Unified equations for the slope, intercept, and standard errors of the best straight line

摘要: It has long been recognized that the least-squares estimation method of fitting best straight line to data points having normally distributed errors yields identical results for slope and intercept as does maximum likelihood estimation. We show that, contrary previous understanding, these two methods also give standard in intercept, provided expressions are evaluated at least-squares-adjusted rather than observed done traditionally. This unification holds when both x y observations subject correlated vary from point point. All known correct regression solutions literature, including various special cases, can be derived original York equations. present a compact set equations slope, newly unified errors.