Define the linear functional relationship with parameters, α, β, by μ = α + βv. This paper considers the problem of confidence interval estimation of α and β separately, based on a sample of independent pairs, (xi,yi),i= 1, 2, ···,n, withExi= vi,Eyi= μi. The pairs, (xi,yi), are assumed to be independent (i≠i′), to have a common (unknown) covariance matrix Σ, and to follow the bivariate normal distribution. It is known that under these circumstances (providing instrumental variates are available) one can define a variance ratio with 2 and (n− 2) degrees of freedom,F2,n–2say, as a function of α, β, sample statistics and instrumental variates to yield a confidence region on (α, β) based on