When interpreting the covariance between variables x and y, which of the following statements is the most accurate?
A) A negative value of covariance that, on average, if x is below its mean, then y tends to be below its mean.
B) A positive value of covariance indicates that, on average, if x is above its mean, then y tends to be above its mean.
C) A positive value of covariance indicates that, on average, if x is above its mean, then y tends to be below its mean.
D) A negative value of covariance indicates that, on average, if x is above its mean, then y tends to be above its mean.

Question

Quizplus · Accepted Answer

The definition of covariance is that if two variables have a positive covariance, it means that they tend to move in the same direction. Therefore, if x is above its mean, y also tends to be above its mean, and similarly, if x is below its mean, y also tends to be below its mean. This is represented by a positive covariance. Choice A is incorrect because it states that a negative covariance indicates that if x is below its mean, y tends to be below its mean, which is not necessarily true. Choice C is incorrect because it states that a positive covariance indicates that if x is above its mean, y tends to be below its mean, which is the opposite of what is true. Choice D is incorrect because it states that a negative covariance indicates that if x is above its mean, y tends to be above its mean, which is also not necessarily true.

When Interpreting the Covariance Between Variables X and Y, Which