Define the linear structural relation with parameters α, β, by μ = α +βv. This paper considers the problem of confidence region estimation of α and β based on a sample of independent pairs, (yi,xi),i= 1, 2, ···, withEyi= μi,Exi=vi. The pairs (yi,xi) are assumed to have a common (unknown) covariance matrix and to follow the bivariate normal distribution. Point estimates