Simple Linear Regression Model

${\displaystyle E(y_{i}|X=x_{i})=\beta _{1}+\beta _{2}x)}$

Estimates of ${\displaystyle \beta _{1}}$ and ${\displaystyle \beta _{2}}$:

${\displaystyle b_{1}}$ and ${\displaystyle b_{2}}$ are the LS Estimates of <math\beta_1[/itex] and ${\displaystyle \beta _{2}}$.

${\displaystyle b_{1}={\bar {y}}-b_{2}{\bar {x}}}$

${\displaystyle b_{2}={{\sum _{i=1}^{n}(x_{i}-{\bar {x}})(y_{i}-{\bar {y}})} \over {\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}}}$

Estimated regression line:

${\displaystyle {\hat {y}}=b_{1}+b_{2}x}$