是因变量与自变量的线性关系

可是有时候做模型的时候经常将某个自变量的平方也加入方程中，那样的话因变量和该自变量不是二次函数关系吗？

In statistics, nonlinear regression is the problem of inference for a model

based on multidimensional x,y data, where f is some nonlinear function with respect to unknown parameters θ. At a minimum, we may like to obtain the parameter values associated with the best fitting curve (usually, least squares). Also, statistical inference may be needed, such as confidence intervals for parameters, or a test of whether of not the fitted model agrees well with the data.

The scope of nonlinear regression is clarified by considering the case of polynomial regression, which actually is best not treated as a case of nonlinear regression. When f takes a form such as

f(x) = ax² + bx + c

our function f is nonlinear as a function of x but it is linear as a function of unknown parameters a, b, and c. The latter is the sense of "linear" in the context of statistical regression modeling. The appropriate computational procedures for polynomial regression are procedures of (multiple) linear regression with two predictor variables x and x² say. However, on occasion it is suggested that nonlinear regression is needed for fitting polynomials. Practical consequences of the misunderstanding include that a nonlinear optimization procedure may be used when the solution is actually available in closed form. Also, capabilities for linear regression are likely to be more comprehensive in some software than capabilities related to nonlinear regression.

非线性模型的形式有很多种的!

而且是很难的发现因变量与自变量到底是一个怎么样的关系!