Question: Which of the following statement(s) is/are true? I. If all the points fall on the regression line, the explained variation is equal to the total variation. II. If all the points fall on the regression line, the unexplained variation will be equal to zero. III. The values (y - y ′) are called residuals. IV. The mean of the residuals is always zero. A ) I, II and IV only B ) all are correct C ) II, III and IV only D ) I, II and III only Steps to derive 1 If all the points fall on the regression line, the explained variation ∑ (y ′ - y ‾ )2 is equal to the total variation ∑ (y - y ‾ )2 , since y ′ will be equal to y for each x .2 If all the points fall on the regression line, the unexplained variation ∑ (y - y ′)2 will be equal to zero, since y ′ will be equal to y for each x .3 A residual is the difference between the actual value of y and the predicted value y ′ for a given value of x . 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