National Counselor Exam (NCE)

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True variance or the coefficient of determination is calculated by which mathematical operation?

  1. Adding the correlation coefficient

  2. Multiplying the correlation coefficient

  3. Squaring the correlation coefficient

  4. Subtracting the correlation coefficient

The correct answer is: Squaring the correlation coefficient

The coefficient of determination, denoted as \( R^2 \), is derived from the correlation coefficient, which measures the strength and direction of a linear relationship between two variables. To find the coefficient of determination, you take the correlation coefficient and square it. Squaring the correlation coefficient effectively transforms the value into a proportion that reflects how much of the variability in one variable can be explained by the variability in the other variable. This mathematical operation is critical in research and data analysis as it allows for an understanding of the extent to which one variable is predictive of another. In summary, squaring the correlation coefficient provides a valuable insight into the relationship between the two variables, making it the correct operation for calculating the true variance or coefficient of determination.

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