Total SSCP (T) refers to which of the following?

Total SSCP (T) refers to which of the following?

• A. The sum of squares for an entire single variable.
• B. The cross-products of residuals in regression.
• C. The sum of squares and cross-products matrix for a subset of observations.
• D. The total sum of squares and cross-products matrix for an entire set of observations; the multivariate analogue of the total sum of squares.

Answer: (D)

Total SSCP captures all the variability and relationships among multiple variables across every observation. It is the sum over all observations of the outer product of each observation’s deviation from the mean vector, producing a p × p matrix (where p is the number of dependent variables). This serves as the multivariate analogue of the univariate total sum of squares, encapsulating how spread out the data are in all directions and how the variables covary with each other. It is computed as T = Σ (x_i − x̄)(x_i − x̄)′. Because it uses the entire dataset, it is not restricted to a subset of observations, and it specifically refers to the total cross-products matrix for all observations.

Total SSCP captures all the variability and relationships among multiple variables across every observation. It is the sum over all observations of the outer product of each observation’s deviation from the mean vector, producing a p × p matrix (where p is the number of dependent variables). This serves as the multivariate analogue of the univariate total sum of squares, encapsulating how spread out the data are in all directions and how the variables covary with each other. It is computed as T = Σ (x_i − x̄)(x_i − x̄)′. Because it uses the entire dataset, it is not restricted to a subset of observations, and it specifically refers to the total cross-products matrix for all observations.