Which of the following statements is (are) true with respect to the coefficient of determination ...

By Investopedia Staff AAA

Which of the following statements is (are) true with respect to the coefficient of determination?
I. Coefficient of determination and correlation coefficient must always have the same algebraic sign (i.e. plus or minus).
II. As the sum of squares of the error terms increases, coefficient of determination will increase as well.
III. Coefficient of determination measures the proportion of the total variation in Y that is accounted for by the variation in X.
IV. As the ratio of regression sum of squares to total sum of squares increases, correlation coefficient will increase.
a) II and III only.
b) I, II, and IV only.
c) III and IV only.
d) I and III only.


The correct answer is: c)

(I) is incorrect because coefficient of determination will always be positive, whereas correlation coefficient may be positive or negative.


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