First, show that for a linear regression model that has an intercept, Xn i=1 ei = Xn i=1 (Yi bYi) = 0 (Hint: consider the equation resulting form S 0 = 0 as in class or in the book on page 13).

6. Next, show that Xn i=1 bYi(Yi bYi) = Xn i=1 bYiei = 0 or, equivalently in vector notation, show that Yc0 e = 0. (Hint: use vector notation and recall that H2 = H. This is property 5 on page 20, and is the same as you were asked to check numerically in question 3c) above. Use this property to show that Yc0 e = 0). 2

7. Finally, use the results in properties 1 and 5 on page 20 in the textbook (and also in questions 5 and 6 above), to show that the crossterm in what is called the "total" sum of squares (SStotal), defined as: SStotal = Xn i=1 (Yi Y ) 2 = Xn i=1 [( bYi Y ) + (Yi bYi)]2 is equal to zero, so that the expression above simplifies to: SStotal = Xn i=1 ( bYi Y ) 2 + Xn i=1 (Yi bYi) 2 which gives the desired partition of the total variability used in Analysis of Variance (ANOVA).