#### 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.