Refer to the log-likelihood function for the baseline-category logit model (Section 7.14). Denote the sufficient statistics by np_j = ∑_i y_ij and S_jk = ∑_i x_ik y_ij, j = 1,... J – 1,...,p. Let S = (S₁₁,...,S_1t,...S_J1,...,S_Jt)’. Condition on ∑_i y_ij, j = 1,...,J. Under the null hypothesis that explanatory variables have no effect, show that E(S) = n(p ⨂ m), var(S) = n(V ⨂ ∑) where p = (p₁,....,p_J)’; m = (x̅₁,....,x̅_t)’, where x̅_k = (∑_i x_ik)/n; ∑ has elements (S²_kυ), where S²_kυ = [∑_i(x_ik – x̅_k)(x_iυ – x̅_υ)]/(n – 1); V has elements υ_ii = p_i(1 – p_i) and υ_ij = –p_i p_j, and ⨂ denotes the Kronecker product (Zelen 1991).