#### Purpose of regression analysis

The purpose of regression analysis is to analyze relationships among variables. The analysis is carried out through the estimation of a relationship

y = f(x1, x2,..., xk)

and the results serve the following two purposes:

• Answer the question of how much y changes with changes in each of the x's (x1, x2,...,xk), and
• Forecast or predict the value of y based on the values of the X's

##### Simple regression

A model with only one independent variable (x).

##### Multiple regression

A model with more than one independent variable. (The model above represents a multiple regression model with k independent variables.)

##### Linear versus nonlinear regression models

A regression model is called linear if the equation y = f(x1, x2,...,xk) can be written as:

y = b0 + b1 x1 + b2 x2 +...+ bk xk + e

where b0, b1,...,bk are parameters to be estimated, and e is an error term.

Note. For more details on the simple and multiple linear regression model, go to their respective maps.