Estimation of Linear Functional Relationships: Approximate Distributions and Connections with Simultaneous Equations in Econometrics

Abstract

When both variables are subject to error, a straight line may be fitted by minimizing the sum of squared distances of the observed points to the line. Approximate distributions of the slope of this lineand of the angle it makes to one axis are given when the errors are normal, uncorrelated, and with equal variances. These distributions and corresponding ones for the line fitted by ordinary least squares are found by making the model equivalent to a model of simultaneous equations in econometrics.