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The question asks to find the **coefficient of determination** given the **correlation coefficient (r-value)** of 0.908.

The coefficient of determination, \( R^2 \), is calculated as the square of the correlation coefficient:

\[
R^2 = r^2
\]

Given that \( r = 0.908 \), we can compute:

\[
R^2 = (0.908)^2
\]

Let's calculate that.The coefficient of determination \( R^2 \), rounded to three decimal places, is **0.824**.

The correct answer is **B. 0.824**.

Would you like further details or have any questions?

Here are some related questions you might find helpful:
1. How is the correlation coefficient different from the coefficient of determination?
2. What does a coefficient of determination of 0.824 tell us about the data set?
3. How do we interpret a correlation coefficient of 0.908 in practical terms?
4. Can the coefficient of determination ever be negative?
5. What is the relationship between \( r \) and \( R^2 \) when \( r \) is exactly 1 or -1?

**Tip**: The closer the coefficient of determination \( R^2 \) is to 1, the better the model explains the variability of the response data.

If the r-value, or correlation coefficient, of a data set is 0.908, what is the coefficient of determination to three decimal places?

Learn how to calculate the coefficient of determination from a correlation coefficient (r-value) of 0.908. This problem involves the use of key statistical concepts such as the correlation coefficient (r) and the coefficient of determination (R²), which is the square of the r-value. The correct answer is 0.824. Suitable for students in Grades 9-12.

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