# Boolean Dummy Indicator Variable

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A Boolean Dummy Indicator Variable is a boolean learning task variable that takes only the value 0 or 1 to indicate the absence (or presence) of some categorical effect that may be expected to change an outcome.

**Example(s):**- In an ANOVA model with one qualitative variable $Y_{i} = \alpha_{1} + \alpha_{2} D_{2i} + \alpha_{3} D_{3i} + u_{i}$ where $Y_{i}$ is the average annual salary of public school teachers in state $i$, $D$'s are dummmy variables:
- $D_{2i} = 1$ if the state
*i*is in the North Region, $D_{2i} = 0$ otherwise (any region other than North), - $D_{3i} = 1$ if the state
*i*is in the South Region, $D_{3i} = 0$ otherwise,

- $D_{2i} = 1$ if the state
- …

- In an ANOVA model with one qualitative variable $Y_{i} = \alpha_{1} + \alpha_{2} D_{2i} + \alpha_{3} D_{3i} + u_{i}$ where $Y_{i}$ is the average annual salary of public school teachers in state $i$, $D$'s are dummmy variables:
**Counter-Example(s):****See:**Credit Score, Regression Analysis, Mutually Exclusive Events, Time Series Analysis, Strike Action, Truth Value, Qualitative Data, Dependent And Independent Variables, Coefficient, Economic Forecasting.

## References

### 2022

- (Wikipedia, 2022) ⇒ https://en.wikipedia.org/wiki/Dummy_variable_(statistics) Retrieved:2022-8-14.
- In statistics and econometrics, particularly in regression analysis, a
**dummy variable**is one that takes only the value 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome.^{[1]}They can be thought of as numeric stand-ins for qualitative facts in a regression model, sorting data into mutually exclusive categories (such as smoker and non-smoker).^{[2]}A dummy independent variable (also called a dummy explanatory variable) which for some observation has a value of 0 will cause that variable's coefficient to have no role in influencing the dependent variable, while when the dummy takes on a value 1 its coefficient acts to alter the intercept. For example, suppose membership in a group is one of the qualitative variables relevant to a regression. If group membership is arbitrarily assigned the value of 1, then all others would get the value 0. Then the intercept would be the constant term for non-members but would be the constant term plus the coefficient of the membership dummy in the case of group members.Dummy variables are used frequently in time series analysis with regime switching, seasonal analysis and qualitative data applications.

- In statistics and econometrics, particularly in regression analysis, a

- ↑ "Interpreting the Coefficients on Dummy Variables" (PDF). Archived from the original (PDF) on August 18, 2003.
- ↑ Gujarati, Damodar N. (2003). Basic Econometrics. McGraw Hill. ISBN 0-07-233542-4.

### 2008

- (Upton & Cook, 2008) ⇒ Graham Upton, and Ian Cook. (2008). “A Dictionary of Statistics, 2nd edition revised." Oxford University Press. ISBN:0199541450
- QUOTE: A variable, taking only the values 0 and 1, derived from a polytomous categorical variable. If the categorical variable has [math]\displaystyle{ k }[/math] categories then [math]\displaystyle{ (k - 1) }[/math] dummy variables are required. For example, with four categories the three dummy variables [math]\displaystyle{ (x_1, x_2, x_3) }[/math] could be assigned the values (1, 0, 0] for category l, (0, 1, 0) for category 2, (0, 0, 1) for category 3, and (0, 0, 0) for category 4. Dummy variables enable the inclusion of categorical information in regression models.