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 = β_{0} + β_{1} X_{1} + β_{2} X_{2} + .........β_{1} X_{1} + ?
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 =β_{0} + 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} + λx^{2} + ?
The problem is still one of linear regression that is linear in x and x^{2 }respectively even though the graph on x by itself is not a straight line.