An engineer tries three different methods for selecting a linear model. First she uses an informal method based on the F statistic, as described in Section 8.3. Then she runs the best subsets routine, and finds the model with the best adjusted R² and the one with the best Mallows’ Cp. It turns out that all three methods select the same model. The engineer says that since all three methods agree, this model must be the best one. One of her colleagues says that other models might be equally good. Who is right? Explain.

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An engineer tries three different methods for selecting a linear model. First she uses an informal method based on the F statistic, as described in Section 8.3. Then she runs the best subsets routine, and finds the model with the best adjusted R² and the one with the best Mallows’ Cp. It turns out that all three methods select the same model. The engineer says that since all three methods agree, this model must be the best one. One of her colleagues says that other models might be equally good. Who is right? Explain.

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