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

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 equations. The parameters involved in the curve are estimated by solving the 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 estimating the parameters becomes more complicated. For this reason, one more convenient method has been search for computing the estimates of the parameters. The method has been developed by the stepwise application of the principle of least squares. The method innovated 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 maximum temperature at Guwahati.