The following represents observations (whyl), (9:2, ya), . . . , (an, 3;\"), n = 8, of two variables X, Y: a I 4!.\" m We've obtained the regression t via the nonlinear model 3'}: = a}? + a + 5,, where a is unknown, and the random noise 6, has distribution N(0,02). We'll view the above values of :12, as xed, i.e., they are not random, but K's are random and independent. For the above t on the right, we derived a least-squares estimator E: for the unknown a, and already computed a = 22.95 on the above data (so you would not have to). (a) Derive the least-squares estimator 6; of a, i.e., the a minimizing the squared-error on the data (931.91), - - - (lmy?!)- No need to argue second order conditions (i.e., the squared error is convex in terms of a). (b) Derive the distribution of 6;, and be explicit about its mean and variance. (c) As stated earlier, the right least-squares formula yields ii = 22.95 for the above data. Using this value of as, derive a 98% condence interval for a, assuming 02 is known. No need to compute the exact interval, but express it in terms of critical values of a known distribution (and other necessary quantities). (:1) Suppose we don't know or\". Which of the following two quantities (i) and (ii) is a more reasonable estimate for 02? Give a brief reason why. (0 $20K.- Y)\". (ii) $204 4? a)