lecture 5

Question 1

zero conditional mean

Answer 1

• knowing x tells us nothing about the expected value
• expected value is on the line

Question 2

we’ve assumed that the error distribution is centered on the regression line BUT

Answer 2

our idealized picture suggests something more
- that the variance is constant for all values of X

Question 3

error distribution is centered on the regression line IS NOT

Answer 3

this is not one of our assumptions

Question 4

in reality our little normal distributions don’t look even

Answer 4

they have different spreads

Question 5

having all the exact same little normal distributions, variance of the error term in a regression model is constant

Answer 5

homoskedastic

Question 6

little normal distributions do not look at the same; variance of the error term in a regression model is not constant

Answer 6

heteroskedastic

Question 7

two assumptions that we have not made

Answer 7

1. errors are homoskedastic
2. errors are normally distributed

Question 8

robust SE

Answer 8

• if errors are heteroskedastic and you use plain SE, you estimates of the standard error will be wrong
• use robust so all estimates will be fine, even if there isn’t heteroskedasticity

Question 9

when variance of u decreases/increases estimate of slope gets more precise

Answer 9

decreases

Question 10

as n increases/decreases our estimate of the slope gets more precise

Answer 10

increases

Question 11

less variance for —- more variance for —-

Answer 11

u, x

Question 12

as the variance of x increases/decreases our estimate of the slope gets more precise

Answer 12

increases

Question 13

gauss-markov theorem

Answer 13

• three least squares assumptions hold and if the errors are homoskedastic then the OLS slope estimator is BLUE

Question 14

BLUE

Answer 14

B- best, minimum variance estimator
L- linear function of the dependent variable; restriction on how we estimate the line
U-
E-

Question 15

sweet spot for our 1-3 assumptions

Answer 15

OLS is unbiased
- now, even other linear estimators may do better

Question 16

in addition to the least squares assumptions, there are additional regression assumptions that can be made

Answer 16

homoskedastic and normality

Question 17

problem with homoskedastic and normality of the error term

Answer 17

assumptions care too unrealistic

Question 18

what we can do with homoskedastic and normality of the error term

Answer 18

• small sample inference
• easier OLS variance estimators
• BLUE