Regression - Straight Line

For  a particular value X_i of the independent variable, we can find the predicted value _i by using the equation of a straight line:

The difference between _i and Y_i is called the residual ε_i and represents the error which is made when predicting Y_i as the response to variable X. The best fit for all available points X_i can be found by minimizing the sum of all squared ε_i. In fact, the criterium for minimizing the error could be any other suitable function. However the sum of squares has certain mathematical advantages. A more detailed discussion on the mathematics behind the regression can be found elsewhere.
 

Please note that the linear regression  is based on several assumptions, which have to be fulfilled when applying regression methods to the data.