Linear Model (Graphical)

A linear model specifies a linear relationship between a dependent variable and n independent variables:

where y is the dependent variable, {x_i} are independent variables, {a_i} are parameters of the model.

For example, consider that for a sample of 25 cities, the following model was estimated for a relationship between newspaper circulation (the dependent variable, so-named because it depends on the other variables) and retail sales and population density (the independent variables):

where

y = newspaper ciculation (x 1,000)

x₁ = Total retail sales (x 1,000,000)

x₂ = Population per square mile

This translates as

Newspaper circulation (in thousands) is equal to retail sales (in millions) times .067, plus population density (people per square mile) times .025, plus .381.

See linear regression for an explanation of how sample data are used to estimate a linear model.