# 3.9 — Logarithmic Regression - Class Notes

## Contents

*Thursday, November 5, 2020*

## Overview

Today, we finish up our view of *nonlinear* models with **logarithmic models**, which are more frequently used. We also discuss a few other tests and transformations to wrap up multivariate regression before we turn to panel data: **standardizing variables** to compare effect sizes, and **joint hypothesis tests**.

Interpretting logged variables can often be difficult to remember, so here I reproduce the tables that describe the interpretations of the marginal effect of \(X \rightarrow Y\), as well as some visual examples from the slides:

Model | Equation | Interpretation |
---|---|---|

Linear-Log |
\(Y=\beta_0+\beta_1 \mathbf{ln(X)}\) | 1% change in \(X \rightarrow \frac{\hat{\beta_1}}{100}\) unit change in \(Y\) |

Log-Linear |
\(\mathbf{ln(Y)}=\beta_0+\beta_1X\) | 1 unit change in \(X \rightarrow \hat{\beta_1}\times 100\)% change in \(Y\) |

Log-Log |
\(\mathbf{ln(Y)}=\beta_0+\beta_1\mathbf{ln(X)}\) | 1% change in \(X \rightarrow \hat{\beta_1}\)% change in \(Y\) |

- Hint: the variable that gets logged changes in
**percent**terms, the variable not logged changes in*unit*terms

Linear-Log | Log-Linear | Log-Log |
---|---|---|

\(\hat{Y_i}=\hat{\beta_0}+\hat{\beta_1}\mathbf{ln(X_i)}\) | \(\mathbf{ln(\hat{Y_i})}=\hat{\beta_0}+\hat{\beta_1}X_i\) | \(\mathbf{ln(\hat{Y_i})}=\hat{\beta_0}+\hat{\beta_1}\mathbf{ln(X_i)}\) |

\(R^2=0.65\) | \(R^2=0.30\) | \(R^2=0.61\) |

## Slides

## Practice Problems

Today you will be working on newpractice problems (on nonlinear models). Answers will be posted on that page later.

## Assignments: Problem Set 5 (Due Sun Nov 8)

Homework 5 (on 3.1-3.5) is due by 11:59 PM Sunday November 8. **This is likely your final graded homework**In the past, I have always released a HW 6 on Imperfect Competition just for practice for the Final Exam.

## Live Class Session on Zoom

The live class Zoom meeting link can be found on Blackboard (see `LIVE ZOOM MEETINGS`

on the left navigation menu), starting at 11:30 AM.

If you are unable to join today’s live session, or if you want to review, you can find the recording stored on Blackboard via Panopto (see `Class Recordings`

on the left navigation menu).