Question:
If the correlation coefficient between \(X\) and \(Y\) is \(0.8\), what is the coefficient of determination?
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
Concept:
The coefficient of determination is the square of the correlation coefficient. It represents the proportion of the variation in the dependent variable that is explained by the independent variable. If the correlation coefficient is \(r\), then: \[ R^2 = r^2 \] where \(R^2\) is called the coefficient of determination.
Step 1: Identify the given correlation coefficient.
\[ r = 0.8 \]
Step 2: Square the correlation coefficient.
\[ R^2 = (0.8)^2 \] \[ R^2 = 0.64 \]
Step 3: Interpret the result.
Thus, the coefficient of determination is: \[ 0.64 \] \[ \therefore \text{The correct answer is } 0.64. \]
The coefficient of determination is the square of the correlation coefficient. It represents the proportion of the variation in the dependent variable that is explained by the independent variable. If the correlation coefficient is \(r\), then: \[ R^2 = r^2 \] where \(R^2\) is called the coefficient of determination.
Step 1: Identify the given correlation coefficient.
\[ r = 0.8 \]
Step 2: Square the correlation coefficient.
\[ R^2 = (0.8)^2 \] \[ R^2 = 0.64 \]
Step 3: Interpret the result.
Thus, the coefficient of determination is: \[ 0.64 \] \[ \therefore \text{The correct answer is } 0.64. \]
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