linear vs nolinear

A regression model is called nonlinear, if the derivatives of the model with respect to the model parameters depends on one or more parameters. This definition is essential to distinguish nonlinear from curvilinear regression. A regression model is not necessarily nonlinear if the graphed regression trend is curved. A polynomial model such as y = b₀ + b₁x + b₂x² + e appears curved when y is plotted against x. It is, however, not a nonlinear model. To see this, take derivatives of y with respect to the parameters b₀, b₁, and b₂: dy/db₀ = 1, dy/db₁ = x, dy/db₂ = x² None of these derivatives depends on a model parameter, the model is linear. In contrast, consider the log-logistic model y = d + (a - d)/(1 + exp{b log(x/g)}) + e Take derivatives with respect to d, for example: dy/dd = 1 - 1/(1 + exp{b log(x/g)}). The derivative involves other parameters, hence the model is nonlinear

.http://www.ats.ucla.edu/stat/sas/library/SASNLin_os.htm