Estimation of the Parameters Under Linear and Nonlinear Least Squares Methods

Abstract

Estimating parameters using linear and nonlinear least squares algorithms is a crucial method in statistical modeling and data analysis. Under certain presumptions, the least squares approach minimizes the sum of squared variances between actual and expected values to produce accurate and objective estimations. The linear least squares method shows the model's parameters linearly, and analytical solutions can be produced using normal equations. The nonlinear least squares method, on the other hand, works with models where parameters enter nonlinearly and requires iterative numerical approaches, such as the Gauss-Newton or Levenberg-Marquardt algorithms. These methods are widely used for model fitting and prediction in the social, biological, engineering, and economic sciences. The accuracy and dependability of parameter estimate depend on a number of factors, including model definition, convergence criteria, and data quality. Thus, least squares estimation remains a dependable and adaptable method for the exploration of both linear and nonlinear interactions.