Linear  regression is  a regression methods  that models  the  relationship  between  a dependent variable   independent variables ? X1 i = 1 .........p and a random term . the model  can be  written as:

Y = β₀ + β₁ X₁ + β₂ X₂ + .........β₁  X₁ + ?

Where  β0  is the constant  term the β_s are the respective  parameters of independent variables  and p  is the  number  of parameters to be estimated in the  linear  regression. Linear  regression can be contrasted with  nonlinear  regression.

This  methods  is called linear because the relation of the  response ( the dependent  Y ) to the  independent variables is assumed to be a linear function of the parameters .it is often erroneously  thought that the reason the techniques is called  linear regression  is that the graph  of Y =β₀ + β _x is a straight  line or that Y  is a linear function of the X  variables. But if the model  is for example.

Y = α + β _x + λx² + ?

The problem  is still  one of  linear  regression  that is  linear in x and x² respectively  even though the  graph  on x by  itself is not a  straight line.