Regression Analysis

Question 1

When do we use regression analysis?

Answer 1

linear regression: How does x affect y?
Does the effect depend on other variables?

multiple regression: how do P predictors affect y?
B0+B1x1+…

Question 2

What are different types of predictors?

Answer 2

• numeric
• factors
• polynomials
• interactions

nature of x does not affect estimation but impact interpretation

Question 3

What does the stochastic error term E include?

Answer 3

• omitted predictors
• measurement errors in Y
• random shocks (sth happens in the world that throwss off the model)
• noise inherent in human behavior

Question 4

What are the assumptions about the predictors?

Answer 4

1. The predictors are fixed (there is no uncertainty aboutvthe values these predictors take)
2. No micronumerosity: n»P
3. No perfect multicollinearity: No predictor is a perfect linear function of the remaining predictors.

Question 5

What are the assumptions about the errors?

Answer 5

1. The errors are normally distributed.
2. Errors are on average equal to 0, no central tendency that pushes in one direction; they cancel each other out, so eg. sometimes we overestimate, sometimes we underestimate
3. No Homiskedasticity: Variance around the regressiom line/plane is constant
4. No autocorrelation: The errors are uncorrelated with each other

Question 6

What is weak exogenity?

Answer 6

The errors are uncorrelated with the predictors ->

1. all omitted predictors are uncorrelated with the predictors in the model
2. the functional form has been correctly specified
3. There is no feedback loop (y cannot feedback into x because then x would become stochastic and is no longer fixed and it would violate the assumption that errors are uncirrelated with the predictors)

Question 7

What are the properties of the regression coefficients?

Answer 7

B is consistent, asymptotically efficient and asymptotically normal (given the assumption of weak exogenity and about the errors are true)

B is BLUE: best linear unbiased estimator

Question 8

How can we interpret regression analysis?

Answer 8

1. Discrete change
2. Marginal effects
3. Elasticities (percentage change in the outcome for a one percent change in the predictor)

Question 9

How do we interpret factors?

Answer 9

Bd is the difference in means between two groups