Let's assume that the independent variable is x → = [ x 1 , x 2 , … , x m ] {\displaystyle {\vec {x}}=[x_{1},x_{2},\dots ,x_{m}]} and the model's parameters are β → = [ β 0 , β 1 , ⋯ , β m ] {\displaystyle {\vec {\beta }}=[\beta _{0},\beta _{1},\cdots ,\beta _{m}]} , then the model's prediction would be y ≈ β 0 + ∑ i = 1 m β i × x i {\displaystyle y\approx \beta _{0}+\sum _{i=1}^{m}\beta _{i}\times x_{i}} . If x → {\displaystyle {\vec {x}}} is extended to x → = [ 1 , x 1 , x 2 , … , x m ] {\displaystyle {\vec {x}}=[1,x_{1},x_{2},\dots ,x_{m}]} then y {\displaystyle y} would become a dot product of the parameter and the independent variable, i.e. y ≈ ∑ i = 0 m β i × x i = β → . x → {\displaystyle y\approx \sum _{i=0}^{m}\beta _{i}\times x_{i}={\vec {\beta }}\,\,.\,{\vec {x}}} . In the least-squares setting, the optimum parameter is defined as such that minimizes the sum of mean squared loss: