Linear regression

In statistics, linear regression is a regression method that models the relationship between a dependent variable Y, independent variables Xi, i = 1, ..., p, and a random term ε. The model can be written as

where β1 is the intercept ("constant" term), the βis 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 method is called "linear" because the relation of the response (the dependent variable Y) to the independent variables is assumed to be a linear function of the parameters. It is often erroneously thought that the reason the technique is called "linear regression" is that the graph of Y = β0 + βx is a straight line or that Y is a linear function of the X variables. But if the model is (for example)

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.