If covariance (x,y)

Q: If covariance (x,y) < 0, then the relation between two variables is:

The correct option is 2: Covariance is a statistical measure used to assess the directional relationship between two random variables, X and Y. It indicates whether the two variables tend to move in the same direction or in opposite directions. The core rule governing covariance interpretation is based entirely on its sign. When covariance (x,y) is less than zero (Cov(x,y) \< 0), it means that as the values of variable X tend to increase, the values of variable Y tend to decrease, and vice versa. This indicates an inverse or **negative** relationship between the two variables. It is important to remember that covariance measures the direction of the linear relationship, but unlike the correlation coefficient, it does not standardize the strength or magnitude of this relationship. The incorrect option is 1: A **Positive** relation occurs when the covariance is greater than zero (Cov(x,y) \> 0). In a positive relationship, both variables tend to move in the same direction; as X increases, Y also increases, or as X decreases, Y also decreases. The incorrect option is 3: **Perfect Positive** correlation is a measure of the *strength* of a positive linear relationship, which is measured by the correlation coefficient (r = +1), not just covariance. While a perfect positive relationship would imply a positive covariance, a negative covariance explicitly rules out any positive relationship, let alone a perfect one. The incorrect option is 4: The relation between the variables **Do not exist** would typically be associated with a covariance value close to zero (Cov(x,y) ≈ 0), indicating that there is no *linear* relationship between the variables. Since a negative covariance value (Cov(x,y) \< 0) clearly defines a linear direction, the relationship certainly exists.

Question

If covariance (x,y) < 0, then the relation between two variables is:

Accepted Answer

The correct option is 2:
Covariance is a statistical measure used to assess the directional relationship between two random variables, X and Y. It indicates whether the two variables tend to move in the same direction or in opposite directions. The core rule governing covariance interpretation is based entirely on its sign. When covariance (x,y) is less than zero (Cov(x,y) \< 0), it means that as the values of variable X tend to increase, the values of variable Y tend to decrease, and vice versa. This indicates an inverse or **negative** relationship between the two variables. It is important to remember that covariance measures the direction of the linear relationship, but unlike the correlation coefficient, it does not standardize the strength or magnitude of this relationship.

The incorrect option is 1:
A **Positive** relation occurs when the covariance is greater than zero (Cov(x,y) \> 0). In a positive relationship, both variables tend to move in the same direction; as X increases, Y also increases, or as X decreases, Y also decreases.

The incorrect option is 3:
**Perfect Positive** correlation is a measure of the *strength* of a positive linear relationship, which is measured by the correlation coefficient (r = +1), not just covariance. While a perfect positive relationship would imply a positive covariance, a negative covariance explicitly rules out any positive relationship, let alone a perfect one.

The incorrect option is 4:
The relation between the variables **Do not exist** would typically be associated with a covariance value close to zero (Cov(x,y) ≈ 0), indicating that there is no *linear* relationship between the variables. Since a negative covariance value (Cov(x,y) \< 0) clearly defines a linear direction, the relationship certainly exists.