102. Here is a method for obtaining the variance of the residuals in simple (one predictor) linear regression, as given by Equation (12.13).

a. We have shown in Equations (12.26) and

(12.27) that Cov( )  s2H and Cov( ) 

s2(I  H). Now show that 

s2  V .

b. Use part

(a) and V from Section 12.4 to show Equation (12.13) for simple linear regression V1Yi  Y ˆ

i 2  s2 # c 1 

1 n



1xi  x22 Sxx d

1Y ˆ

i 2 1Y ˆ

i 2 V1Yi