A Geometric Interpretation and Comparison of the Methods Of Ordinary Least Square (OLS) and Bivariate Lagrange Interpolation

Abstract

In this study, the consumer prices, real gross domestic product (GDP) and unemployment for Germany and Turkey between 2006 and 2011 are geometrically interpreted by using Lagrange interpolation and OLS method. The coefficients of linear regression models are obtained by matrix display of OLS method. The Lagrange interpolation polynomial is considered in bivariate situation and we aim a different formulation. Thanks to the considered methods, it will be possible to have an idea about the unemployment rate status in Germany and Turkey. We use two different methods for the prediction of unemployment rates, which are developed by different equations in order to predict third variable by using two variables. Our main purpose is to determine whether an equation gives the correct guess rather than numerical expression. Besides, we have tried to state geometric display to data.

Keywords: Lagrange interpolation, ordinary least square (OLS), regression, geometrical display, matrix display