Question

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

• A. \(0.64\)
• B. \(0.80\)
• C. \(0.16\)
• D. \(1.60\)

Hint:

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.

Answer 1

The Correct Option is A

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: \[ 0.64 \] \[ \therefore \text{The correct answer is } 0.64. \]