The sum of squares and cross-products (SSCP) matrix has which of the following properties?

• A. It is identical to the variance-covariance matrix
• B. It expresses only variances, not covariances
• C. It is a square matrix where diagonals are sums of squares and off-diagonals are cross-products
• D. It contains correlation coefficients

Answer: (C)

The sum of squares and cross-products (SSCP) matrix is built from the deviations of the data and forms a square matrix. Each diagonal entry is the sum of squared deviations for that variable, and each off-diagonal entry is the sum of cross-products of the deviations for a pair of variables. In other words, it collects the total variability and the pairwise relationships between variables without normalizing. The SSCP is related to the variance-covariance matrix—covariance is just the SSCP scaled by 1/(n−1)—and it does not contain correlation coefficients, which are standardized covariances. So describing the matrix as square with diagonals as sums of squares and off-diagonals as cross-products fits exactly.