Thanh Huyen - Week 3- Final test answer.docx - (a Consider the usual linear model where y = X\u03b2 \u03b5 We now compare two regressions which differ in how

Thanh Huyen - Week 3- Final test answer.docx - (a Consider...

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(a) Consider the usual linear model, where y = Xβ + ε. We now compare two regressions, which differ in how many variables are included in the matrix X. In the full (unrestricted) model p1 regressors are included. In the restricted model only a subset ofp0 < p1 regressors are included. Show that the smallest model is preferred according tothe AIC ifs02s12< 2n(p1p0) e n 0 1 0 1 1 0 e (b) Argue that for very large values of n the inequality of (a) is equal to the conditions02s12s122n(p1p0)
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2 n 0 0 0 0
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