Consider 2 models: yi = β1 + β2xi + ei (1) Y = X0β + e;...

Consider 2 models:

yi = β1 + β2xi + ei	(1)
Y = X0β + e;	(2)

where Equation (1) represents a system of n scalar equations for individuals i = 1; ...; n , and
Equation (2) is a matrix representation of the same system. The vector Y is n x 1. The matrix X0
is n x 2 with the first column made up entirely of ones and the second column is x1; x2; ...; xn.
a. Set up the least squares minimization problems for the scalar and matrix models.
b. Show that the β terms from each model are algebraically equivalent, i.e. the β1 and β2
you get from solving the least squares equations from Equation (1) and the matrix algebra
problem from Equation (2) are identical.

Solutions

Expert Solution

Here we just obtain the estimates and observe that they are same in both approaches

milcah answered 8 months ago

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