第三章 经典线性回归模型

Quiz 1

1、单选题:

‎Consider the following data generating process (DGP) 

‎                       

‎where  and  are mutually independent

‎Find the unconditional mean .

‎选项:
A: 0
B: 1
C: 5
D: 2
答案: 【 0

2、单选题:

Consider the following data generating process (DGP) 

                        

where  and  are mutually independent 

‌Find the conditional mean 

‎选项:
A:
B:
C:
D:
答案: 【 

3、单选题:

Consider the following data generating process (DGP) 

                        

where  and  are mutually independent 

‌Find the marginal effect of  on

‎选项:
A:
B:
C:
D:
答案: 【 

4、单选题:

Consider the following data generating process (DGP) 

                        

where  and  are mutually independent 

‏Suppose now a linear regression model 

‏                 

‏where , is specified to approximate this DGP.

‏Find the best LS approximation coefficient :

‍选项:
A:
B:
C:
D:
答案: 【 

5、单选题:

Consider the following data generating process (DGP) 

                        

where  and  are mutually independent 

Suppose now a linear regression model 

                 

​where , is specified to approximate this DGP.

​Find the best linear LS predictor 

‌选项:
A:
B:
C:
D:
答案: 【 

6、单选题:

​Suppose  where random variables  and  are independent, and  and 

​Find 

​选项:
A: 0
B: 1
C: 1.5
D: 2
答案: 【 0

7、单选题:

‌Suppose  where random variables  and  are independent, and  and 

‌Find 

‏选项:
A:
B:
C:
D:
答案: 【 

8、单选题:

‏Choose the assumption that is not required for the consistency of OLS  estimator : for  

​选项:
A:
B:
C:
D:
答案: 【 

9、单选题:

‎Choose the assumption that is not required for the normality of  that for any nonstochastic matrix , we have

‎选项:
A:
B:
C:
D:
答案: 【 

10、单选题:

‏Consider the following two bivariate linear regression models for the same  

‏                                      

‏                                      

‏where .  Find the correct relation between two OLS estimators  and 

​选项:
A:
B:
C:
D:
答案: 【 

11、单选题:

Consider the following two bivariate linear regression models for the same  

                                      

                                      

where .  Find the correct relation between two centered  and :

​选项:
A:
B:
C:
D:

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