β ^ → = arg min β → L ( D , β → ) = arg min β → ∑ i = 1 n ( β → . x i → − y i ) 2 {\displaystyle {\vec {\hat {\beta }}}={\underset {\vec {\beta }}{\mbox{arg min}}}\,L(D,{\vec {\beta }})={\underset {\vec {\beta }}{\mbox{arg min}}}\sum _{i=1}^{n}({\vec {\beta }}\,.\,{\vec {x_{i}}}-y_{i})^{2}} Now putting the independent and dependent variables in matrices X {\displaystyle X} and Y {\displaystyle Y} respectively, the loss function can be rewritten as: