ORDINARY LEAST SQUARES (OLS) METHODS AND ISSUES: THEORETICAL FOUNDATIONS, CHALLENGES, AND METHODOLOGICAL REMEDIES

Abstract

Ordinary Least Squares (OLS) is a foundational estimation technique widely used in econometrics, statistics, and data analysis for examining linear relationships between variables. This paper reviews the theoretical underpinnings of OLS, its classical assumptions, and the conditions under which it provides Best Linear Unbiased Estimators (BLUE). It further explores the key practical challenges associated with real-world applications, such as heteroscedasticity, autocorrelation, multicollinearity, and endogeneity. Drawing upon empirical literature, the study evaluates the limitations of OLS and presents solutions including robust standard errors, generalized least squares, instrumental variable approaches, and regularization techniques. The integration of modern econometric tools with machine learning methodologies is also discussed as a promising direction for improving OLS-based inference in high-dimensional and complex data environments. The paper concludes that while OLS remains a central tool for empirical researchers, its effectiveness depends on rigorous diagnostics, adherence to assumptions, and methodological adaptability.

Keywords (Ordinary Least Squares, Heteroscedasticity, Multicollinearity, Endogeneity, Autocorrelation, Econometrics, Instrumental Variables, Regression Diagnostics).