Question

The numerical value of the coefficient of determination

A) is always smaller than the coefficient of correlation
B) is negative if the coefficient of determination is negative
C) can be larger or smaller than the coefficient of correlation
D) is always larger than the coefficient of correlation

Answer 1

The coefficient of determination, r², is always equal to the square of the correlation coefficient, r. Therefore, the numerical value of the coefficient of determination is always larger than or equal to the coefficient of correlation.

Step-by-step explanation:

The coefficient of determination, also known as r², is always equal to the square of the correlation coefficient, r. Therefore, the numerical value of the coefficient of determination is always larger than or equal to the coefficient of correlation.

For example, if the correlation coefficient is 0.5, the coefficient of determination will be 0.5² = 0.25. If the correlation coefficient is -0.8, the coefficient of determination will be (-0.8)² = 0.64. So, option D) is correct.