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 βs 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.