Midterm Review Questions

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# Midterm Review Questions
## ECON 480 • Econometrics • Fall 2021
### Ryan Safner<br> Assistant Professor of Economics <br> <a href="mailto:safner@hood.edu"><i class="fa fa-paper-plane fa-fw"></i>safner@hood.edu</a> <br> <a href="https://github.com/ryansafner/metricsF21"><i class="fa fa-github fa-fw"></i>ryansafner/metricsF21</a><br> <a href="https://metricsF21.classes.ryansafner.com"> <i class="fa fa-globe fa-fw"></i>metricsF21.classes.ryansafner.com</a><br>

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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?

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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

`$$Wages_i=\beta_0+\beta_1Education+u_i$$`

a. What is in `$u_i$`?

b. 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 
## -27.047  -2.690   0.232   2.509  18.752 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.09958    0.23493  -0.424    0.672
## x            0.20116    0.14049   1.432    0.153
## 
## Residual standard error: 5.253 on 498 degrees of freedom
## Multiple R-squared:  0.0041,	Adjusted R-squared:  0.002101 
## F-statistic:  2.05 on 1 and 498 DF,  p-value: 0.1528
```

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# Question 11

Interpret all of these numbers:

<table class="huxtable" style="border-collapse: collapse; border: 0px; margin-bottom: 2em; margin-top: 2em; ; margin-left: auto; margin-right: auto;  " id="tab:unnamed-chunk-3">
<col><col><tr>
<th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0.4pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(1)</th></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(Intercept)</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;">-0.100 </td></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.235)</td></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">x</th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">0.201 </td></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.4pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.140)</td></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">N</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;">500     </td></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">R-Squared</th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">0.004 </td></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.8pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;">SER</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.8pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;">5.253 </td></tr>
<tr>
<th colspan="2" style="vertical-align: top; text-align: left; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;"> *** p < 0.001;  ** p < 0.01;  * p < 0.05.</th></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!

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# Question 16

Suppose we ran that hypothesis test on our finding. What can we conclude?

.pull-left[
.smallest[

.pull-right[
.smallest[
<table class="huxtable" style="border-collapse: collapse; border: 0px; margin-bottom: 2em; margin-top: 2em; ; margin-left: auto; margin-right: auto;  " id="tab:unnamed-chunk-5">
<col><col><tr>
<th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0.4pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(1)</th></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(Intercept)</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;">-0.100 </td></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.235)</td></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">x</th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">0.201 </td></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.4pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.140)</td></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">N</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;">500     </td></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">R-Squared</th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">0.004 </td></tr>
<tr>
<th style="vertical-align: top; text-align: left; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.8pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;">SER</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.8pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;">5.253 </td></tr>
<tr>
<th colspan="2" style="vertical-align: top; text-align: left; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0pt 0pt;    padding: 6pt 6pt 6pt 6pt; font-weight: normal;"> *** p < 0.001;  ** p < 0.01;  * p < 0.05.</th></tr>
</table>

]
]