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:
1. Answer the question of how much y changes with changes in each of the x's
(x1, x2,...,xk), and
2. 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.
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Note. For more details on the simple and multiple linear regression model, go
to their respective maps.