To solve this problem, we need to calculate the correlation coefficient $r$ and the coefficient of determination $R^2$ based on the bivariate data set. Here's how we can approach it:

The data set provided:

Step 1: Calculating the correlation coefficient $r$

The correlation coefficient $r$ is calculated using 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.
• $\sum{xy}$ is the sum of the products of each pair $x_i y_i$.
• $\sum{x}$ and $\sum{y}$ are the sums of $x$-values and $y$-values respectively.
• $\sum{x^2}$ and $\sum{y^2}$ are the sums of the squares of $x$-values and $y$-values.

Step 2: Coefficient of determination $R^2$

The coefficient of determination $R^2$ is simply the square of the correlation coefficient $r$:

$R^2 = r^2$

Now, let me calculate the values for you!The correlation coefficient $r$ is approximately $-0.954$, and the coefficient of determination $R^2$ is about $91.0\%$. This means that about 91% of the variation in $y$ can be explained by the variation in $x$.

Would you like further details on the calculations or have any questions?

Here are some related questions you might find interesting:

1. What does a negative correlation coefficient indicate?
2. How do you interpret the value of $R^2$?
3. What are some factors that can affect the strength of a correlation?
4. How do outliers impact the correlation coefficient?
5. What is the difference between correlation and causation?

Tip: Always check if there are any outliers in your data, as they can significantly affect the correlation coefficient.