Least-squares fit to a straight line when each variable contains all equal errors

Abstract

The least squares fit to a straight line, when both variables are affected by all equal uncorrelated errors, leads to very simple results for both the estimated parameters and their standard errors, of widespread applicability. In this paper several formulas are derived, presenting a full set of results about the estimated parameters and their standard errors. All the results have been validated with extensive Monte Carlo simulations. The emphasis of the paper is on the calculation and properties of the best-fit parameters and their standard errors.

Section IV-D was corrected; reference to the published paper added; 31 pages and 53 figures