Elimination of parameters and principle of least Squares: fitting of linear curve to average maximum Temperature data in the context of Assam

Abstract

The principle of least squares, innovated by the French mathematician Legendre, when applied to observed data in order to fit a mathematical curve yields normal equation. The parameter involved in the curve are eliminated by solving normal equations. The number of normal equations becomes larger when the number of parameters associated to the curve becomes larger. In this situation, the solution of the normal equations for eliminating the parameters becomes more complicated. For this reason one more convenient method has been search for computing the estimate of the parameters. The method has been developed by the stepwise application of the principle of the least square. The method involved here consists of the elimination of parameters first and then the minimization of the sum of squares of the errors. In this paper the method has been described with reference to the estimation of parameters of a linear curve based on observed data on monthly average temperature at Guwahati.