3.8 Qualitative Predictors

• Dummy variables: if there are \(k\) levels, introduce \(k-1\) dummy variables which are equal to one (“one hot”) when the underlying qualitative predictor takes that value. For example if there are 3 levels, introduce two new dummy variables and fit the model:

\[y_i = \beta_0 + \beta_1 x_{i1} + \beta_2 x_{i2} + \epsilon_i\]

Qualitative Predicitor	\(x_{i1}\)	\(x_{i2}\)
level 0 (baseline)	0	0
level 1	1	0
level 2	0	1

• Coefficients are interpreted the average effect relative to the baseline.

• Alternative is to use index variables, a different coefficient for each level:

\[y_i = \beta_{0 1} + \beta_{0 2} +\beta_{0 3} + \epsilon_i\]