1. [42 points] We consider using the variable “Airline Travel” (i.e. how much we consume on airline travel) as our dependent variable ( ) and “Income” (i.e. how much we earn) as the explanatory variable ( ). Suppose that the OLS regression is given by

(0.5) (0.11)
where = 100 and the numbers in parentheses are standard errors. Denoting the true slope parameter by , supp

1. [42 points] We consider using the variable “Airline Travel” (i.e. how much we consume on airline travel) as our dependent variable ( ) and “Income” (i.e. how much we earn) as the explanatory variable ( ). Suppose that the OLS regression is given by

(0.5) (0.11)
where = 100 and the numbers in parentheses are standard errors. Denoting the true slope parameter by , suppose that we

The weight of each question is in square bracket. Good luck!
1. [30 points] About the Weak Law of Large Numbers (WLLN).
(i) State clearly what is the WLLN.
(ii) Prove the WLLN
(iii) Explain why the WLLN is important when studying the OLS estimator. (You don’t have to prove anything here. Just explain!)

2. [30 points] About the White test for heteroscedasticity.
(i) State clearly how to implement the White test.
(ii) Supp

The weight of each question is in square bracket. Good luck!
1. [30 points] About the Weak Law of Large Numbers (WLLN).
(i) State clearly what is the WLLN.
(ii) Prove the WLLN
(iii) Explain why the WLLN is important when studying the OLS estimator. (You don’t have to prove anything here. Just explain!)

2. [30 points] About the White test for heteroscedasticity.
(i) State clearly how to implement the White test.
(ii) Suppose that the