Linear and Nonlinear Regression Functions

A model is said to be linear if the first derivative of the regression model with respect to the parameters ] is not a function of any of the parameters. A regression model whose first derivatives with respect to the parameters depend on the parameters is called a nonlinear model. For example, y = is a linear model 

A nonlinear model can occasionally be converted into a linear model by transforming the model to obtain a linear model. However, it should be noted that transforming the model introduces problems into the model by changing the error structure, which may imply that the assumptions of linear regression are not satisfied. In this case, the parameter estimates obtained from a linearised model can then be used as the initial guess for the nonlinear regression case. 

Consider the following nonlinear models. Linearise them so that linear regression methods can be applied. Explain in which cases the error structure will be that of the standard, linear model (additive error) and where it will not be. 

Arrhenius s Equation I K = Ae e, where K is the reaction rate, A the reaction cmistant, the activation energy, R the universal gas constant, and T the temperature. 

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