1. 2. In a simple linear regression anaiysis, n independent paired data (in. X1}, ...., iv", xi.) are tted to the model M1 in = 1(xi-a)+.z . i= 1.....n. where the regressor x is a random variable with mean x and variance or: . The random error e is statisticaliy independent of x and has mean zero and constant variance 1". a is a given real number (that is, the value of a is known}. The values of ox, 0:, tr2 are all unknown. Before the data for {y , xi are available, we need to construct estimators for the parameters. a) Construct the Ordinary least squares (0L5) estimator of ,61 . Is the OLE. estimator unbiased for 31? why or why not? b) Construct an estimator for or2 . Is the estimator unbiased for or2 ? why or why not? c) Derive the variance of the 0L5 estimator of t in a) and construct an unbiased estimator of this variance. d) Construct an estimator for the expectation E (y), using model M1. e} Construct an estimator for EU), not using model M1. f) Are the two estimators in d) and e} equal? why or why not? In Problem 1, the value of a is unknown. Do a), b) and c)