Y1 = theta + epsilon1
Y2 = 2*theta + xi + epsilon2
Y3 = theta - 2*xi + epsilon3
where E(epsilon(i)) = 0.
Find the least squares estimates of theta and xi.
See attached file for a cleaner version of the problem.
First lets write this system of equations in matrix form.
mat(Y1; Y2; Y3) = mat(1 0; 2 1; 1 -2)*mat(theta; xi) + mat(eps1; eps2; ...
A step-by-step solution shows how to find least squares estimates analytically, given a set of linear equations. A Word document is provided.