Consider the simple linear regression yi = + Xi + ui i = 1, 2, . . . , n with ui IIN(0,

Consider the simple linear regression yi = α + βXi + ui i = 1, 2, . . . , n with ui ∼ IIN(0, σ2). For H0; β = 0, derive the LR,Wand LMstatistics in terms of conditional likelihood ratios as described in Breusch (1979). In other words, compute W = −2 log[max H0

(α, β/σ2)/

max L

α,β

(α, β/σ2)], LM =−2log[max L H0

(α, β/σ2)/max L

α,β

(α, β/σ2)] andLR=−2log[max L H0

(α, β, σ2)/

max L

α,β,σ2

(α, β, σ2)] where σ2 is the unrestricted MLE of σ2 while σ2 is the restricted MLE of σ2 under H0. Use these results to infer that W ≥ LR ≥ LM.