Reconsider the regression models in Problem 12.6, parts a-e. Suppose the error terms in these models were multiplicative, not additive. Rework the problem under this new assumption regarding the error structure.

Data From Problem 12.6

For the models shown below, determine whether it is a linear model, an intrinsically linear model, or a nonlinear model. If the model is intrinsically linear, show how it can be linearized by a suitable transformation.
a. \(y=\theta_{1} e^{\theta_{2}+\theta_{3} x}+\varepsilon\)
b. \(y=\theta_{1}+\theta_{2} x_{1}+\theta_{2} x_{2}^{\theta_{3}}+\varepsilon\)
c. \(y=\theta_{1}+\theta_{2} / \theta_{1} x+\varepsilon\)
d. \(y=\theta_{1}\left(x_{1}\right)^{\theta_{2}}\left(x_{2}\right)^{\theta_{3}}+\varepsilon\)
e. \(\theta_{1}+\theta_{2} e^{\theta_{3} x}+\varepsilon\)