Question: From Exercise 1.17, if A is nonsingular and X = XA (such as in using a different parameterization for a factor), then C(X) = C(X).

From Exercise 1.17, if A is nonsingular and X∗ = XA (such as in using a different parameterization for a factor), then C(X∗) = C(X). Show that the linear models with the model matrices X and X∗ have the same hat matrix and the same fitted values.

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