linreg¶
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linea.linreg(X, flux, error)[source] [edit on github]¶ Least squares linear regression.
We solve for the least-squares estimators \(\hat{\beta}\),
\[\hat{\beta} = ({\bf X}^{\rm T} {\bf N}^{-1} {\bf X})^{-1} {\bf X}^{\rm T} {\bf N}^{-1} f.\]Uncertainties on each of the least-squares estimators are computed with the pre-computed matrix inversion,
\[\sigma_{\hat{\beta}}^2 = ({\bf X}^{\rm T} {\bf N}^{-1} {\bf X})^{-1}.\]We’ve defined the uncertainty matrix \(\bf N\),
\[{\bf N} = {\bf I_M} \sigma_f^2,\]where \(\bf I_M\) is the identity matrix.
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