# Definition:Dummy Variable

## 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**.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**dummy variable** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**dummy variable**