Question

True or False: Assuming a linear relationship between X and Y, if the coefficient of correlation...

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).

Homework Answers

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).

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