Question:medium

If the correlation coefficient between \(X\) and \(Y\) is \(0.8\), what is the coefficient of determination?

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The coefficient of determination is simply the square of the correlation coefficient: \[ R^2 = r^2 \] It indicates the proportion of variation in one variable explained by the other.
Updated On: Mar 16, 2026
  • \(0.64\)
  • \(0.80\)
  • \(0.16\)
  • \(1.60\)
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The Correct Option is A

Solution and Explanation

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.
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