Suppose { } is a sequence of n independent normal random variables with mean 0 and variance o2 . Consider the simple linear regression model: Yi = Bo + BIXi+ ci, i = 1, ..., n. Recall from class that Bo = y - Bix and B1 = Sxx Sxy where Sxy = _(x; - x)(vi - y) and Sxx = _(x; -x)2. i=1 The residual sum of squares (or sum of squared error) is defined by SSE = Ye. 1= 1 where ei = yi - y; and y; is the i-th fitted value, i.e., yi = Bo + Bixi. Show that: (a) Zi=lei = 0 (b) Et=1 xie; =0 (c) E [EL-(e - 2)2] = (n- 1)62