Множественная регрессия
.pdfn
ei = 0
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+ 1 "-
+ 2 :
R 2 = 1 − |
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+ +2 1 1 + 2 :
.11. $! "
& + R2y|x1 ,x2 = 0.812 1 ,
+ 1 "
R2y|x2 = 0.71897 R 2y|x3 = 0.4080 . ' 3 ! ,
1 + 8 51 1 8 !,
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(n − k) |
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$ 8 + R2(adj)y|x |
= 0.683 , R2(adj)y|x |
= 0.334 , |
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= 0.758 . '! |
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(! -
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1 1 ! 3 1:
Sb = s2 (XT X)−1 . |
(6) |
+3 " ! "
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" , 1 i ¹ j; i, j = 1, k.
$!
3 1 8 :
.12.
1 .
. 10 3 ! 8 !- ! .
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(7) |
t(γ, n − k) – + 1 : 1 &-
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3 1 ). 9 ! 1 1 -
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n–k (k – - ! ), sbp - -
+ 2 (!
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! n-k.
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1 ! , 1 1 1 1 -
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H0: R2=0,
!:
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1 ! H0 1 1 F- , !
1 F- 8: |
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F = |
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(8) |
(1- R 2 )(k - |
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1 8 ! (1, n-k).
F> F(1- g,1, n - k) , H0 +
1 1 + : 1 -
1 3 " +-
1 , + – + -
" + +.
# 1 F(1- g,1, n - k) 2 +
F*. % + " + 1 1 1 1
1 1− γ , 1
! n − k .
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H0 : bp = 0, p = 1, k
!:
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1 ! H0 + 1
1 t- &:
t p = b p . s bp
t- , !
(9)
, + 1 - ! 1 t(g, n - k) – + 1
: 1 & ! n-k.
tp > t(g, n - k) , H0 1 + :,
+ – + " + +.
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1 -
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4.4 '
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1 . , 1
+ ! - ! ! 1 , 2 1,
2 1 ! !,
! ! ! .
& + ( ) -
M{y}= Xt ×b.
+ 3 1, -
( )
y= Xt ×b + u
+ + y.
! 1 3 +
y = Xt × b. |
(10) |
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y + + . " - |
+ 1 8 8
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1 1 +:
se2 = s2XTt (XT X)−1 Xt . |
(11) |
!
1 y :
[yˆ - t(g, n - k)se , yˆ + t(g, n - k)se ], |
(12) |
se – 8 ( -
1) , se = s2e ; t(g, n - k) – + 1 : 1 1 & ! n-k.
, 1 y + (10)
8 1 1 +:
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= s |
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−1 |
Xt ) . |
(13) |
s |
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(1 + Xt |
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! +-
1 y :
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[yˆ − t(γ, n − k)se , yˆ + t(γ, n − k)se ], |
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(14) |
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1 8 1 . ,
! + 1
8 1. 7 ,
1 , -
+ 1.
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$1 8 + +. # +
x2 + ! . 1 -
+ :
.13. ( 1 .
, + (10) -
y 1 3 !
( , ! + !). , " + , 1,
+ 1 3 :
.14. $!
3 1 .
+ , 1, -
+ 1 + 3 :
.15. $!
+ ! .
( 1 1 1 !
! 1 -
3 1 + !
! 1 + 2 :
.16. ( 1 !
1 1 x 3 .
% ! 3 y
! -
x 3 1 2 1 x 2 .
.17. ( 1 !
1 1 x 2 .