Exercise 3.2 (*** - Linear regression (40%)). Let $1, ...,, ER be known constants. Suppose Yi = Bot Blitzi, i = 1, . ...n, where 61, ..., En ~ N(0, o'). The unknown vector of parameters is 0 = (Bo, 31, ?) EO = R x R x R+.2. (10%) Let Say = Eli(Yi - Y)(x; - x) and Six = Et(; - x)', where I = Et, r; and Y = Et Yi. From STAT 3008, we know that a 95% CI for B1 is given by I = B1 -t1-0/2,n-21/ 62 SHI B1 + 1-0/20-21 62 STI where 1-a/2,n-2 is the 1 - o/2 quantile of tn-2 distribution, and B1 = Scy SHI Bo = y - BIT, 62 n - 2 E( Yi - Bo - BIZi). i= Does the confidence interval / obey the sufficiency principle?\fDefinition 4.2. Sufficiency principle: If T = T(Xi:) is a "sufficient statistic" for 0, then any inference on 0 will depend on X1:n only through T