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?
Question 7
\[Wages_i=\beta_0+\beta_1Education+u_i\]
 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 Rsquared 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 Rsquared: 0.0002671, Adjusted Rsquared: 0.00174
Fstatistic: 0.133 on 1 and 498 DF, pvalue: 0.7155
Question 11
Interpret all of these numbers:

y 
Constant 
−0.06 

(0.25) 
x 
−0.05 

(0.15) 
n 
500 
R^{2} 
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 onesided or twosided?
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 Rsquared: 0.0002671, Adjusted Rsquared: 0.00174
Fstatistic: 0.133 on 1 and 498 DF, pvalue: 0.7155

y 
Constant 
−0.06 

(0.25) 
x 
−0.05 

(0.15) 
n 
500 
R^{2} 
0.00 
SER 
5.54 
^{} * p < 0.1, ** p < 0.05, *** p < 0.01 