Obtaining the equation of the bivariate least squares regression line in high school using only quadratic functions

Abstract

In this paper, following and adapting the ideas of Casella & Berger (2002) and Niven (1981), we present, using only quadratic functions, a simple derivation of the formulas for the coefficients of the bivariate least squares regression line. Therefore, this approach is very suitable for High School students when Calculus and Linear Algebra are not available (as it is the case of Brazil and other countries). We also present an interactive companion GeoGebra applet to enhance graphically and algebraically the keys ideas.