Math — Least Squares (Normal Equations)
The matrix solution to linear regression.
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\hat{\boldsymbol{\beta}} = (X^\top X)^{-1}X^\top \mathbf{y}
\text{minimise } \|X\boldsymbol{\beta} - \mathbf{y}\|^2
X^\top X\,\boldsymbol{\beta} = X^\top \mathbf{y}
\hat{\mathbf{y}} = X\hat{\boldsymbol{\beta}}