Ordinary Least-Squares Regression System

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An Ordinary Least-Squares Regression System is a least-squares regression system that is an Linear Regression System which implements an ordinary least-squares regression algorithm to solve an ordinary least-squares regression task.



References

2017a

2017b

  • (StatsModels, 2017) ⇒ http://www.statsmodels.org/stable/regression.html Retrieved:2017-09-10
    • QUOTE: The statistical model is assumed to be

      [math]\displaystyle{ Y = X\beta + \mu }[/math],

      where [math]\displaystyle{ \mu\sim N\left(0,\Sigma\right) }[/math]

      Depending on the properties of [math]\displaystyle{ \Sigma }[/math], we have currently four classes available:

      • GLS : generalized least squares for arbitrary covariance [math]\displaystyle{ \Sigma }[/math]
      • OLS : ordinary least squares for i.i.d. errors [math]\displaystyle{ \Sigma=\textbf{I} }[/math]
      • WLS : weighted least squares for heteroskedastic errors [math]\displaystyle{ \text{diag}\left (\Sigma\right) }[/math]
      • GLSAR : feasible generalized least squares with autocorrelated AR(p) errors [math]\displaystyle{ \Sigma=\Sigma\left(\rho\right) }[/math]

      All regression models define the same methods and follow the same structure, and can be used in a similar fashion. Some of them contain additional model specific methods and attributes.