The LRM with a dummy variable

Summary

Main points:

• In a regression model, a dummy variable is a variable \(d_i, i=1,…,n\) that can take the value 0 or 1.
• Example: We let \(d_i=0\) if individual \(i\) is female and \(d_i=1\) if individual \(i\) is male.
• We can add a dummy variable to our regression model:

\[y_i=β_1+β_2x_{i,2}+β_3x_{i,3}+…+β_kx_{i,k}+γd_i+ε_i i=1,…,n\]

• The intercept of individuals coded as \(d_i=0\) (group 0) will be \(β_1\) .
• The intercept of individuals coded as \(d_i=1\) (group 1) will be \(β_1+γ\) .
• \(γ\) is interpreted as the extra intercept that group 1 observations have compared to group 0 observations.
• You can have many dummy variables in a LRM, for example

\[y_i=β_1+β_2x_{i,2}+β_3x_{i,3}+…+β_kx_{i,k}+γ_1d_{i,1}+γ_2d_{i,2}+ε_i i=1,…,n\]