables, it doesn't imply causation! Always consider additional factors when interpreting results.