A Note On Derivation of the Least Squares Estimator

Abstract

Derivation of Least Squares (LS) estimators of intercept and slope in bivariate regression model has been solely calculus-based. Herein, for the first time in the chronicle of regression, we provide a derivation of the LS estimators in very basic algebra within the grasp of the intended readers of many introductory books in statistics and econometrics. Also, we provide a similar derivation of the LS estimator of a parameter vector for the multiple regression model which takes only a few steps of basic matrix operation.Derivation of LS estimator, bivariate regression, calculus-based, self-contained, multiple regression, matrix calculus, orthogonality