1 True 01' False Questions ngi. The correct formula for an unbiased estimate of U2 is: 1. Assume all the assumptions for CLRM (classical linear regression model) for multiple re- 1 n a; gression are satisfied, except for A4 homoskedasticity. That is, you cannot assume Var (ui) n _ 3 i=1 1 is constant. In this case, the OLS estimators are still unbiased. True or False? [ ] True or False? [ ] (a) True 7 (a) True False (b) (b) False 2. A stochastic process {Y;} is weakly stationary if the following three conditions are met: (1) its mean E [Y1] is constant over time t, (2) its variance Var (Y:) is constant over time, (3) its value of the covariance C017 (Yg, 14-5) depends only on s, not on t. True or False? [ ] 6. In the multiple regression analysis, R2, which is the adjusted R2, never decreases when- ever you add more explanatory variables in the PRF. True or False? [ ] (a) True 9% (a) T (b) False 3. A stochastic process {Y;} is integrated of order 2 (Le, I (2)) if A (An) E (in Y,_1) 7' Consider the time sales {Y9} dened by: (Y[_1 14-2) is stationary True or False? [ l Y: = 14 + 4,164+ m 14: N i.i.d. (0,92) ' (a) True {i0} is (weakly) stationary if = 1 and y = 0. True or False? [ ] (b) False (a) True 4. Suppose size n = 5000 sample of (X1,Y,') are independently drawn from the polulation. (b) F ls a e You know that the PRF has the following form: Y; = 151 + 32X; + ui 14; ~ Uniform [m] , for some positive number a, i.e., you know that the error term follows a uniform distri- bution with mean zero. Then, considering the sample size n = 5000 is large enough, the realized estimate [32 will be very close to #2. True or False? [ ] (a) m (b) False 5. Consider the PRF with two explanatory variables: Yi = 151 + zxzi + aXsi + u,- ui ~ Ltd. (0472) . After you estimated (31, 32, 33) using OLS with sizen sample {Yh X, X3,}'':l, you want to obtain an unbiased estimate of 171. Let 12,- denote the residual 12,- = Y,- [31 Exx