Ordinary Least Squares

Definition

It used to find the Model Parameters of a Linear Regression Model $(y=\beta \cdot x+\alpha )$ 
OLS Method defines $\hat{\beta }$  and  $\hat{\alpha }$  as:

$$\begin{array}{c}\hat{\beta }=\frac{{\sum }_{i=1}^n\left(x_i-\bar{x}\right)\cdot \left(y_i-\bar{y}\right)}{{\sum }_{i=1}^n{\left(x_i-\bar{x}\right)}^2}\\ \hat{\alpha }=\bar{y}-(\hat{\beta }\cdot \bar{x})\end{array}$$

$\bar{x},\bar{y}\to$ average value of the $x,y$ components. $n\to$ cardinality