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

• DOI: 10.48550/arxiv.2301.01854
• Publication Date: 2023-01-01
• Authors: Vered Madar; Sandra L. Batista
• Keywords: Orthogonalization; Normalization; Triangular matrix

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.