Midterm Review

ECON 480 • Econometrics • Fall 2022

Dr. Ryan Safner
Associate Professor of Economics

safner@hood.edu
ryansafner/metricsF22
metricsF22.classes.ryansafner.com

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

ECON 480 — Econometrics