Estimation of Non-Linear Regression Parameters by Newton Raphson’s Method of Nonlinear Equations

Abstract

In this research, we estimate the parameters of the nonlinear regression using the SPSS program and the least square method, in order to show that approaching the root of nonlinear equations using nonlinear regression is logarithmic, quadratic and cubic. These types of models were confirmed by a set of examples. The results showed that the cubic model is closer to the real The study's methodology involved finding the value of the parameters for both the polynomial regression (quadratic and cubic) and the logarithmic regression. Subsequently, the study established the value of nonlinear regression parameters using the SPSS program and least square method for nonlinear equations. Using the least squared method, the features were estimated for both types of nonlinear regression (polynomial and logarithmic). Then it utilized the Mabel program to find the roots of the equation. Results from table 2 show the correlation coefficient R, R Square, Adjusted R Square and standard error of the estimate for four nonlinear equations in the interval [0.1, 1]. In estimating the parameters for nonlinear regression, the study used logarithmic, quadratic and cubic models. The study established that in all nonlinear equations, the cubic model has the largest value of R Square and has a standard error of less than 0.05, making it the best model. The study showed that for the cubic model, both the Newton Raphson’s method and the Least squares method are better than the quadratic and logarithmic model. There no difference between Newton Raphson's method and the least square method for solving nonlinear equations and that the parameter estimation of nonlinear regression models using SPSS program is easier and better than the least-squares method.  root than other models.

Keywords:-nonlinear regression models, nonlinear equation, least square method, estimate the parameters.