For a sequence of s nested models M 1 ,..., M s , model M s is the most complex. Let denote the difference

For a sequence of s nested models M₁,..., M_s, model M_s is the most complex. Let ν denote the difference in residual df between M₁ and M_s.

a. Explain why for j < k, G²(M_j | M_k) ≤ G²(M_j | M_s).

b. Assume model M_j, so that M_k also holds when k > j. For all k > j, as n → ∞, P[G² (M_j | M_k) > X²_v (α)] ≤ α. Explain why?