9. Multivariate Regression

Question 1

Interpretation for B0 and B1 in multivariate regression OLS

Answer 1

Question 2

What are the predicted values, and residuals for multivariate regressionD

Answer 2

Question 3

What are the mathematical properties of OLS in multivariate regression

Answer 3

Analogous to bivariate regression, OLS is always true

1. OLS residuals are mean 0
2. OLS residuals are uncorrelated with all regressors
3. Predicted value useing average of each x is the average y

hold wethere sample or population, or if estimates do not have a causal interpretation

Question 4

Answer 4

Question 5

Answer 5

Question 6

Answer 6

Question 7

What is matching

Answer 7

focus on groups of observations with the same value of confounders, within these groups we look at avg outcomes for treatmebt and control w/o confounder bias

Question 8

How does multivariate regression relate to matching

Answer 8

Multivariate regression automates the calculation of a weighted average for matchign when estimating treatement effects

it is “automated matching”

Question 9

Answer 9

Question 10

If we have controlled for all confounders, then do our regression results havea causal interpretation?

Answer 10

We could only observe a proxy of a confounder e..g iq and intelligence

we can only hope that the control completely capture the effect of the confounder

Question 11

What assumption does a causal interpretation require

Answer 11

‘selection on observables’

factors that determine the treatement and outcome are captured by observable controls

Question 12

What is the mathematical assumption needed for causal interpretaion

Answer 12

After conditioning on
𝑋𝑖

Treated and untreated individuals have the same average outcome they would have had without treatment

Question 13

If there is a factor in ui which affects only the outcome, and not the treatement, is it a confounder?

Answer 13

No it is not a confounder

Question 14

If we have controlled for all confounder, what do we call treatement

Answer 14

as good as random conditional on controls

meaning that holding fixed controls, variation in treatement is not associated with any other determinant of the outcome changing, and thus we isolate th causal effect of treatement on the outcome

Question 15

What happens to residual variation ( Var(uhat i) when you add regressors?

Answer 15

Adding regressors weakly lowers the variance of the residuals

Question 16

Prove that adding regressors weakly lowers the variance of the residuals

Answer 16

Question 17

How does (Var (uhat)/ Var(y)) compare to (Var(uhat short)/Var(Y))

Answer 17