Matrix X should be easy to get if you just write the given equations in matrix notation. So, again, FIRST write the system of the three given equations and then rewrite it using matrix-vector notation. It is always in this order, not in the reverse order. If B is the vector of parameters, and Y is the vector with the data, then the coefficient matrix of B should be X.

Regarding the second question, for two estimable linear combinations, once you get the best linear unbiased estimates there are two r vectors (r1 and r2). The covariance (covered in IE 516) of λ1Tβ(hat) and λ2Tβ(hat) is equal to E[(λ1Tβ(hat) - λ1Tβ) (λ2Tβ(hat) – λ2Tβ)] = E[(r1TXTY - λ1Tβ) (r2TXTY – λ2Tβ)] = … =E[(r1TXTe)(eT Xr2)]. You can simplify this by noting that E[eeT] = σ2. The variance of the estimate of a linear combination is the covariance with itself. I hope this helps.

Subject | Mathematics |

Due By (Pacific Time) | 07/15/2015 09:00 pm |

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