quality:correction
Formulation and computation

α ^ = y ¯ − β ^ x ¯, β ^ = ∑ i = 1 n (x i − x ¯) (y i − y ¯) ∑ i = 1 n (x i − x ¯) 2 = ∑ i = 1 n Δ x i Δ y i ∑ i = 1 n Δ x i 2 {\displaystyle {\begin{aligned}{\widehat {\alpha }}&={\bar {y}}-{\widehat {\beta }}\,{\bar {x}},\\{\widehat {\beta }}&={\frac {\sum _{i=1}^{n}\left(x_{i}-{\bar {x}}\right)\left(y_{i}-{\bar {y}}\right)}{\sum _{i=1}^{n}\left(x_{i}-{\bar {x}}\right)^{2}}}={\frac {\sum _{i=1}^{n}\Delta x_{i}\Delta y_{i}}{\sum _{i=1}^{n}\Delta x_{i}^{2}}}\end{aligned}}}