(a) Suppose we assume that, in (1),
β0i = β0,1 + b0i,β1i = β1,1 if ai = 1
β0i = β0,2 + b0i,β1i = β1,2 if ai = 2 (2)
β0i = β0,3 + b0i,β1i = β1,3 if ai = 3
where E(b0i|ai) = 0, var(b0i|ai) = D > 0, and b0i are independent across i and are independent of eij for all (i,j). Give expressions for var(Yij|ai), cov(Yij,Yij|ai), and corr(Yij,Yij|ai) implied by the model given by (1) and (2
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