Interpreting parameters in the log-linear model

Problem

In the model

\[\log{y_i} = β_1+β_2x_{i,2}+β_3x_{i,3}+ε_i\]

\(b_3=0.03\) . Select the best option:

  1. E(y|x) increases by approximately 0.03 units when x3 increases by 1 unit
  2. E(y|x) increases by approximately 3% when x3 increases by 1 unit
  3. E(y|x) increases by approximately 0.03 units when x3 increases by 1%
  4. E(y|x) increases by approximately 3% when x3 increases by 1%

Solution

Answer: b