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From "Phil Steitz (JIRA)" <>
Subject [jira] Commented: (MATH-217) OLS regression should use QR decomposition
Date Sat, 12 Jul 2008 21:59:31 GMT


Phil Steitz commented on MATH-217:

Here is what I have in mind:
Start with the normal equations
X^T X b = X^T y
Let QR be decomp of X.  Then
(QR)^T (QR) b = (QR)^T y
R^T (Q^T Q) R b = R^T Q^T y
R^T R b = R^T Q^T y
(R^T)^{-1} R^T R b = (R^T)^{-1} R^T Q^T y
R b = Q^T y
Solve this directly by back-substitution.

> OLS regression should use QR decomposition
> ------------------------------------------
>                 Key: MATH-217
>                 URL:
>             Project: Commons Math
>          Issue Type: Improvement
>            Reporter: Phil Steitz
> Inverting the normal equations to estimate OLS regression parameters does not give good
numerics.  The newly added QR decomposition implementation in commons math could be used to
improve performance and numerics.  

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