i. A coefficient of correlation r close to 0 (say, 0.08) shows that the relationship between two variables is quite weak. ii. The coefficient of determination is the proportion of the total variation in the dependent variable Y that is explained or accounted for by its relationship with the independent variable X.
iii. If the coefficient of correlation is -0.90, the coefficient of determination is -0.81.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

Statement (i) is correct as a coefficient of correlation close to 0 indicates weak relationship between two variables. Statement (ii) is also correct as the coefficient of determination shows how much of the variability in Y is explained by X. However, statement (iii) is incorrect as the coefficient of determination cannot be negative. The coefficient of determination is always between 0 and 1, indicating the proportion of variance in Y that is explained by X. The correct coefficient of determination for a correlation coefficient of -0.90 would be 0.81, as the square of the correlation coefficient gives the coefficient of determination. Therefore, only statements (i) and (ii) are correct, and statement (iii) is false.

I a Coefficient of Correlation R Close to 0 (Say