Vol. 10, Issue 5, Part C (2024)

Abstract
Regression analysis is a statistical technique used to examine the relationship between (dependent and independent) variables. Regression analysis is typically used by academics to examine the impact of several independent factors, or explanatory variables, on a single variable, or response variable. The regression equation is used by the investigators to explain how the response and explanatory variables relate to one another. We need to meet many assumptions to estimate the relationship (model). Several techniques, including the ordinary least squares (OLS), and maximum likelihood approach (MLE) can be used to estimate the parametric regression model. Moreover, the Spline or Kernel methods can be used for estimating nonparametric regression. In this work, we attempt to demonstrate the significant and practical method for estimating the nonlinear model. Separable nonlinear least squares (SNLS) method is a special case of nonlinear least squares (NLS) method, for which the objective function is a mixture of linear and nonlinear functions. In this technique, the nonlinear function (model) can be linearized by applying special transformation or by using expanded Taylor expansion to linearize functions. The separable nonlinear least squares (SNLS) are a very flexible technique that is used to linearize the nonlinear functions. The SNLS can be used after linearizing the nonlinear function through the transformation of the variable of interest. Moreover, the SNLS can be used to approximate a wide variety of functional shapes. The results show that the SNLS performed very well in comparison with the NLS. We can observe from the model goodness residuals standard error, AIC, and BIC, that the SNLS method has provided an estimate equivalent to that NLS provided. Therefore, we can say that it is useful to estimate nonlinear model separable. Furthermore, we plan to apply the SNLS to a more complex model using different simulation studies to check the validity of the method.