For presentation schedule and makeup test signups, see: QM222 Dec. 7 Presentations For presentation schedule and makeup test signups, see: https://docs.google.com/spreadsheets/d/1pcfaSpsS6 TISPccPsJf7ykuhTIzqsWN7OqURMO_BLM4/edit#gid= 0 QM222 Fall 2016 Section D1

Reminder: Makeup Test Makeup on the parts of the test about omitted variable bias/causality v. correlation: Part I Question 5(both parts) and Question 6(first part) plus Part III, together worth a total of 24 points) Friday December 9th during “section” Or: during the QM222 final (Sat night Dec. 17) Makeup on the entire test: Sat night Dec. 17. You will get a special version for our section. Test Grading If you got less than 84 on the original midterm, you will get the better of the two tests. If you got 84 or more on the original midterms, you will get the last grade if it is the best. If the last grade is worse, you will get the average of the two grades. I will pass out a signup on Mon Dec 12 for one of the two tests during the final. QM222 Fall 2016 Section D1

Today’s Presenters Tea Sulkaj Sergio Portela Kay Zhang Ryan Ng Moe Alhassan Clarification questions allowed during the presentation. (I will clarify things to class during presentation if I think it is needed.) 5 minutes Q/A after the presentation: Save your major comments or questions until then. I will give you additional suggestions in writing. QM222 Fall 2016 Section D1

Review: Omitted Variable Bias QM222 Fall 2016 Section D1

Condo’s Price = 520729 – 46969 BEACON Price = 6981 + 409 SIZE + 32936 BEACON Why are the coefficients on Beacon so different? The coefficient on Beacon in the first (simple) regression says: Across all the properties in our dataset, those on Beacon cost $46,239 less on average.   In contrast, the coefficient on Beacon in the multiple regression says: If we compare two condos of the same size, one on Beacon and one not on Beacon, the one on Beacon costs $32,946 more. QM222 Fall 2016 Section D1

Condo’s Price = 520729 – 46969 BEACON  Price = 6981 + 409 SIZE + 32936 BEACON Which of these two equations should the executive use for to figure out how much of a premium she will have to pay for an equivalent condo on Beacon Street? The multiple regression. Which of these two equations should the realtor care most about, since realtors get a percent of the sale price? The simple regression QM222 Fall 2016 Section D1

If you really want to measure the effect of X alone (e. g If you really want to measure the effect of X alone (e.g. Beacon), you need to control for possibly confounding factors. If you don’t, the coefficient on X is biased. We call this omitted or missing variable bias. Omitted variable bias occurs when The omitted variable has an effect on the dependent variable, AND The omitted variable is correlated with the explanatory variable of interest. QM222 Fall 2016 Section D1

Omitted variable bias Price = 520729 – 46969 BEACON Price = 6981 + 409 SIZE + 32936 BEACON In a simple regression of Y on X1, the coefficient b1 measures the combined effects of: the direct (or often called “causal”) effect of the included variable X1 on Y PLUS an “omitted variable bias” due to factors that were left out (omitted) from the regression THAT WERE CORRELATED WITH X1 If you want to measure the direct, causal effect, the coefficient in the regression without the omitted variables is biased. QM222 Fall 2016 Section D1

Graphical representation of Omitted Variable Bias Really, both being on Beacon and price affect price. Y = b0 + b1X1 + b2X2 Let’s call this the Full model. Let’s call b1 and b2 the direct effects. QM222 Fall 2016 Section D1

The mis-specified or Limited model However, in the simple regression, we measure only a (combined) effect of Beacon on price. Call its coefficient c1 Y = c0 + c1X1 Let’s call c1 is the combined effect. QM222 Fall 2016 Section D1

Background relationship between X’s We also know that there is a relationship between X­1 (Beacon) and X2 (Size). We call this the Background Relationship: . correlate price size Beacon_Street (obs=1085) | price size Beacon~t -------------+--------------------------- price | 1.0000 size | 0.8655 1.0000 Beacon_Str~t | -0.0552 -0.1081 1.0000 This background relationship, shown here as a1, is negative. QM222 Fall 2016 Section D1

Let’s combine all 3 pictures: the full model, the limited model & the background relationship The effect of X­1 on Y has two channels. The first one is the direct effect b1. The second channel is the indirect effect through X­2. When X­1 changes, X2 also tends to change (a1) This change in X­2 has another effect on Y (b2) QM222 Fall 2016 Section D1

Y = b0 + b1 X1 + b2 X2 Y = c0 + c1 X1 Y = c0 + [ + ] X1 b1 bias FULL MODEL IN A MULTIPLE REGRESSION Y = b0 + b1 X1 + b2 X2 MIS-SPECIFIED MODEL WHEN MISSING A VARIABLE Y = c0 + c1 X1 Y = c0 + [ + ] X1 b1 bias QM222 Fall 2015 Section D1

X2 = a0 + X1 a1 a1 Y = b0 + X1 + X2 Y = b0 + X1 + ( a0 + X1) To understand the bias, note that there is a relationship between the X’s we call the BACKGROUND MODEL X2 = a0 + X1 Remember the FULL MODEL (MULTIPLE REGRESSION) Y = b0 + X1 + X2 Y = b0 + X1 + ( a0 + X1) Y = (b0+b2a0) + [ + ] X1 Y = c0 + [ + ] X1 a1 b1 b2 a1 b1 b2 b1 b2 a1 b1 bias QM222 Fall 2015 Section D1