AbstractThe least‐squares estimate θn=Xn+ynof the parameter θ in the linear modelYn=Xnθ + ϵnmay not be consistent, but there may be directionsusuch thatu'θntends tou'θ in some sense. This set of directionsuhas been characterized in two different papers: Drygas (1976) and Wu (1980). The conditions for consistency appear to be different in the two papers. The purpose of this note is to show that the two conditions are equivalent and that they both show that the consistent directions depend upon the geometry of the row vectorsvi, i= 1,…,n, ofXnwith respect to the d