Hypothesis SSCP (H) refers to which of the following?

Hypothesis SSCP (H) refers to which of the following?

• A. The residual sum of squares and cross-products matrix
• B. The total sum of squares and cross-products matrix
• C. The cross-covariance matrix of the predictors
• D. The hypothesis sum of squares and cross-products matrix

Answer: (D)

In a multivariate linear model, the total variability in the response can be broken into what the model explains and what remains as error. The piece that represents the variation explained by the predictors is called the hypothesis sum of squares and cross-products matrix, abbreviated as H. This matrix is central to testing hypotheses about the model parameters because it captures how much of the response variation is attributed to the fitted model (the portion due to the hypotheses about β). It’s used together with the error (or residual) SSCP matrix to form test statistics like F-tests or Wilks’ lambda. The other matrices describe different things: the residual SSCP measures unexplained variation, the total SSCP is the overall variation, and the cross-covariance matrix of the predictors is a separate descriptor of how the predictors relate to each other, not a SSCP used for hypothesis testing. Therefore, the correct identification is the hypothesis sum of squares and cross-products matrix.

In a multivariate linear model, the total variability in the response can be broken into what the model explains and what remains as error. The piece that represents the variation explained by the predictors is called the hypothesis sum of squares and cross-products matrix, abbreviated as H. This matrix is central to testing hypotheses about the model parameters because it captures how much of the response variation is attributed to the fitted model (the portion due to the hypotheses about β). It’s used together with the error (or residual) SSCP matrix to form test statistics like F-tests or Wilks’ lambda. The other matrices describe different things: the residual SSCP measures unexplained variation, the total SSCP is the overall variation, and the cross-covariance matrix of the predictors is a separate descriptor of how the predictors relate to each other, not a SSCP used for hypothesis testing. Therefore, the correct identification is the hypothesis sum of squares and cross-products matrix.