APPLIED MULTIVARIATE STATISTICS: WITH SAS® SOFTWARE

3.10. Regression Diagnostics

As in univariate regression, to assess various assumptions on the multivariate regression model and the validity of the model, diagnostics should be an integral part of the analysis. Such diagnostics tools also include data scrutiny to notice any striking or unusual features present in the data. Certain quantities such as the matrices of predicted values, Ŷ=XB=X(X′X)⁻¹X′Y = PY, of residuals, =Y−Ŷ=(I−P)Y, and of estimated error variances and covariances, =E/(n−k−1)=Y′(I−P)Y/(n−k−1), where P=X(X′X)⁻¹X′=(p_ij) is the projection ...