Cross-product deviations measure what in a bivariate relation?

Cross-product deviations measure what in a bivariate relation?

• A. Product of standardized deviations
• B. Covariance of centered variables
• C. Sum of products of deviations
• D. Cross-product deviations

Answer: (D)

Cross-product deviations capture how two variables move together around their means. For each observation, you multiply the deviation of X from its mean by the deviation of Y from its mean, and then sum those products across all observations. This sum shows whether large deviations in X tend to occur with large deviations in Y (positive contributions) or with deviations in the opposite direction (negative contributions). That raw sum, the cross-product deviations, is the backbone of covariance; dividing by n−1 gives the covariance, and further standardizing by the standard deviations yields the correlation. So the cross-product deviations quantify the joint deviation of the two variables from their means, i.e., how they co-vary across observations.

Cross-product deviations capture how two variables move together around their means. For each observation, you multiply the deviation of X from its mean by the deviation of Y from its mean, and then sum those products across all observations. This sum shows whether large deviations in X tend to occur with large deviations in Y (positive contributions) or with deviations in the opposite direction (negative contributions). That raw sum, the cross-product deviations, is the backbone of covariance; dividing by n−1 gives the covariance, and further standardizing by the standard deviations yields the correlation. So the cross-product deviations quantify the joint deviation of the two variables from their means, i.e., how they co-vary across observations.