Question

True or False: Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals 0.50, this means that 50% of the variation in the dependent variable (Y) is due to changes in the independent variable (X).

Answer 1

Given statement, " Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals 0.50, this means that 50% of the variation in the dependent variable (Y) is due to changes in the independent variable (X)." is False.

Because, correlation coefficient = r = 0.50

=> coefficient of determination (R²) = (0.50)² = 0.25

Therefore, Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals 0.50, this means that 25% of the variation in the dependent variable (Y) is due to changes in the independent variable (X).