In regression-style thinking, which term refers to the error term's multivariate counterpart of the residual sum of squares?

In regression-style thinking, which term refers to the error term's multivariate counterpart of the residual sum of squares?

• A. Extraction
• B. Error SSCP (E)
• C. Factor analysis
• D. Eta squared (η2)

Answer: (B)

In a multivariate model, the unexplained variation is summarized by a matrix rather than a single number. This is the error sum of squares and cross-products, abbreviated as the error SSCP and denoted E. It is computed as E = (residuals)'(residuals), capturing both the magnitude of residuals for each dependent variable and how those residuals covary with one another. The trace of E gives the total squared error across all outcomes, playing the same role as the residual sum of squares in univariate regression, and it is the quantity used in multivariate tests (like Wilks’ Lambda). The other terms mentioned relate to different concepts (factoring or effect size) and don’t represent this multivariate error structure.

In a multivariate model, the unexplained variation is summarized by a matrix rather than a single number. This is the error sum of squares and cross-products, abbreviated as the error SSCP and denoted E. It is computed as E = (residuals)'(residuals), capturing both the magnitude of residuals for each dependent variable and how those residuals covary with one another. The trace of E gives the total squared error across all outcomes, playing the same role as the residual sum of squares in univariate regression, and it is the quantity used in multivariate tests (like Wilks’ Lambda). The other terms mentioned relate to different concepts (factoring or effect size) and don’t represent this multivariate error structure.