8 Multiple Regression II

8.1 Extra Sums of Squares

  • Defination

An extra sum of squares measures:

  1. the marginal reduction in the error sum of squares (SSE)
  2. the marginal increase in the regression sum of squares (SSR)

when one or several preictor variables are added to the regression model, given that other predictor variables are already in the model

  • Example:

SSR(X1|X2) = SSR(X1,X2) - SSR(X2) = SSSE(X2) - SSE(X1,X2)

  • Decomposition of SSR into Extra Sums of Squares

SSTO = SSR(X1) + SSE(X1) = SSR(X1) + SSR(X2|X1) + SSE(X1,X2)

SSR(X1,X2,X3) = SSR(X1) + SSR(X2|X1) + SSR(X3|X1,X2) = SSR(X1) + SSR(X2,X3|X1)

  • ANOVA Table Containing Decomposition of SSR