2.
   2024
/   
     - VI
 : 3     :100
:     -    ,          
                
  -
1.              
            
2. -      
       β-   
   ,             
  - 
3.        -        
4.()      ?             
  
(b) X  Y                     
:
     5     '   :
2.
 
60
90
110
125
150
170
180
200
220
230

100
150
200
250
300
350
400
450
500
550
  - 
5.                
6. (a)        :


       X₂          

()     -    -       

  -
7. -    
  ? -    -    
      
8.()           
()          ?
2.
   2024
/   
     - VI
 : 3     :100
:     -    ,          
                
  -
1.              
            
:󷄧󷄫       
             ,
        :
             
            
      
󹶆󹶚󹶈󹶉   :    
               ,
            
 : 
        ,     
  , 
 :
󰇛󰇜
2.
   : "  '   "
 
    :

         
 
󷷑󷷒󷷓󷷔      :          
       
      '  :
  
     
 
  (    ,  )
    
            
󹵍󹵉󹵎󹵏󹵐: -          
    
          :


10
100
12
95
15
80
20
60

  : "   '    ?"
  
 
    :

       :

2.
    ""      -   
 
   :


 
a  b             
󷄧󼿒  (   )
   


 (-)

 + 
   
    
 ()
 ()


 
  
󷷑󷷒󷷓󷷔 :
             
          
󷄧󷄬       
   '    -     
 ,         
 -  ,
  ,             
  (u)   
󷈷󷈸󷈹󷈺󷈻󷈼   ?
    :
 󰇛󰇜
2.
   ,      -      

?
    '   :


  



     
 
  
 :

 u (   )    
 
󷷑󷷒󷷓󷷔           
󷄧󷄭    (     )
""   -            
' 
󷄧󷄫   
      

         
 
:   '   :


  

 
 
      
2.
            
󷷑󷷒󷷓󷷔 :   =     
󷄧󷄬  
          
:
     
   
 
    
       ,      
 
        
󷄧󷄭   
    -  ,  
     
:  :
 
 
 :

     
,      
        
󷄧󷄮    
     '   
2.
   :



              
   
 ,       
󷄰󷄯  
        :
 
 
 
     
 
  ,      
       
󷄧󷄱       
      :
 



  
        
  
      
2.
󷄧󷄲  
     ,  - 
 
:
  
   
 
      
󷄧󷄮  
 ?
   ,    
 
 :


     -    
    :


 
 
      
󷄰󷄯 
          ,  ,
  ,    ,  ,   
    
          
          ,   
       
2.
2. -      
       β-   
   ,             
:󷋇󷋈󷋉󷋊󷋋󷋌     
     :
:
=   (  
   )
=   ()
=  (Y    X = 0  )
=  (Y   X    )
=   (    )
          
󷊨󷊩-   
-     ()          
 ()    ()   
Residual
 :
󰇛
󰇜
  
              
󷙣󷙤󷙥 β-    
 1:        (RSS)   
 󰇛
󰇜
 2: β₀  β₁     

    RSS     ,    (-  ) 
   


󰇛
󰇜
2.



󰇛
󰇜
 3:    
  :



  :



 4:        
:


:
󰇛
󰇜󰇛
󰇜
󰇛
󰇜
󷈷󷈸󷈹󷈺󷈻󷈼
():      X      Y   
():  X = 0    Y   
  
    -         ' 
     
󷊨󷊩          
     ,       :
1.  :
o X  Y    
o :  X =   , Y =  ,   - 
 
2.    :
o -  ()     
o  - 
(-    )
2.
3.  (  ):
o    X      
o  X    ,    
  
4.      :
o    '   ,      
 
5.   -  
:
o   ,        , 
     '   
6.   :
o   X     

o     ,      
󷙣󷙤󷙥     
  
   (X)    (Y) '     
10     
   -     
,             5    
,         0   ,   20   
    

󽆪󽆫󽆬
-             ,  
        , ,  ,   
 '  
  - 
3.        -        
:󷈷󷈸󷈹󷈺󷈻󷈼-   (    )
1.     
,            
              :

2.
     :
       
    (  )
β ( )    (   
  
)
ε ()   
   :
󷷑󷷒󷷓󷷔   =   +  
2. -       
            "  " 
(1) 
    :

       '    (β      
)
(2)   
󰇛󰇜
,           '  

(3)   ()
󰇛󰇜
        
󷷑󷷒󷷓󷷔      "" 

2.
(4)  - 
  :
󰇛
󰇜 󰇛 󰇜
      

(5) X  
     - 

  
         
3. -    
  :
󷷑󷷒󷷓󷷔- :      , β   - 
(OLS)        () 
4.     ?
       :
󷄧󼿒
 Y     
OLS :
󰆹
󰇛
󰆒
󰇜

󰆒
 Y   
2.
󷄧󼿒
󰇛
󰆹
󰇜
, OLS    
󷄧󼿒  
"  "         - 
󷷑󷷒󷷓󷷔      OLS    

5. -     (--)

    OLS  
 1: OLS  
OLS :
󰆹
󰇛
󰆒
󰇜

󰆒
 :

 :
󰆹
󰇛
󰆒
󰇜

󰆒
󰇛󰇜
󰇛
󰆒
󰇜

󰆒
󰇛
󰆒
󰇜

󰆒
󰇛
󰆒
󰇜

󰆒
 2:   
 :
2.
󰇛
󰆹
󰇜󰇟󰇛
󰆒
󰇜

󰆒
󰇠
󰇛
󰆒
󰇜

󰆒
󰇛󰇜

:
󰇛󰇜
 :
󰇛
󰆹
󰇜
󷄧󼿒OLS  
 3: OLS  
    :
󰆹
󰇛
󰆒
󰇜

󰆒
:
󰇛
󰆹
󰇜 󰇟󰇛
󰆒
󰇜

󰆒
󰇠
   :
󰇛󰇜 󰇛󰇜
󰆒
 :
󰇛
󰆹
󰇜 󰇛
󰆒
󰇜

󰆒
󰇛󰇜󰇛
󰆒
󰇜

:
󰇛󰇜
 :
2.
󰇛
󰆹
󰇜
󰇛
󰆒
󰇜

 4:       '   
    :

 C   
 :
󰇛
󰇜󰇛󰇜 
β    :

           :

 5:      
   :
󰇛
󰇜 󰇛󰇜
󰆒
:
󰇛󰇜
 :
󰇛
󰇜
󰆒
2.
 6: OLS    C  

 :

OLS :
󰇛
󰆒
󰇜

󰆒
 :
󰇛
󰆒
󰇜

󰆒
:

 7:  
:
󰇛
󰇜
󰇟󰇛
󰆒
󰇜

󰆒
󰇠󰇟󰇛
󰆒
󰇜

󰆒
󰇠
:
󰇟󰇛
󰆒
󰇜

󰆒
󰇠
 :
󰇛
󰇜󰇛
󰆹
󰇜
󰆒
 8: -   

:
󰆒
2.
( -)
 :
󰇛
󰇜 󰇛
󰆹
󰇜
 :
󷷑󷷒󷷓󷷔      OLS    

  (  )

 :
OLS  
OLS  
OLS  -  
 :
OLS is the BLUE estimator
6.  
   
       :
󷷑󷷒󷷓󷷔     

       
 -   :
󷷑󷷒󷷓󷷔  ()   ,
󷷑󷷒󷷓󷷔OLS        
  OLS   
 -    '   
7.     
2.
   
 :
󽆱    

  0   
     :
󷷑󷷒󷷓󷷔OLS    
      :
-
-
 
8. -  
   
     
:
 -     
 OLS '   
   OLS  

:
󷷑󷷒󷷓󷷔       
4.()      ?             
  
:4(a)      ?
   
   
           
      '         ', 
  
       '        
 
                
  (   ) 
 
2.
      
 :
󷷑󷷒󷷓󷷔     ?
󷷑󷷒󷷓󷷔             ?
        (R²)   
 
   (R²)      
       
     ()    
  :
            

-  
        
 R² = 0.90 →    90%    
 R² = 0.50 →  50%    
 R² = 0.10 →   10%    
       
   (   )
 
    ,        
:      -   :
  

  

  
2.
                   
     
:
Explained Variation
Total Variation
 :
       
     
 
:
² = 0   

² = 1  
² = 0.75 75%     
  
         R² = 0.80      
  :
󷷑󷷒󷷓󷷔    80%        
󷷑󷷒󷷓󷷔20%   (, , , )   
   
     
 :
󷷑󷷒󷷓󷷔 
          
 
2.
:   
        :
  
  
 
             : 
   ,      

    ,    
      (  R²)
 
 R², R²              
   :
󷷑󷷒󷷓󷷔           ?
󷷑󷷒󷷓󷷔      '   ?
   
               
        
  :
󷷑󷷒󷷓󷷔         
󷷑󷷒󷷓󷷔      
 
?
             :
  1:  R² = 0.70
  2:   +    R² = 0.71
2.
       
                
     
 
   
 
      
 ()
   :
  
    
       '         
  '    
  
     
 
  :
:
  
R² = 0.65   R² = 0.64
  :
:


2.
  
   
R² = 0.68   R² = 0.63
:
 (0.65 → 0.68)
  (0.64 → 0.63)
:
󷷑󷷒󷷓󷷔        

󷷑󷷒󷷓󷷔    
   
     '  
1.  
²:
         
  R²:
              
2.    
²:
       
  R²:
    
3.      
²:
    
 
2.
  R²:
      
4.   
²:
-           

  R²:
     
5.  
²:
   
  R²:
      
  

    (R²)
 

%   
  

0  1
1     
   
  
  
   
 

  
 

 
 


 :  
  
     :
    
  
 
     
 
2.
   
         
:
 A: 90/100 ( )  B: 85/100 (  )
     A    -       B  
 :
R² =  
  R² =  
      
    :
 
      
  
    :
 
   
 
   
   (R²)             
                  

,      
  
      
    -       ,     
  ( R²)  ,          
    
2.
(b) X  Y                     
:
     5     '   :
 
60
90
110
125
150
170
180
200
220
230

100
150
200
250
300
350
400
450
500
550
:󷋇󷋈󷋉󷋊󷋋󷋌 1:  

 
100
60
150
90
200
110
250
125
300
150
350
170
400
180
450
200
500
220
550
230
  n = 10  
󷊨󷊩 2:   








󷙣󷙤󷙥  3:     β₁ ( )
 :
󰇛
󰇜󰇛
󰇜
󰇛
󰇜
2.
  :

󷈷󷈸󷈹󷈺󷈻󷈼 4: β₀     ()
󰇛󰇜󰇛󰇜 
 ,    :

󷊨󷊩 5: R²   
 :
󰇛
󰇜
󰇛
󰇜
  :

     Y  98%     ,      
󷙣󷙤󷙥  6:         
β₁ ( ) :
 :
:
 :
󰇛
󰇜
  , t-     (5%  '    ,   df = 8 
 2.306 )
 , β₁    
β₀ () :
2.
 ,     ,        ' 
  
󽆪󽆫󽆬
   :

 (0.38)   : X     , Y  0.38   
 (30.75)   :  X = 0,   Y 30.75  
 
           

  5%   '   '   
󷊨󷊩
   X  Y         
  
    ,  X Y     0.98  ,  Y 
      ,      
  - 
5.                
:󷈷󷈸󷈹󷈺󷈻󷈼     
   
            

      
 :     
-  :    
 :    
     ()     
󷷑󷷒󷷓󷷔     (     )  

     
  :
             
  

 :
2.
    ( )
   ( )
󽁔󽁕󽁖  
    
,       
   -    -   '  
󷄧󷄫  
 , 
 (  )   
   
  
        
     :
󷷑󷷒󷷓󷷔     
    :
  
  
:               

󷄧󷄬 -  -
           ,  : "
     ?"
     :
-    
-  
 
    :
         
󷷑󷷒󷷓󷷔       
2.
󷄧󷄭   (OLS    
)
OLS ( - )      :
OLS       ()  (    )
   :
OLS     
    

:
󷷑󷷒󷷓󷷔       
  
     
󷄧󷄮    

       :
        
           
: -             
󷄰󷄯    
  :
²
   
   ,        
             
󷄧󼿒     
2.
                '
      
󷄧󷄫 
       
 :

  
 
:        :  ()   ()  

 
  :
󷷑󷷒󷷓󷷔    
      
        
󷄧󷄬        (WLS)
 
      ,  
 -    
:
-   
-   
    
:
󷷑󷷒󷷓󷷔      
  WLS     
󷄧󷄭     
    :
2.
 -  
(        )
  
       
:
 -
 F-      
       
󷄧󷄮       
       
     
:             
           
:
󷷑󷷒󷷓󷷔   
󷷑󷷒󷷓󷷔    
   '  
 
󷄰󷄯    
      :
:    
:       
        
 
󷄧󷄱    
    :         
2.

?       
    
,       
 
󷘹󷘴󷘵󷘶󷘷󷘸  (    )
   
          
    
    ' -     
      ,     
      ,   , OLS
    ,   ,     
  OLS    ,         
   

              
  (    ),   -  
, -      ,   
     ,       ,    
    ,          
    
6. (a)        :


       X₂          

:󷋇󷋈󷋉󷋊󷋋󷋌  

      :


:
=  


=  
= 
2.
=  
󷊨󷊩: 
  
       
 :

                 

 :

    
  "if and are correlated"      
(exogenity)       ,     

󷙣󷙤󷙥      
        :
Cov󰇛
󰇜
Var󰇛
󰇜
         
 :
   ,  ,    

Cov󰇛
󰇜
  - ,   -       ' 
 
󷈷󷈸󷈹󷈺󷈻󷈼 
   
   (Y) '    (X1)       
  
   
  (X2)     
 
       
,    
-  
       
          ( ),  

            
                 
 
2.
    
󷊨󷊩     
 ,             :
󰇟

󰇠
 OLS     
 
󷙣󷙤󷙥   
1.    :      


2.    :         ( ,
 '      ),     
    
3.   R²:     ""  ,   
 
󽆪󽆫󽆬
      :

Cov󰇛
󰇜
Var󰇛
󰇜
      
           
 ()         '   
  :            
       ,       

()     -    -       

:1.  -   
󷊆󷊇  
  (         )      '
 :
2.
             , 
-   
  :   X₁ X₂, X₃, X₄,       ,  
        
 -   -
󼩏󼩐󼩑     (--)
       :
         :
 1:     (X₁ )
 2:    '  :

 3:     (R²)   
 4:    
󹵍󹵉󹵎󹵏󹵐
  (1  ) → X₁ X₂    '     X₃ →
-   
      - 

   :
       
      

󹵙󹵚󹵛󹵜  (   )
   
 (Y)       :
 (X₁)
2.
 (X₂)
 (X₃)
     '     
 
   '      R² = 0.95   ,  
              
         
󷄧󼿒    
   

         
  
󽆱  
     
(    
)
  (" R²")
 -   
 
   , -         
 - - 
2. -   - 
-  -          
            
    :
 1 →      
 2 →     
 3 →  
  1: -   
2.
, 
            

   -         - 
  :
󰇡

󰇢
:
n =   
k =    
|R| = -   

 χ² >  χ² → -     
 χ² ≤  χ² →       - 

    :  -   ?
  2:   
  1 -    ,  
      

   :
 X ' X₁   (   )
  
 F-:
󰇛󰇜
󰇛
󰇜󰇛
󰇜

 F    X₁     
 F   
 X₁  
2.
          
  3:    - 
 , 
t-              :


 rᵢⱼ = Xi  Xj  

  t → Xi  Xj    
  
     
  
     -    
󹵍󹵉󹵎󹵏󹵐  
           
 :
         ?”     
  
 -  :
 1:       ?  2:      ? 
3:     ?
3.  :    - 

 
 -  


 

 
3-  


χ², F, t 
    


   


2.


4.   
-       
 :
  
 
  
 
    
    
 
  -          
-         
󽆤 
     -       
     -     
 
            
         - 


 -           : 
χ² ,  F-,   t-,   -   , 
        
  ,            
      ,       
    
2.
  -
7. -    
  ? -    -    
      
:󷋇󷋈󷋉󷋊󷋋󷋌  ?
  ,         ()      -
           -       
      
  : (  )      
   
:  -     ,      
    
 :  ,        
   ,   -     
󷊨󷊩-   
?
1.     :OLS    ,     -
  

2.   :     ,   -
 -  

3.    :  , -    
   
󷙣󷙤󷙥 -  
- (DW)     -       
    
  :
󰇛


󰇜

:
=   
=   
:
2.
:  - 
:  -
:  -
  :
DW            
:  -   
:  - 
: 
 :
  
  
   DW = 1.2    
  2   , 
     -    
󷈷󷈸󷈹󷈺󷈻󷈼-   
 -    ,        :
1.      
        
      (
,  ,   )
:          
2.   
    :   , 


  -    -   
3.     (GLS)
GLS   -    ,     
4. - 
-  -       
   ()   
       
5. -  
 -   ,        
       
2.
󽆪󽆫󽆬  
, ,    -   -   '  
-      '   ,     '
-  -   
 
GLS  Cochrane-Orcutt         
 
󷊨󷊩
               ,
  OLS      -      
    ,   2      

 
     ,   , GLS   , 
       
8.()           
()          ?
:8(a)       
󷊆󷊇  :     

    ,       
        
 :
    
 ,    

    ,   -  
     ,        
           
  
    :

 :
2.


:     ,  ,  ,  '   
󷷑󷷒󷷓󷷔     
󺡜󺡝󺡞󺡟      
    ,          :
   ( )




- (    )
    
 
       
󷈷󷈸󷈹󷈺󷈻󷈼     
      
          '  
:


      -    
󷷑󷷒󷷓󷷔 :          ,  ,    

󷄧󹹯󹹰     
2.
     :



     :





 :








      
     󷘹󷘴󷘵󷘶󷘷󷘸
:
󰇛󰇜





󷘹󷘴󷘵󷘶󷘷󷘸    
      :


    
:
   X  
  Y
   
󷷑󷷒󷷓󷷔   
󹲉󹲊󹲋󹲌󹲍    
2.
  :
     '   
's 
' 
       

󽇐    
      
- 
 
   
 
 
󽁔󽁕󽁖  
    ( 
 )
  -   
    
󼩏󼩐󼩑- 
    :
      ,          
 :
   =      +   
     
8(b)          
     
2.
󷇓󷇔󷇕󷇖󷇗󷇘  :    - ?
         -     -  
:
     
   
    
 

  :
󷷑󷷒󷷓󷷔       ?
󹵍󹵉󹵎󹵏󹵐   :   
              
:
  :
   β =    β?
     :
   
    
 
  -      :
󷷑󷷒󷷓󷷔  
󷬭󷬮󷬯󷬰    ?
     0-1   
2.
:
󰇥
after reform
before reform
󼩺󼩻    

       :
󰇛󰇜
         
󹺔󹺒󹺓   
β₀ →     
β₁ →    
β₂ →      
β₃ →      
 :
   (D=0):
   (D=1):
󰇛
󰇜󰇛
󰇜
󷘹󷘴󷘵󷘶󷘷󷘸    !
󷈷󷈸󷈹󷈺󷈻󷈼          

       , 
 
 :
󷷑󷷒󷷓󷷔  
2.
  :
β₂ = 0 →  
β₃ = 0 →   
      

        
      
󽇐     
 
       
    
   
  
󷄧󼿒  
(a)         X   Y    
  ,   '      - 
 
   
        -   
()            ,    
               
                 
      
"                 
 
          ,         
 "