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Nonlinear Regression

  • Some nonlinear models can be modeled by a polynomial function
  • A polynomial regression model can be transformed into linear regression model. For example,

\[ y=w+w_{1}x+w_{2}x^{2}+w_{3}x^{3} \]

    • convertible to linear with new variables: \[ x_{2} = x^{2}, x_{3}= x^{3} \]
      \[ y=w+w_{1}x+w_{2}x_{2}+w_{3}x_{3} \]
  • Other functions, such as power function, can also be transformed to linear model
  • Some models are intractable nonlinear (e.g., sum of exponential terms)
    • possible to obtain least square estimates through extensive calculation on more complex formulae

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