Dummy variable

Dummy variable is a regressor taking only the value 0 or 1 to encode a qualitative distinction inside a regression model.

Also known asindicator variable · binary variable

ByHoang TruongUpdated June 30, 2026

FrameworkOrdinary least squares (OLS)

See it move

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The side-by-side comparison contrasts a baseline group (D = 0, pre-pandemic, intercept β₀) against a dummy group (D = 1, post-pandemic, intercept β₀ + 12), representing a shift of +€12,000 in revenue. Both groups share the same slope β₁; the dummy captures only a parallel upward shift in the fitted line rather than a change in gradient. The note confirms that this intercept-shift interpretation holds whenever the two groups differ by a fixed level but grow at the same rate.

Where it fits

SubjectData Analysis & StatisticsCoreTopicMultiple Regression & InterpretationCore

The formula

LaTeX

Y_i = \beta_0 + \beta_1 D_i + \beta_2 X_i + u_i

Variables

$D_{i}$: Dummy variable: 1 for the target group, 0 otherwise
$β_{1}$: Intercept shift for observations where D = 1, holding X constant
$β_{2}$: Slope on continuous regressor X
$u_{i}$: Error term

β₁ measures the vertical shift in the fitted line for the group coded 1

Check yourself

PracticeCORE

A researcher fits the model: Monthly_Sales = β₀ + β₁·Export_Dummy + β₂·Employees + u, where Export_Dummy equals 1 for exporting firms and 0 for domestic-only firms. The estimated coefficient β̂₁ = €12,000. Which of the following is the correct interpretation?

Select an answer to check your understanding.