Step 1: Understanding the Question
The question provides the correlation coefficient (\(r\)) between two variables and asks for the coefficient of determination (\(R^2\)).
Step 2: Key Formula or Approach
The coefficient of determination, denoted as \(R^2\), is defined as the square of the correlation coefficient, \(r\).
\[
R^2 = r^2
\]
It represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s).
Step 3: Detailed Explanation
We are given the correlation coefficient:
\[
r = 0.8
\]
To find the coefficient of determination, we square this value:
\[
R^2 = (0.8)^2 = 0.8 \times 0.8 = 0.64
\]
Step 4: Final Answer
The coefficient of determination is 0.64. This means that 64% of the variation in one variable can be explained by the variation in the other variable.