Open AccessObtaining the equation of the bivariate least squares regression line in high school using only quadratic functions
Author(s) -
Humberto José Bortolossi,
David Pinho
Publication year - 2015
Language(s) - English
Resource type - Conference proceedings
DOI - 10.52041/srap.15114
Subject(s) - bivariate analysis , quadratic equation , mathematics , line (geometry) , simple linear regression , simple (philosophy) , least squares function approximation , total least squares , quadratic function , algebra over a field , real line , polynomial regression , calculus (dental) , regression analysis , statistics , discrete mathematics , pure mathematics , medicine , philosophy , geometry , epistemology , dentistry , estimator
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.