In the generalized regression model, if the K columns of X are characteristic vectors of
Chapter 10, Problem 5(choose chapter or problem)
In the generalized regression model, if the K columns of X are characteristic vectors of , then ordinary least squares and generalized least squares are identical. (The result is actually a bit broader; X may be any linear combination of exactly K characteristic vectors. This result is Kruskals Theorem.) a. Prove the result directly using matrix algebra. b. Prove that if X contains a constant term and if the remaining columns are in deviation form (so that the column sum is zero), then the model of Exercise 8 below is one of these cases. (The seemingly unrelated regressions model with identical regressor matrices, discussed in Chapter 14, is another.)
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