The sum of the deviations of the true Y scores from the predicted scores is always
A)zero.
B)a very large number.
C)equal to N times the mean of Y.
D)negative.

Question

The sum of the deviations of the true Y scores from the predicted  scores is always
A)zero. 
B)a very large number. 
C)equal to N times the mean of Y. 
D)negative.

Quizplus · Accepted Answer

The sum of the deviations of the true Y scores from the predicted Y scores is always zero because of the equation of the regression line which is Y′ = a + bX. When we calculate the predicted Y scores, we take into account both the mean of X and the correlation between X and Y, so the residual values in the sample balance each other out and sum to zero.

The Sum of the Deviations of the True Y Scores