Linear regression

Question 1

Decomposition of sample variance (OLS)

Answer 1

Question 2

Sample coefficient of determination

Answer 2

Question 3

Assumption 1 of CRM

Answer 3

Question 4

Assumption 2 CRM

Answer 4

Question 5

Random sampling implies

Answer 5

Exogeneity (part of assumption 1)

Part 1 of assumption 2

Question 6

Properties of the CRM estimator

Answer 6

Question 7

Gauss Markov Theorem

Answer 7

Subject to assumption one and tow, the CRM estimator has minimum variance in the class of conditionally unbiased and linear estimators (BLUE)

Question 8

Efficiency of Normal CRM

Answer 8

beta hat has miniimum variance in the class of conditionally unbiased estimators

It attains the Cramer Rao bound for the conditional likelihood model

Question 9

Statistics for individual coefficients

Answer 9

Question 10

Testing for sets of coefficients

Answer 10

Question 11

Asymptotic properties of the CRM (consistency)

Answer 11

Question 12

Asymptotic properties of the CRM (normality)

Answer 12

Question 13

Asymptotic distribution for the case of non linear CEF

Answer 13

Question 14

Properties of residuals and fitted values

Answer 14

Question 15

Estimating s^2

Answer 15

Question 16

Distribution of delta hat under normality

Answer 16