In running the simple linear regression of Y on X, if you know that no observation in your sample has an X value that is equal to $\bar { X }$ , what condition might not be true?
A) The regression line's prediction at $\bar { X }$ is $\bar { Y }$ .
B) The sum of the residuals equals zero.
C) The average of the residuals equals zero.
D) The residual for the observation closest to $\bar { X }$ will be zero.

Question

Quizplus · Accepted Answer

If no observation in the sample has an X value that is equal to $\bar { X }$, then the residual for the observation closest to $\bar { X }$ will not be zero, as stated in choice D. This is because the observation closest to $\bar { X }$ would have the smallest residual if it had an X value of $\bar { X }$, but since it doesn't, its residual will be non-zero. Choices A, B, and C will still be true regardless of whether an observation has an X value equal to $\bar { X }$ or not.

In Running the Simple Linear Regression of Y on X Xˉ\bar { X }Xˉ

In Running the Simple Linear Regression of Y on X $\bar { X }$