Prediction intervals for Y are narrowest when
A)the mean of X is near the mean of Y.
B)the value of X is near the mean of X.
C)the mean of X differs greatly from the mean of Y.
D)the mean of X is small.

Question

Quizplus · Accepted Answer

The prediction interval for Y is based on the variability of Y and the variability of the residuals. The residuals represent the difference between the actual Y values and the predicted Y values based on the X values. When the value of X is near the mean of X, the predicted Y value will be closer to the mean of Y, which reduces the variability of the residuals and, in turn, narrows the prediction interval for Y. Therefore, the choice that provides the narrowest prediction interval for Y is B.

Prediction Intervals for Y Are Narrowest When