When the correlation between X and Y is zero, then the safest prediction of Y which can be made, give information on X,
A) is the mean of X
B) is the mean of Y
C) is the mean of the combined distributions of X and Y
D) none of these

Question

Quizplus · Accepted Answer

If the correlation between X and Y is zero, it means that there is no linear relationship between the two variables. Therefore, any information about X cannot be used to predict Y with more accuracy than the overall average of Y, which is the mean of Y. The mean of X cannot be used because it is not necessarily related to the mean of Y when there is no correlation between them. Option C is also incorrect because combining distributions or finding joint probabilities requires some relationship between the two variables.

When the Correlation Between X and Y Is Zero, Then