Practical Regression: Log vs. Linear Specification

This is the seventh in a series of lecture notes which, if tied together into a textbook, might be entitled “Practical Regression.” The purpose of the notes is to supplement the theoretical content of most statistics texts with practical advice based on nearly three decades of experience of the author, combined with over one hundred years of experience of colleagues who have offered guidance. As the title “Practical Regression” suggests, these notes are a guide to performing regression in practice. 
This note explains how to choose between log and linear specification. The note emphasizes the economic interpretation of a log model and how to interpret coefficients in a log regression. The note concludes by explaining how to choose between log and linear specifications on econometric grounds, including an explanation of the Box-Cox test.