Easy2Siksha.com
   2021
/  
  VI
 : 3   :100
:               
   
I.   ,      
II     ?     ,     
   
X
4
6
10
8
12
16
18
Y
6
8
4
6
8
10
III.      
IV.            :
:
65, 57, 57, 54, 66
  :
26, 13, 16, −7, 27
Y = α + βX            , 5%
     β ≠ 0   β = 0     
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V.       ?      
?
VI.       ,     ?
VII.     ?           
 
VIII. -      ,       
Easy2Siksha.com
   2021
/  
  VI
 : 3   :100
:               
   
I.    ,      
: 
          ,        
                 
  ?   ,           
       ?       
             
  ,            
 ,             
  ,           
     ,          
   
   " "            
      :
1. ,     
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         ,        
  
     ,  "   ,   "
           
             
  
  ,               ,
               
2.    
            ( )
   ,      ,          
 
          "    
     "   ,          
  
3.    
   ,      ,  
    
  :  = 5000 + 0.8 ( )
               
     
4. 
      
            ,  
         ,        
          
   ,          
   
5.  
                
   ,            
     
Easy2Siksha.com
      ,           
 
  
""               
             
1.    
                
   
  ,          ,    
               
2.  
           
        ?
        ?
      ?
             
  
3.  
             
  :
     
    
    
     
        ,          
         
4.   
Easy2Siksha.com
,       ,          
      
           :
        ?
     ?
      ?
            
5.  
          
           :
 
   
  
   
  ,              
     
6.    
    ,    ,       
      
 ,                
    
7.  
             ,  ,
            
     ,       
      
  
Easy2Siksha.com
    ,        ,  
 
1.     
                ,  
 ,    
   : "   "       
2.      
      ,     
  ,  ,            
        
3.    
   ,      ,   
         
  ,              
   
4.     
               ,
     
            
5.  -      
          ,       
     
  ,             , 
            
6.
  
              ,    
         
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,        
7.     
             
,       
,  -    

          -    
     ,     ,
           
  ,        ,   ,
 , ,      ,   
            ,    
    
  -  ,          
  ,          ,
           
II.      ?     ,     
    
X
4
6
10
8
12
16
18
Y
6
8
4
6
8
10
:       
                
          ,        
   ()   
1.      ?
          :
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o   (X):
o   (Y):         
  
       :
:
=   (Y    X = 0)
=  (X       Y  )
=   ( X         )
󷷑󷷒󷷓󷷔  :       "- "  ,    
Y, X    
2.    () 
         
              
 ()    ()     :
󰇛
󰇜󰇛
󰇜
󰇛
󰇜
3.   


󷷑󷷒󷷓󷷔  : X  7    Y   6           
,  (X, Y)                   
     :
󰇛
󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛
󰇜
4. --  
a)    





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b)  ()     
󰇛
󰇜󰇛
󰇜
X

4
-5.33
-1
5.33
6
-3.33
1
-3.33
10
0.67
-3
-2.00
8
-1.33
-1
1.33
12
2.67
1
2.67
16
6.67
3
20.00
Sum 
)        ()
󰇛
󰇜
X

4
-5.33
28.44
6
-3.33
11.11
10
0.67
0.44
8
-1.33
1.78
12
2.67
7.11
16
6.67
44.44
Sum 
)      



󰇛󰇜
5.   

󷷑󷷒󷷓󷷔:
,  
X   1     , Y  0.26    
6.    
:  X   Y       
  :    X, Y     
 :,       

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                
          
   ,      :

󷷑󷷒󷷓󷷔  :     Y  4.6       X     -
( 0.26 ) 
III.      
: -     
          ,     
        -     
                
()          
               
󷄧󼿒-   ? ()
-    :
        ,    ()
     
    ,     (BLUE)
        :
     (   )  
      
,       
           
          :
󷷑󷷒󷷓󷷔    ,       OLS     
       
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󷄧󼿒    ?
                 
        
              ,  -
     :
󷷑󷷒󷷓󷷔           
            
 
󷄧󼿒-   
    ,           
     
1.  
       

:
=  
=  
= 
=  
2.    
󰇛󰇜
        ,   
   
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3.   ()
󰇛󰇜
          
                   
4.   
      
  ,           
5.     
         
  ,              
󷄧󼿒   
OLS      :
󰆹
󰇛
󰆒
󰇜

󰆒
          -        
    
󷄧󼿒-   
          
  :
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󷷑󷷒󷷓󷷔 
󷷑󷷒󷷓󷷔     
        
 1:     
󰆹
󰇛
󰆒
󰇜

󰆒
      :
󰇛
󰆹
󰇜
  
 2:        
     :

 C   
    :
󰇛
󰇜
  :

(   )
 3:     
        :
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󰆹

       :

(     )
 4:    
  :
󰇛
󰆹
󰇜
󰇛
󰆒
󰇜

   :
󰇛
󰇜󰇛
󰆹
󰇜
      :
󰇛
󰇜󰇛
󰆹
󰇜󰇛󰇜
   -   :
󰇛󰇜
,
󰇛
󰇜󰇛
󰆹
󰇜
󽇐   
   :
  
              
        OLS    
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  :
     ()
󷄧󼿒         
󷄧󼿒   
                 
              () 
   
          
     ,       -  
󷷑󷷒󷷓󷷔      
-      
󷄧󼿒    
(  )
          ,       
 :
󷷑󷷒󷷓󷷔:  
󷷑󷷒󷷓󷷔:  ,   ,  ,    ,    

󷷑󷷒󷷓󷷔  :            

           
󷄧󼿒 
     -           
󽆱   
     :
Easy2Siksha.com
󷷑󷷒󷷓󷷔 +  
        -        
󷄧󼿒         ?
          :
 

    
 
         ,  :
󷷑󷷒󷷓󷷔  -     
󷄧󼿒 
-               
  
             ,    
       
           ,    -   
-                    
IV.            :
:
65, 57, 57, 54, 66
  :
26, 13, 16, −7, 27
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Y = α + βX            , 5%
     β ≠ 0   β = 0     
:           
          :
1.      
2.            
3.   ()       
,   -       
1. R²    
R² ( ):
o       (Y)           (X)
   
o :




: - SSR =      - SSE =      - SST =    
 R²:
o          
o       -   
o :
Adjusted
󰇧
󰇛
󰇜󰇛
󰇜
󰇨
: - =    - =    
󷷑󷷒󷷓󷷔  :
          
                
     
2.   
  (X = ):65, 57, 57, 54, 66
  (Y =   ):26, 13, 16, -7, 27
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    :

3. --  
a)    



󰇛󰇜


b)     ()
󰇛
󰇜󰇛
󰇜
󰇛
󰇜
X

65
5.2
11
57.2
57
-2.8
-2
5.6
57
-2.8
1
-2.8
54
-5.8
-22
127.6
66
6.2
12
74.4
󰇛
󰇜󰇛
󰇜
󰇛
󰇜
󰇛
󰇛󰇜
󰇛󰇜
󰇛󰇜

󰇜




)     ()
󰇛󰇜
)  

4. R²   


 1:  Y          ,
:
󰇛󰇜
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(   X     )
 2:  ( )   
󰇛
󰇜
 3:  ( )   
󰇛
󰇜
 4:  =  - 
 ,

󷷑󷷒󷷓󷷔            
5. 
       (k = 1)  n = 5   ,
Adjusted
󰇧
󰇛
󰇜󰇛
󰇜
󰇨
        
6.  
   :
 (): (   )
  ():
 :
󰆹
󰇛
󰆹
󰇜
     󰇛
󰆹
󰇜
 t-    (5%       )   ,
 
  ≈ 3.182.
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     ,    - (    )  
   ,            

            
           
    :

            ,     
     
󷷑󷷒󷷓󷷔  :      ,      ,
               
V.       ?    
  ?
:      :    
  ,            
            (  
    )       (   
)          ,     
     ,          
,       ,     
              ,  
                  
  ?
                 
       ,          
 
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                
         (  -  ),   
                
               
               
               :
   ( )
  
  
    -                
      ,         
       
    ?
  ,             
                
1.   
       ,         
         
  ,              
 ,       ,        
           
2.       
               
       
             ,    
        ,       ,  -
    
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3.   
                
     ,           
    
          ,   
 
4.    
-          ,     
    ,           
    
5.      
           ,  
            ,   
      
      
        ,    
                 
  
1.  
                
  +1  -1   ,     
   , 0.8  0.9        
,                 
      
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2.    ()
  ,          ,  
   
               
 :
VIF = 1 →    
VIF 1  5    
VIF 5   (    10  ) →   
               
3.  
, VIF   
:
 = 1 / VIF
   (0.1  0.2  )      
4.   
          
30           
            
     ,   
    
        ,         ,
       
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1.        
      ,          
  , "  "  "  "      , 
            
          
2.    
-            
  :
          
       
         
3.    
                
                
4.    
          ,   (  ) 
     
         ,       
5.      
         :
 :          
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 :       ,       
 
   ():       
            

                
     ,         
  ,     ,     ,
    
 ,        , ,  
              
      ,   ,   ,
              
    ,            
                 , 
    -      
VI.      ,     ?
:    
       ,         ( ) 
            (   ) 
           X       
  (  )            ,
       
1.   
              
     :
    :          
       
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- :    ,        
,           
 :           
   :          
         
  :          
 -   
󷷑󷷒󷷓󷷔  :         ""        
     
2.   
        ,    
 
   :        ,
      (      )
  :      ,   -
     
  :      ,   (
    )     
   :    ,  X    
     
󷷑󷷒󷷓󷷔  :        ,     
    
3.    
          :
a)  
           
          ,     
b) - 
            
:  ( )
      ,     
)   
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              
    /-         
)  - 
          
     ,   
)  / 
          
    
4.   
    ,      ,      :
:          
  :-       (  ,
   )
   ():       

5.  



 , - ,  ,  

   ,   ,  

 , -, ,   -,  /

 ,  ,   

        
  ,            
          
     -,     -  
       
  ,       
󷷑󷷒󷷓󷷔  :       ,     
              
 
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VII.    ?         
  
:           
                  , 
         ,      
         
󷈷󷈸󷈹󷈺󷈻󷈼        
               ?
  -             
               
   
              ,     
         
󷄧󼿒    ?
   (DLM)            ( ) 
      ( )       ,  
      
  :
   =      +       +  
     + ...
  ,             ()   
      ,        
  
           
󷄧󼿒  ?' ?
    ..         
     
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      ,            
         
󹵋󹵉󹵌    :
      
      
   -      
  :
 
  
 
100%
 
60%
 
36%
 
21.6%
      
󷄧󼿒     '
          -    , 
            :
󷷑󷷒󷷓󷷔  
󷷑󷷒󷷓󷷔  
  :
Yₜ = βXₜ + βλXₜ₋₁ + βλ²Xₜ₋₂ + ...
       :
Yₜ = α + βXₜ + λYₜ₋₁ + uₜ
              
󷄧󼿒  ?'   ?
       
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󽇐1.     
     ,  10, 20,        
       
        
󽇐2.     
           ,      
(     )
      
󽇐3.     
               
:               
      ,     
          
󽇐4.      
          -    
   :
    
     
         
           
󽁔󽁕󽁖     '   
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      ,      
         
  -  
󽆶󽆷1.  
    
       (Yₜ₋₁)  ,      
   
󷷑󷷒󷷓󷷔            
:
 (  )      
    ,       
󽆶󽆷2.        
           
        
-:
        
      
   
  :               
        
        
󽆶󽆷3.         
   ,   :
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     ?
       ?
      ,          
󷷑󷷒󷷓󷷔    
󽆶󽆷4.       )
λ               
 λ 1         
 λ        
λ                

󽆶󽆷5.   
     ,           ,
      
         
󽆶󽆷6.   
            
     ?
      ,   
󷄧󼿒
   ,          
        -   ,  
    
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 :
󷷑󷷒󷷓󷷔             
󷷑󷷒󷷓󷷔    
󷷑󷷒󷷓󷷔    
󷷑󷷒󷷓󷷔     
,        :
    
     
    
󷈷󷈸󷈹󷈺󷈻󷈼 
                  
             
   ,              
              
VIII.-    ,       
:  ?
   (       )         
 ()            
   ,               
         ,         
        ,        , 
             ""  

  ,              - 
  ,         , 
  ( -  -)   
   ()
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                 , 
      
1.  
-,           ,     
    
  ,                ,
                
      ,        - 
   
2.   
           ,   
  ,              
 ,           
3. -  ( )
            
   :
 
  
 
                   
  
4.       
        (        ),   
       ,      
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5.  
          -     ,  
          
6.    
     , ,  ,     
 ,     -  
      
          ,   
              
 
1. -  ( )
- ()            

    :
      
DW  0  4     :
 2 →   
0     
4    
:
            , DW  0  
,        
:
   
     
     
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 :
  -        
          
2.  
    
    :
            
     (   )       
 
        ,        
3. - 
       
   ?
-       
          
   ,        -    
  
4. 
           
    (+  )         ,    
 
    ?
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   ,           

   :
󷄧󼿒      
󽆱    
󽆱      
󽆱    
󽆱   
    ,              
 
    
              
   
1.   
          ,     
  :
    
   
    
       
2.    
-,      
    :

  :
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ₜ₋₁
       
  -    
3.     
        
  :
 
- 
  
           
4.    ()    
      ,     ()  
    
            , 
      
5. - 
                 
 
             
  
          ,    
    
6.    
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-               
     
   
           :
 :
                
 :
               
      

                  
           ,   
          
     ,   , - ,   
    ,    - , -
,             
       ,    ,   , 
   ,          -  
          
    ,              
        ,      
  ,             
      
              
       ,      