Please answer the question below:

Question 1) Assume we have longitudinal data for which a linear model for the response over time holds: Yij = Bo + Bitij + Eij (1) for i = 1, ..., N and j = 1, . ..,n, where the measurement times t; are common to all N individuals (ti = t;) and all planned measurements have been collected. We can also write Yi = XiB +ei for the vector of measurements for individual i and Y = XB+E for the vector of measurements for all individuals, for suitably chosen design matrices X; and X. We denote, for the zero-mean vector e, its block-diagonal matrix as V, with blocks denoted as Vi, i = 1, ..., N. We investigate the properties of two estimators for B: the ordinary least squares estimator BOLS = (XTX)-1XTY, and the generalized least squares estimator BGLS = (XTV-1X)-1XTV-ly. 1. Write down the design matrices X; and X. 2. Derive expressions for the covariance matrices of the two competitive estimators: the ordinary least squares estimator BOLS = (XTX)-'XTY, and the generalized least squares estimator BGLS = (XTV- 1 X)-1xTV-ly in terms of X and V. 3. Assume we have n = 7 and measurement times -3, -2, -1, 0, 1, 2,3. Suppose that the (j, k) element of E; is 02 pli-kl (2) Write out E; in full