Solving The Ordinary Least Squares in Closed Form, Without Inversion or Normalization

Vered Senderovich Madar; Sandra L. Batista

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arXiv · 2301.01854

Solving The Ordinary Least Squares in Closed Form, Without Inversion or Normalization

Vered Senderovich Madar·Sandra L. Batista

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Abstract

By connecting the LU factorization and the Gram-Schmidt orthogonalization without any normalization, closed-forms for the coefficients of the ordinary least squares estimates are presented. Instead of using matrix inversion explicitly, each of the coefficients is expressed and computed directly as a linear combination of non-normalized Gram-Schmidt vectors and the original data matrix and also in terms of the upper triangular factor from LU factorization. The coefficients may computed iteratively using backward or forward algorithms given.

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Vered Senderovich Madar, Sandra L. Batista. 2023-01-04. Solving The Ordinary Least Squares in Closed Form, Without Inversion or Normalization. https://arxiv.org/abs/2301.01854

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