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https://issues.apache.org/jira/browse/MATH-217?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12613132#action_12613132
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Phil Steitz commented on MATH-217:
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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: https://issues.apache.org/jira/browse/MATH-217
> 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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