# Definition:Dummy Variable

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## Definition

A dummy variable is a quantity written in a mathematical expression in the form of a variable, even though it does in fact represent a constant.

It is usual for a dummy variable to take on the value either $0$ or $1$.

## Examples

### Regression Equation

Consider the regression equation with the two explanatory variables $x_1$ and $x_2$:

$y = \beta_0 + \beta_1 x_1 + \beta_2 x_2$

It is sometimes more convenient to write it as:

$y = \beta_0 x_0 + \beta_1 x_1 + \beta_2 x_2$

where in this context $x_0$ is a dummy variable which always takes the value $1$.

Hence, if we also want to consider the regression model where $\beta_0 = 0$, this can be accommodated by setting the dummy variable $x_0$ equal to $0$.

## Also defined as

It is often the case that the term dummy variable is used to apply to what on $\mathsf{Pr} \infty \mathsf{fWiki}$ is called a bound variable.

This usage, while common, is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$ to reduce the chance of ambiguity.

## Also see

• Results about dummy variables can be found here.