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

Orthogonalization Normalization Triangular matrix
DOI: 10.48550/arxiv.2301.01854 Publication Date: 2023-01-01
ABSTRACT
By connecting the LU factorization and Gram-Schmidt orthogonalization without any normalization, closed-forms for coefficients of ordinary least squares estimates are presented. Instead using matrix inversion explicitly, each is expressed computed directly as a linear combination non-normalized vectors original data also in terms upper triangular factor from factorization. The may iteratively backward or forward algorithms given.
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