0/1 variable (dummy variable)

Also called: dummy variable, indicator variable, binary variable, 0/1 variable

An input that is either 1 (a condition holds) or 0 (it does not). In ŷ = b₀ + b₁x + b₂·d its coefficient b₂ shifts the prediction when d = 1.

A 0/1 variable (a dummy variable) turns a yes/no fact into a number a formula can use: exam month = 1, other months = 0. In a model with several inputs

$\hat{y} = b_0 + b_1 x + b_2 d$

its coefficient b₂ is the shift in the prediction when d switches from 0 to 1, holding x fixed. When d = 0 the term vanishes.

Graphically, a dummy moves a line up or down without tilting it. To let the slope differ between the two groups as well, add an interaction b₃·x·d: then the slope of x is b₁ when d = 0 and b₁ + b₃ when d = 1. A category with k values needs k − 1 dummies; the missing one is the baseline.

Example

New families a month: ŷ = 40 + 0.15·spend + 25·exam (spend in thousand UAH).

Exam month, spend 120: 40 + 18 + 25 = 83; other month: 58.
With an interaction + 0.10·spend·exam, an exam month at spend 200 gives 40 + 30 + 25 + 20 = 115, and the gap grows from 25 to 45.

Common mistakes

Reading the coefficient as a percent. b₂ = 25 is 25 units of y, not 25%.
One dummy per category value. With k values use k − 1, or the model cannot separate them from the intercept.
Ignoring interactions. If the effect of x differs between groups, a single slope misleads.

Learn it in the course

Several variables · Formulas with several inputs: ŷ = b₀ + Σ bⱼxⱼ, 0/1 variables and interactions, a driver-based forecast, ±10% sensitivity and scenarios.