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.