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# tutorial 9 - Tutorial 9 1 Suppose Y has 5 covariates X1 X2...

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Tutorial 9 1. Suppose Y has 5 covariates X 1 , X 2 , X 3 , X 4 , X 5 denote any model Y = β 0 + β i X i + β j X j + β k X k + ε by ( ijk ). All the models can be listed as (0), (1), (2), (3), (4), (5), (12), (13), (14), (15), (23), (24), (25), (34), (35), (45), (123), (124), (125), (134), (135), (145), (234), (235), (245), (345), (1234), (1235), (1245), (1345), (2345), (12345). With n = 40, their respectively SSE are 95.2261, 73.3037, 95.2139, 90.8737, 69.2889, 73.6588, 73.0233, 70.9692, 53.2715, 42.4473, 90.8726, 69.2660, 73.2872, 63.9012, 72.6848, 25.0160, 70.5948, 52.8136, 42.4440, 49.9665, 42.4467, 0.2618, 63.7998, 72.4197, 24.7802, 24.4749, 49.3597, 42.4432, 0.2512, 0.2496, 24.3022, 0.2406. And their respectively BIC are 0.9596, 0.7902, 1.0517, 1.0050, 0.7338, 0.7950, 0.8786, 0.8500, 0.5632, 0.3361, 1.0972, 0.8257, 0.8822, 0.7451, 0.8739, -0.1927, 0.9370, 0.6468, 0.4282, 0.5914, 0.4283, -4.6600, 0.8358, 0.9625, -0.1099, -0.1223, 0.6714, 0.5204, -4.6093, -4.6157, -0.0372, -4.5600. (a) Based on BIC, which model should be preferred (b) Based on BIC and using forward selection, which model is selected. Please indicate which models are calculated (c) Based on BIC and using backward elimination, which model is selected. Please indicate which models are calculated (d) using backward elimination and F-test, start from the full model, test whether X 2 and X 3 can be removed simultaneously. 2. Consider the Gaoline consumption and automotive variables. Y : Miles/Gallon; X 1 : Displacements; X 2 : Horsepower; X 3 : Torque; X 4 : compression ratio; X 5 : real axle ratio; X 6 : Carburetor; X 7

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