How do I set up and interpret dummy variables in a regression?

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AcadiFi · Accepted Answer

For a categorical variable with k levels, you include k−1 dummy variables in the regression (the omitted one becomes the reference category).

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Suppose Windermere Analytics regresses P/E ratio on sector and two continuous controls across 200 stocks, with sectors {Tech, Healthcare, Financials, Energy, Consumer}. Choose Consumer as the reference (the one you drop). The regression becomes: P/E = α + β1 × Tech + β2 × Healthcare + β3 × Financials + β4 × Energy + γ × Controls + error.

Results (illustrative): α = 18.2, β1 = 9.8, β2 = 4.3, β3 = −2.1, β4 = −5.6. Each β is the average P/E difference versus the Consumer reference, holding controls constant. Tech stocks trade at 9.8 multiples higher than Consumer; Energy at 5.6 lower.

A key exam trap: if you include all five dummies AND the intercept, you create perfect multicollinearity (the five dummies sum to a vector of ones, identical to the intercept column). Software usually drops one automatically, but be deliberate about which one.

Choice of reference category matters for interpretation, not for fit or predictions. Choose the 'natural baseline' — industry average, lowest-risk group, or the most populous category — so the remaining coefficients tell a clean story. Changing the reference changes all coefficient values but overall R-squared and predictions are identical.

How do I set up and interpret dummy variables in a regression?

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