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The question asks for the value of the correlation coefficient (denoted as \( r \)) given that the coefficient of determination (denoted as \( r^2 \)) is 0.81.

The coefficient of determination, \( r^2 \), is the square of the correlation coefficient. To find the correlation coefficient, we take the square root of the coefficient of determination:

\[
r = \pm \sqrt{0.81} = \pm 0.9
\]

Thus, the correlation coefficient can be either +0.9 or -0.9, depending on the direction of the relationship between the variables.

### Correct Answer:
**c) Either +0.9 or -0.9**

Do you want further details or explanations? 

Here are some related questions to expand understanding:
1. What is the significance of the correlation coefficient being positive or negative?
2. How do you interpret a coefficient of determination of 0.81 in terms of data fit?
3. What happens if \( r^2 \) is 1? What would the value of \( r \) be?
4. Can the correlation coefficient be greater than 1? Why or why not?
5. How does the correlation coefficient relate to linear regression?

**Tip:** The coefficient of determination \( r^2 \) shows how much of the variation in the dependent variable is explained by the independent variable in regression models.

What is the value of the correlation coefficient if the coefficient of determination is 0.81?

Explore how to determine the correlation coefficient from a given coefficient of determination, specifically demonstrating calculation for an r^2 value of 0.81. This guide is suitable for high school or introductory college statistics courses.

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