Assume that X and Y correlate .6,are in Z-score form,and that a particular value of X is 1.What is the value of the Y residual?
A) 0
B) .4
C) .6
D) 1

Question

Quizplus · Accepted Answer

Since X is in z-score form, a value of X being 1 means it is one standard deviation above the mean. Given that X and Y correlate .6, we know that for every one standard deviation increase in X, Y will increase by .6 standard deviations. Therefore, the Y value corresponding to X=1 will be .6 standard deviations above the mean. This means that the Y residual (the difference between the observed Y value and the predicted Y value based on X) will be equal to the distance between the observed Y value (which we do not know) and the mean Y value, which is 0 since Y is in z-score form. Therefore, the Y residual will be .6 standard deviations, which corresponds to choice B.

Assume That X and Y Correlate