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  "body": "\n## Summary\n\nNonlinear regression fits a model in which the mean response is a nonlinear function of the unknown parameters.\nExamples are an exponential decay or a growth curve.\nThe parameters are usually estimated by nonlinear [[least squares|0BYTQ4X1HC]], which has no closed formula and is solved by iterative methods such as Gauss–Newton or Levenberg–Marquardt.\nInference relies on a linear approximation of the model near the estimate, so it is approximate and asymptotic.\nIt is the natural tool when a scientific theory dictates the form of the mean function.\n\n## Explanations\n\n### L1 human\n\nIn [[linear regression|41FVC4P5JB]] the unknowns enter as coefficients of known terms, and one formula gives the fit.\nIn a model like $y = \\theta_1 e^{\\theta_2 x}$, the unknown $\\theta_2$ sits inside the exponential, and no such formula exists.\nOne starts from a guess, approximates the model by a linear one near that guess, solves that, and repeats.\nA polynomial $y = \\theta_0 + \\theta_1 x + \\theta_2 x^2$ looks curved but is still linear regression, because it is linear in the parameters.\n",
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