Abstract
The main objective of this article is to specify a nonlinear regression model, formulate the assumptions on them and aquire its linear pseudo model. A model may be considered a mathematical description of a physical, chemical or biological state or process. Many models used in applied mathematics and Mathematical statistics are nonlinear in nature one of the major topics in the literature of theoretical and applied mathematics is the estimation of parameters of nonlinear regression models. A perfect model may have to many parameters to be useful. Nonlinear regression models have been intensively studied in the last three decades. Junxiong Lin et.al [1] , in their paper, compared best –fit equations of linear and nonlinear forms of two widely used kinetic models, namely pseudo-first order and pseudo=second-order equations. K. Vasanth kumar [2], in his paper, proposed five distinct models of second order pseudo expression and examined a comparative study between method of least squares for linear regression models and a trial and error nonlinear regression procedures of deriving pseudo second order rare kinetic parameters. Michael G.B. Blum et.al [3] proposed a new method which fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics and then adaptively improves estimation using importance sampling.
Highlights
Nonlinear regression analysis is currently the most fertile area of research in the modern theory of Statistical Science and Applied Statistics
In the nonlinear regression models, if only the variables enter into nonlinearity, that is, nonlinear models which are linear in parameters, these models can be handled in the linear model framework
If the nonlinearity enters into the parameters or into both the variables and parameters, and the nonlinear regression model can be expressed in the linear specification by means of a suitable transformation, that is, the nonlinear model which is intrinsically linear, the model can be again handled in the linear model framework
Summary
In many cases it may not be possible to transform a nonlinear regression model into a linear statistical model. If the nonlinearity enters into the parameters or into both the variables and parameters, and the nonlinear regression model can be expressed in the linear specification by means of a suitable transformation, that is, the nonlinear model which is intrinsically linear, the model can be again handled in the linear model framework. The general nonlinear regression model (2.2) is of exactly the same form as the general linear regression model except that the E Y ’s are nonlinear functions of the parameters.
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