Consider 2 models:
| yi = ?1 + ?2xi + ei | (1) |
| Y = X0? + e; | (2) |
where Equation (1) represents a system of n scalar equations forindividuals i = 1; ...; n , and
Equation (2) is a matrix representation of the same system. Thevector Y is n x 1. The matrix X0
is n x 2 with the first column made up entirely of ones and thesecond column is x1; x2; ...; xn.
a. Set up the least squares minimization problems for the scalarand matrix models.
b. Show that the ? terms from each model are algebraicallyequivalent, i.e. the ?1 and ?2
you get from solving the least squares equations from Equation (1)and the matrix algebra
problem from Equation (2) are identical.
