Estimating Some Nonlinear Regression Models by Employing the Whale Algorithm

Abstract

The nonlinear regression model is one of the regression models used when the relationship between explanatory variables and the response variable is nonlinear. It is considered one of the most common and widely used models in analyzing the impact of explanatory variables on the response variable. Two nonlinear regression models, MEYER and MEYER5, were studied. The study's problem lies in the difficulty of obtaining parameter estimates of the models directly using classical methods because they are nonlinear. To obtain accurate parameter estimates, traditional methods were used as iterative methods to estimate these parameters (nonlinear least squares method and maximum likelihood method) and employed one of the artificial intelligence algorithms, the Whale Optimization Algorithm (WOA). Using simulation techniques to compare estimation methods with different sample sizes and the mean squared error criterion to obtain the best method, the results showed that the nonlinear least squares method employing the Whale Optimization Algorithm (NLSWOA) is the best for both models.