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In the context of introductory econometric methods, the algebraic properties of estimators, especially those obtained through the Ordinary Least Squares (OLS) method, play a foundational role in understanding the reliability and functionality of econometric models. These properties are derived based on the assumptions of the classical linear regression model and are instrumental in interpreting the estimators for coefficients in linear regressions. The key algebraic properties of OLS estimators are as follows: The first property is that the OLS residuals sum to zero. Mathematically, this means that the sum of the residuals $e_i = y_i - \hat{y}_i$ across all observations equals zero: $$ \sum_{i=1}^{n} e_i = 0 $$ This property implies that the OLS regression line passes through the mean of _________ ____ __________ ____ _____ ______ ______ _________ ___.
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