28. In a regression situation, suppose that the observed values and lj of the independent and dependent variable differ from certain true values Xl and lj' by errors 1l.J, V; which are independently normally distributed with zero means and variances 0& and o~o The true values are assumed to satisfy a linear relation : lj' = a + PXlo However, the variables which are being controlled, and which are therefore constants, are the rather than the Xj. Writing xj for ~, we have xj = Xl + 1l.J, lj = lj' + Jj, and hence lj = a + pXj + »j, where »j = Jj - P1l.J . The results of Section 7 can now be applied to test that P or a + pXo have a specified value.