Simple Linear Regression Model

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

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

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

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

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

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