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# Variable Selection and Model Building

10.1 a. With α = 0.10, the model chosen is y = β0 + β2x2 + β7x7 + β8x8 + ε.
b. With α = 0.10, the model chosen is y = β0 + β2x2 + β7x7 + β8x8 + ε.
c. With αIN = 0.05 and αOUT = 0.10, the model chosen is y = β0 + β2x2 + β7x7 + β8x8 + ε.
d. The three procedures chose the same model.
10.3 The choice of cut-off values is to prevent the circular addition-subtraction of the variables.
10.5 a. The model involves just x1 with R2p = 75.3%. Cp = −1.8 and = 3.12.
b. Stepwise leads to the same model involving just x1.
10.7 When FIN = FOUT = 4.0, the model involves only x6. However, when FIN = FOUT = 2.0, the model involves x6 and x7.
10.9 The model involves x1, x2, x3, and x4 with R2p = 95.3%, Cp = 5 and = .002.
10.11 The model is y = β0 + β1x1 + β2x2 + β4x4 which has a PRESS = 85.35 and R2Pred = 96.86%.
10.13 a. From Section 3.7, we get = (W′W)−1 W′y0 with . Therefore, which means that .
b. Since we are fitting a model with only one regressor, the ...

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