Econometrics 3: Multiple Linear Regression

Question 1

Explain the structure and purpose of a multiple linear regression model in econometrics.

Answer 1

Question 2

Describe the OLS estimation process for multiple linear regression.

Answer 2

Question 3

List and explain the classical assumptions required for OLS to be unbiased and efficient in multiple regression.

Answer 3

6. CLRA6: Normality of errors:
   εbottom righti ∣ X∼N(0,σ^2)
   These ensure OLS estimators are unbiased, efficient, and normally distributed.

Question 4

Explain the distributional properties of OLS estimators in multiple regression.

Answer 4

Variance for Beta hat2 is same for as Beta hat1, but with xbottom right1 squared in denominator instead of xbottom right2
Error variance estimate:

σ^2=(∑εbottom righti^2) / n-(k+1)

Question 5

Explain the difference between R^2 and adjusted R^2 in model evaluation.

Answer 5

Model B: 3 regressors (one irrelevant) → R^2 = 0.91, Rbar^2 = 0.87 → Prefer Model A based on
Rbar^2

Question 6

Discuss the sources that influence the precision of OLS estimates.

Answer 6

Question 7

Explain how to test whether a single regression coefficient equals a specific value.

Answer 7

Question 8

How do we test multiple linear restrictions in regression models?

Answer 8

Question 9

Explain how model comparison reveals omitted variable bias and supports hypothesis testing.

Answer 9

Question 10

Explain the concept of multicollinearity and its impact on OLS estimation.

Answer 10

Question 11

Describe methods for identifying and dealing with multicollinearity in regression.

Answer 11

Question 12

What are alternative functional forms in regression and how can they be estimated?

Answer 12