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Question: Which of the following statement(s) is/are true?
I. If the correlation coefficient is significant, the equation of the regression line cannot be determined.
II. The values of the dependent variable can be predicted for the values of the independent variable using the regression line equation.
III. For the value of r to be close to + 1 or - 1, the observed values must be closer to the predicted values.
IV. The total variation is equal to the sum of the explained variation and the unexplained variation.


A ) I, II and III only
B ) all are true
C ) II, III and IV only
D ) II and IV only

Steps to derive

1 The equation of the regression line can be determined only when the correlation coefficient is significant.

2 For the various values of the independent variable x, the corresponding values of the dependent variable y can be predicted, using the regression line equation y′ = a + bx.

3 For r to be close to + 1 or - 1, the observed values y must be closer to the predicted values y′.

4 Total variation is the sum of the explained and the unexplained variations.

5 So, only statements II, III and IV are correct.



Hence the right answer is Option C

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