Which term describes the measure of the average cross-product deviation between two variables?

Which term describes the measure of the average cross-product deviation between two variables?

• A. Correlational coefficient
• B. Regression coefficient
• C. Standard deviation
• D. Covariance

Answer: (D)

Covariance measures how two variables vary together by averaging the product of their deviations from their means. If X and Y tend to be above their means at the same time, the deviations have the same sign and the product is positive, giving a positive covariance; if one is above its mean while the other is below, the product is negative, giving a negative covariance; if their deviations don’t show a consistent pattern, the covariance is near zero. This cross-product deviation is the essence of the measure, capturing both direction and the extent to which the variables co-vary. The correlational coefficient is simply a standardized version of covariance, the standard deviation pertains to a single variable’s spread, and the regression coefficient describes the expected change in one variable for a unit change in the other, not the joint deviation itself.

Covariance measures how two variables vary together by averaging the product of their deviations from their means. If X and Y tend to be above their means at the same time, the deviations have the same sign and the product is positive, giving a positive covariance; if one is above its mean while the other is below, the product is negative, giving a negative covariance; if their deviations don’t show a consistent pattern, the covariance is near zero. This cross-product deviation is the essence of the measure, capturing both direction and the extent to which the variables co-vary. The correlational coefficient is simply a standardized version of covariance, the standard deviation pertains to a single variable’s spread, and the regression coefficient describes the expected change in one variable for a unit change in the other, not the joint deviation itself.