Midterm Review Questions

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# Midterm Review Questions
## ECON 480 · Econometrics · Fall 2019
### Ryan Safner Assistant Professor of Economics <a href="mailto:safner@hood.edu"> safner@hood.edu</a> <a href="https://github.com/ryansafner/metricsf19"> ryansafner/metricsf19</a> <a href="https://metricsF19.classes.ryansafner.com"> metricsF19.classes.ryansafner.com</a>

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# Question 1

What does **endogenous** mean, in words? What about statistically?

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# Question 2

If a regression is biased (from endogeneity), what can we learn about the bias?

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# Question 3

What does heteroskedasticity mean? Does heteroskedasticity **bias** `$\hat{\beta_1}$`?

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# Question 4

Is this data likely heteroskedastic or homoskedastic?

![](midterm-review_files/figure-html/unnamed-chunk-1-1.png)

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# Question 5

- What three things impact the variation of `$\hat{\beta_1}$`? How?

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# Question 6

What are the four assumptions we make about the error term?

Which is most important?

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# Question 7

`$$Wages_i=\hat{\beta_0}+\hat{\beta_1}Education+u_i$$`

What is in `$u_i$`?

Is `$\hat{\beta_1}$` likely biased?

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# Question 8

What does `$R^2$` measure? What does it mean? How do we calculate it?

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# Question 9

What does `$\sigma_u$` (SER) measure? What does it mean?

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# Question 10

Interpret all of these numbers (except Adjusted R-squared and the last line):

```
## 
## Call:
## lm(formula = y ~ x, data = het_data)
## 
## Residuals:
## Min 1Q Median 3Q Max 
## -5.2447 -0.5159 0.0207 0.4802 5.5260 
## 
## Coefficients:
## Estimate Std. Error t value Pr(>|t|) 
## (Intercept) -0.02432 0.10617 -0.229 0.819 
## x 1.05812 0.09219 11.478 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.149 on 498 degrees of freedom
## Multiple R-squared: 0.2092,	Adjusted R-squared: 0.2076 
## F-statistic: 131.7 on 1 and 498 DF, p-value: < 2.2e-16
```

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# Question 11

Interpret all of these numbers:

<table class="huxtable" style="border-collapse: collapse; margin-bottom: 2em; margin-top: 2em; width: 50%; margin-left: auto; margin-right: auto; ">
<col><col><tr>
<td style="vertical-align: top; text-align: center; white-space: nowrap; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0pt 0pt; padding: 4pt 4pt 4pt 4pt;"></td>
<td style="vertical-align: top; text-align: center; white-space: nowrap; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0.4pt 0pt; padding: 4pt 4pt 4pt 4pt;">(1)</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; white-space: nowrap; padding: 4pt 4pt 4pt 4pt;">(Intercept)</td>
<td style="vertical-align: top; text-align: right; white-space: nowrap; padding: 4pt 4pt 4pt 4pt;">-0.024    </td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; white-space: nowrap; padding: 4pt 4pt 4pt 4pt;"></td>
<td style="vertical-align: top; text-align: right; white-space: nowrap; padding: 4pt 4pt 4pt 4pt;">(0.106)   </td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; white-space: nowrap; padding: 4pt 4pt 4pt 4pt;">x</td>
<td style="vertical-align: top; text-align: right; white-space: nowrap; padding: 4pt 4pt 4pt 4pt;">1.058 ***</td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; white-space: nowrap; padding: 4pt 4pt 4pt 4pt;"></td>
<td style="vertical-align: top; text-align: right; white-space: nowrap; border-style: solid solid solid solid; border-width: 0pt 0pt 0.4pt 0pt; padding: 4pt 4pt 4pt 4pt;">(0.092)   </td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; white-space: nowrap; padding: 4pt 4pt 4pt 4pt;">N</td>
<td style="vertical-align: top; text-align: right; white-space: nowrap; padding: 4pt 4pt 4pt 4pt;">500        </td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; white-space: nowrap; padding: 4pt 4pt 4pt 4pt;">R-Squared</td>
<td style="vertical-align: top; text-align: right; white-space: nowrap; padding: 4pt 4pt 4pt 4pt;">0.209    </td>
</tr>
<tr>
<td style="vertical-align: top; text-align: left; white-space: nowrap; border-style: solid solid solid solid; border-width: 0pt 0pt 0.8pt 0pt; padding: 4pt 4pt 4pt 4pt;">SER</td>
<td style="vertical-align: top; text-align: right; white-space: nowrap; border-style: solid solid solid solid; border-width: 0pt 0pt 0.8pt 0pt; padding: 4pt 4pt 4pt 4pt;">1.149    </td>
</tr>
<tr>
<td colspan="2" style="vertical-align: top; text-align: left; white-space: normal; padding: 4pt 4pt 4pt 4pt;"> *** p < 0.001; ** p < 0.01; * p < 0.05.</td>
</tr>
</table>

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# Question 12

Suppose `$Y$` is normally distributed with a mean of 10 and a standard error of 5. What is the probability that `$Y$` is between 5 and 15?

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# Question 13

Explain what a `$Z$`-score means.

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# Question 14

Explain what a `$p$`-value means. :)

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# Question 15

We run the following hypothesis test at `$\alpha=0.05$`:

`$$\begin{align*}
H_0: \, & \beta_1=0\\
H_1: \, & \beta_1 \neq 0 \\
\end{align*}$$`

Is this test one-sided or two-sided?

We find the `$p$`-value is 0.02. What is our conclusion? Be specific and precise in your wording!