Lab 4 recap- interpreting log() response

Goal: Interpret the coefficients based on the following regression:

\[ \log(Y) = \beta_0 + \beta_1 x_1 + \beta_2 x_2 +\cdots. \] We don’t want our interpretation based on the \(\log()\) scale:

\[ e^{\log(Y)} = Y = e^{ \beta_0} e^{ \beta_1 x_1}e^{ \beta_2 x_2 }e^{ \cdots}. \] So, say we want to interpret \(\beta_2\) where \(x_2\) is a categorical group membership variable: \[ Y = e^{ \beta_0} e^{ \beta_1 x_1}\color{red}{e^{ \beta_2 \times 1 }}e^{ \cdots}. \]

Application exercise: ae-12