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Letting p* denote the restricted least-squares or constrained least-squares estimator, one can show that p* can be estimated by the following formula*:

p* = p + (X'X)-1 R'[R(X'X)—1 R']—1V — R p) (6)

where p is the usual (unconstrained) estimator estimated from the usual formula (X' X)-1'X' y.

b. Given this 0 vector, verify that the R matrix and r vector given in (5) do in fact incorporate the restrictions in (4).

c. Write down the R and r in the following cases:

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