This is a multiple linear equations problem

Focus on the fact that the only unknowns in these equations are 31 and 12! Let A = X1 - X1, C = X1 - X2 = X3 -X1, D = X2 - X2 which are all known. Note that the left-side quantities are also known numbers. Thus we have a 2x2 system of linear equations that must be solyed for only two unknowns: 31: 5'2. The Normal Equations can be written as Y~X1=A1+02; Y-X3=C,81+D,82 If you have taken linear algebra you will probably realize that this could be expressed as a 232 matrix (:22) = (3 3) (2;) equation. The general linear trend line model is y = me: + b, which can be written in vector torm as Y N 111K + bU where U = (1,1, 1,. . .1] is a repeated version of unity. This is a two -variable design problem. Note that it ts the format Y N 1X1+ QXQ where ,81 = m, 2 = [1,211 = X,X3 = U. Note further that if X has been mean-centered. then X - U = . A. Show that of X is mean-centered, then the entry C = D; and then use this fact to solve for 161 and B. B. If Y is also mean-centered, what simplifications occur in the computation of [3? Are these results about mean-centered data consistent with the previous chapter'? C. If X is NOT mean-centered. what is the general fon'nula for t and 3. expressed in terms of A, C, D? [You will need to solve the system of two linear equations symbolically.)