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