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→General: Replaced the link to Lorenz curve (describing income inequality) with a link to the Cauchy distribution (often called the same thing, and highly nonlinear) Tags: Mobile edit Mobile web edit |
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[[Systematic error]] may be present in the independent variables but its treatment is outside the scope of regression analysis. If the independent variables are not error-free, this is an [[errors-in-variables model]], also outside this scope.
Other examples of nonlinear functions include [[exponential function]]s, [[Logarithmic growth|logarithmic functions]], [[trigonometric functions]], [[Exponentiation|power functions]], [[Gaussian function]], and [[Cauchy distribution|Lorenz curve]]s. Some functions, such as the exponential or logarithmic functions, can be transformed so that they are linear. When so transformed, standard linear regression can be performed but must be applied with caution. See [[#Transformation|Linearization§Transformation]], below, for more details.
In general, there is no closed-form expression for the best-fitting parameters, as there is in [[linear regression]]. Usually numerical [[Optimization (mathematics)|optimization]] algorithms are applied to determine the best-fitting parameters. Again in contrast to linear regression, there may be many [[local maximum|local minima]] of the function to be optimized and even the global minimum may produce a [[Bias of an estimator|biased]] estimate. In practice, [[guess value|estimated values]] of the parameters are used, in conjunction with the optimization algorithm, to attempt to find the global minimum of a sum of squares.
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