linear least squares

symbols, variables and units

X: design matrix; y: observation vector; β: regression coefficient, units are defined in columns.

applicable conditions and boundaries

X must have full column rank; use QR or SVD in numerical calculations rather than explicitly inverting the matrix.

formula source code

The following is a copyable LaTeX expression.

\hat\beta=(X^{T}X)^{-1}X^{T}y

Reference and Extended Learning

is organized according to model definition and assumptions. Please check actual conditions and original literature before engineering, research and clinical use.