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 ^β1?

Question 4

Is this data likely heteroskedastic or homoskedastic?

Question 5

• What three things impact the variation of ^β1? How?

Question 6

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

Which is most important?

Question 7

Wagesi=β0+β1Education+ui

a. What is in ui?

b. Is ^β1 likely biased?

Question 8

What does R2 measure? What does it mean? How do we calculate it?

Question 9

What does σu (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 
## -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

Question 11

Interpret all of these numbers:

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 α=0.05:

H0:β1=0H1:β1≠0

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 
## -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