Midterm Review

ECON 480 • Econometrics • Fall 2022

Dr. Ryan Safner
Associate Professor of Economics

## Question 1

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

## Question 2

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

## Question 3

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

## Question 4

Is this data likely heteroskedastic or homoskedastic?

## Question 5

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

## Question 6

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

Which is most important?

## Question 7

$Wages_i=\beta_0+\beta_1Education+u_i$

1. What is in $u_i$?
1. Is $\hat{\beta_1}$ likely biased?

## Question 8

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

## Question 9

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

## 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
-20.9518  -2.6972  -0.1055   2.4352  25.9720

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.05633    0.24844  -0.227    0.821
x           -0.05289    0.14502  -0.365    0.715

Residual standard error: 5.552 on 498 degrees of freedom
Multiple R-squared:  0.0002671, Adjusted R-squared:  -0.00174
F-statistic: 0.133 on 1 and 498 DF,  p-value: 0.7155

## Question 11

Interpret all of these numbers:

y
Constant −0.06
(0.25)
x −0.05
(0.15)
n 500
R2 0.00
SER 5.54
* p < 0.1, ** p < 0.05, *** p < 0.01

## 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?

## Question 13

Explain what a $Z$-score means.

## Question 14

Explain what a $p$-value means.

## 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!

## Question 16

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


Call:
lm(formula = y ~ x, data = het_data)

Residuals:
Min       1Q   Median       3Q      Max
-20.9518  -2.6972  -0.1055   2.4352  25.9720

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.05633    0.24844  -0.227    0.821
x           -0.05289    0.14502  -0.365    0.715

Residual standard error: 5.552 on 498 degrees of freedom
Multiple R-squared:  0.0002671, Adjusted R-squared:  -0.00174
F-statistic: 0.133 on 1 and 498 DF,  p-value: 0.7155
y
Constant −0.06
(0.25)
x −0.05
(0.15)
n 500
R2 0.00
SER 5.54
* p < 0.1, ** p < 0.05, *** p < 0.01