# 3.4 — Multivariate OLS Estimators: Bias, Precision, and Fit — Class Notes

## Contents

Thursday, October 15, 2020 and Tuesday, October 20, 2020

## Overview

Today we continue looking at multivariate regression, and see how the introduction of additional variables affects our model: the interpretation of the marginal effects (and we will measure an example of omitted variable bias), the standard errors of the estimators, and the goodness of fit of the regression.

We continue the extended example about class sizes and test scores, which comes from a (Stata) dataset from an old textbook that I used to use, Stock and Watson, 2007. Download and follow along with the data from today’s example:Note this is a .dta Stata file. You will need to (install and) load the package haven to read_dta() Stata files into a dataframe.

I have also made a RStudio Cloud project documenting all of the things we have been doing with this data that may help you when you start working with regressions:

On Tuesday, we will dedicate the class to working on practice problems, in preparation for Problem Set 4.

## Practice Problems

On Tuesday, we will be working on practice problems. Answers will be posted on that page later.

## Assignments: Midterm Corrections and Problem Set 4

Midterm exam corrections are due to me by an emailed PDF by 11:59 PM Sunday October 18. You may redo any question you did not get full points on (do not do questions you did not lose points on), including bonuses. Write the correct answer and explain why it’s the right answer (i.e. show your work, don’t just write $$\hat{\beta_1}$$ when you wrote $$\hat{\beta_1}$$ on the exam.) I want you to demonstrate you are internalizing the answers and learning, not just comparing with your friends to get the correct answer. You can talk to each othjer now, and are welcome to come to my (and the TAs’) office hours to go over the exam together.

Problem Set 4 is due by 11:59PM on Sunday, October 25 by PDF upload to Blackboard.

## 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).