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Finding the least squares estimates given a set of equations

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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.

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A step-by-step solution shows how to find least squares estimates analytically, given a set of linear equations. A Word document is provided.

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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; ...

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