3. Generate data following the scheme used by Zellner (1971, p. 137) for i = 1, . . . , 20 points, namely yi = α + βXi + εi , Xi ∼ N
μX, σ2 η

, xi = Xi + δi , with α = 2, β = 1,μX = 5, σ2 η
= 16 and {ε, δ} have zero means with σ2 ε
= 1, σ2 δ
= 4 (i.e.
λ = σ2 ε /σ 2 δ
= 0.25). Using the {x, y} series thus generated, try the conditional likelihood approach of Zellner (1971) whereby Xi = [λxi + β1(yi − β0)]/

λ + β2 1 
, so that it is not necessary to set a prior density for X. Compare inferences about β1 under three priors on λ, namely

(a) λ = 0.25,

(b) λ ∼ Ga(2.5, 10) (very similar to the informative prior given by Zellner, 1971, p. 139) and

(c) λ ∼ Ga(0.25, 1). Note that λ = τδ/τε when τε = 1/σ 2 ε and τδ = 1/σ 2 δ are precisions. Also consider inferences on β1 in the case when λ→∞, which occurs when there is assumed to be no measurement error.