[10 marks] Suppose that the data follow the model

y=\\\\beta _(0)+\\\\beta _(1)x_(i)+e,eN(0,\\\\sigma ^(2))

. However,\ Jerry includes an additional predictor and fits the model

y=\\\\beta _(0)+\\\\beta _(1)x_(1)+\\\\beta _(2)x_(2)+e,eN(0,\\\\sigma ^(2))

.\ i. [5 marks] Find

Cov(hat(y)_(j),(/bar (y)))

, where

hat(y)_(j)

is the fitted value of the

j

-th observation for Jerry's\ fitted model, and

/bar (y)

is the sample mean.\ ii. [5 marks] Find

E[\\\\sum n(y_(i)-hat(y)_(i))^(2)]

.

5) [10 marks] Suppose that the data follow the model y=0+1x1+e,eN(0,2). However, Jerry includes an additional predictor and fits the model y=0+1x1+2x2+e,eN(0,2). i. [5 marks] Find Cov(y^j,y), where y^j is the fitted value of the j-th observation for Jerry's fitted model, and y is the sample mean. ii. 5 marks ] Find E[n(yiy^i)2]