Simple Linear Regression Model E ( y i | X = x i ) = β 1 + β 2 x ) {\displaystyle E(y_{i}|X=x_{i})=\beta _{1}+\beta _{2}x)} Estimates of β 1 {\displaystyle \beta _{1}} and β 2 {\displaystyle \beta _{2}} :[edit | edit source] b 1 {\displaystyle b_{1}} and b 2 {\displaystyle b_{2}} are the LS Estimates of <math\beta_1</math> and β 2 {\displaystyle \beta _{2}} . b 1 = y ¯ − b 2 x ¯ {\displaystyle b_{1}={\bar {y}}-b_{2}{\bar {x}}} b 2 = ∑ i = 1 n ( x i − x ¯ ) ( y i − y ¯ ) ∑ i = 1 n ( x i − x ¯ ) 2 {\displaystyle b_{2}={{\sum _{i=1}^{n}(x_{i}-{\bar {x}})(y_{i}-{\bar {y}})} \over {\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}}} Estimated regression line:[edit | edit source] y ^ = b 1 + b 2 x {\displaystyle {\hat {y}}=b_{1}+b_{2}x}