Midterm Review

class: center, middle, inverse, title-slide

# Midterm Review
## EC 320: Introduction to Econometrics
### Kyle Raze
### Fall 2019

---

class: inverse, middle

# Prologue

---
# Housekeeping

Problem Set 4

- Due tonight by 23:59 on Canvas

Midterm 2 on Wednesday

- .hi[You still have lab this week!]
- [Maps!](https://socviz.co/maps.html#maps)

Extended office hours

- Tomorrow 15:00 to 17:00
- Room TBA

---
class: inverse, middle

# Midterm II: The Weeds

---
# Midterm Topics

.green[Anything from the lectures, labs, or problem sets] .hi-green[is fair game!]

1. Simple Linear Regression: Estimation I & II

2. Classical Assumptions

3. Simple Linear Regression: Inference

4. Multiple Linear Regression: Estimation

5. Multiple Linear Regression: Inference

6. Regressions in .mono[R]

---
# Midterm Topics

## 1. Simple Linear Regression: Estimation

OLS mechanics

- How does OLS pick parameter estimates?
- What properties are a direct consequence of OLS?
- Residuals *v.s.* errors

Coefficient interpretation (literal)

---
# Midterm Topics

## 1. Simple Linear Regression: Estimation (cont.)

Goodness of fit

- `\(R^2\)` interpretation (literal)
- Understand `\(R^2\)` derivation
- Use and misuse of `\(R^2\)`

OLS by hand

- Estimate coefficients and calculate `\(R^2\)`.
- Don't have to calculate standard errors by hand.

---
# Midterm Topics

## 2. Classical Assumptions

Six assumptions

1. Linearity
2. Sample variation/no perfect collinearity
3. Random sampling
4. Exogeneity
5. Homoskedasticity
6. Normality

What do they buy?

When are they satisfied? When are they violated?

---
# Midterm Topics

## 2. Classical Assumptions (cont.)

**So what?**

- Coefficient interpretation (substantive)
- Hypothesis test validity.

---
# Midterm Topics

## 3. Simple Linear Regression: Inference

Making inferences about population parameters

- Population *v.s.* sample
- What do we mean by "statistical significance?"

Hypothesis testing (*e.g.,* *t* tests)

- Null hypotheses *v.s.* alternative hypotheses
- Left-tailed, right-tailed, and two-tailed
- Type I *v.s.* Type II error

Confidence intervals

---
# Midterm Topics

## 4. Multiple Linear Regression: Estimation

OLS mechanics and properties

Goodness of fit

- `\(R^2\)` interpretation (literal)
- Know the behavior of `\(R^2\)` as the number of explanatory variables increases.

Make predictions for certain values of the explanatory values (*e.g.,* hedonic modeling)

---
# Midterm Topics

## 4. Multiple Linear Regression: Estimation (cont.)

Coefficient interpretation (literal and substantive)

Omitted-variable bias

- Know when omitting a variable causes bias.
- Sign the bias.
- Back out correlations between explanatory variables.

---
# Midterm Topics

## 5. Multiple Linear Regression: Inference

Confidence intervals and *t* tests

- Other than degrees of freedom, same as before.

Multicollinearity

- Standard errors depend on the overlapping variation between the explanatory variable.
- More overlap `\(\implies\)` bigger standard errors `\(\implies\)` less likely to reject null hypothesis.

Irrelevant variables

**No *F* tests on the midterm!** Stay tuned for the final.

---
# Midterm Topics

## 6. Regressions in .mono[R]

Write the code that generates regression output

- I provide the console or R Markdown output and the name of the data file.
- You provide the code that loads the necessary packages, imports the data, runs regressions, and generates a table.
- Write the code as if it's in a .mono[.R] script.

---
# Midterm Structure

## Fill in the Blank

- 10 blanks
- 3 points per blank (30 points total)

## True or False

- 5 questions
- 6 points per question (30 points total)
- Brief explanations required for full credit

## Free Response

- 4 multi-part questions with varying numbers of points (140 points total)
- Explanations required for full credit

---
# Midterm Protocol

## Materials

- Writing utensil
- 3-inch-by-5-inch note card
- Basic or scientific calculator (no graphing or programming capabilities)
- .hi[Nothing else]

## Procedure

- **Randomized** seating chart .red[(penalty for non-compliance)]
- 80 minutes from *"you may begin"* to *"pencils down"*
- First 30 minutes: .hi[quiet period] (no questions, no getting up)
- Last 50 minutes: ask lots of questions

---
class: inverse, middle

# Practice

---
# Regression Table

## Example: Final Grades

Data on 680 students in an introductory microeconomics class.

<table>
<caption>Outcome: Final Exam Score (%)</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> Explanatory variable </th>
   <th style="text-align:center;"> 1 </th>
   <th style="text-align:center;"> 2 </th>
   <th style="text-align:center;"> 3 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Intercept </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 22.7 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 21.8 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> -8.69 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.877) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.973) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (1.49) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Classes Attended (%) </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.039 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.027 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.041 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.011) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.014) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.013) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> HW Turned In (%) </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;">  </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.022 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.023 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.012) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.011) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> ACT Score </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;">  </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.528 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.048) </td>
  </tr>
</tbody>
</table>

---
count: false

# Regression Table

## Example: Final Grades

Data on 680 students in an introductory microeconomics class.

<table>
<caption>Outcome: Final Exam Score (%)</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> Explanatory variable </th>
   <th style="text-align:center;"> 1 </th>
   <th style="text-align:center;"> 2 </th>
   <th style="text-align:center;"> 3 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Intercept </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 22.7 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 21.8 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> -8.69 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.877) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.973) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (1.49) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Classes Attended (%) </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.039 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.027 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.041 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.011) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.014) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.013) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> HW Turned In (%) </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.022 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.023 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.012) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.011) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> ACT Score </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;">  </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.528 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.048) </td>
  </tr>
</tbody>
</table>

---
count: false

# Regression Table

## Example: Final Grades

Data on 680 students in an introductory microeconomics class.

<table>
<caption>Outcome: Final Exam Score (%)</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> Explanatory variable </th>
   <th style="text-align:center;"> 1 </th>
   <th style="text-align:center;"> 2 </th>
   <th style="text-align:center;"> 3 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Intercept </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 22.7 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 21.8 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> -8.69 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.877) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.973) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (1.49) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> Classes Attended (%) </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.039 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.027 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.041 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.011) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.014) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.013) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> HW Turned In (%) </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;"> 0.022 </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.023 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;"> (0.012) </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.011) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;line-height: 110%;font-style: italic;color: black !important;"> ACT Score </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #23373b !important;line-height: 110%;font-weight: bold;"> 0.528 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #23373b !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (0.048) </td>
  </tr>
</tbody>
</table>