магистры Эконометр мод-е / из эконометрики / Лекция2-4-корреляц анализ
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rxy
! " #
% &
S
r(y, x1, . . . , xm) = 1 − Sy ,
Sy ! ' ( S !
) & * + ,
+( #
-
& r(y, x1, . . . , xm)≥r(y, xj ) .j = 1, . . . , m/ 0
' 1
' (
'
#
r&
r(y, x1, . . . , xm) = |
1 − r11 , |
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r |
r =
r(y, x1) |
1 1 |
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r(x1, x2) . . . r(x1, xm) , |
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r(y, x |
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r(y, x2) . . . r(y, xm) |
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r(y, x |
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) r(x |
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r11 |
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. . . |
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r(x |
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2 r11 ( r
. ' /
2 r11
3 (
(
% ( # y=β0+β1x1+β2x2+ε
1 |
2 |
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r2 |
(y, x1) + r2 |
1 − r2(x1, x2) |
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r(y, x |
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) = |
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(y, x2) − 2r(y, x1)r(y, x2)r(x1 |
, x2) |
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% . / (
'
-
%
(
y xj ( -(
( ( (
( (
# 0 4
4 ( # 5
#
#
6 )
(
y = β0 + x1β1 + x2β2 + ε.
%- ! y ( ( x1
x2
+ " ' y x2 yˆ(x2)=αˆ1+αˆ2x2 7 6 S2(y, x2)= (yi − yˆ(xi2))2
8 x1
yˆ(x1, x2)=ˆγ0+ˆγ1x1+ˆγ2x2
9 6 S2(y, x1, x2)= (yi − yˆ(xi1, xi2))2
: ; x1 '
S2(y, x2)−S2(y, x1, x2) 4, 4 x1
y
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S2(y, x2) |
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r(y, x |
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x |
) = |
S2 |
(y, x2)−S2(y, x1 |
, x2) |
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.+/ |
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< y
xj '
xj
S2
= .R2=1 − S2 /
y
.+/
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1| 2 |
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− |
1 − r2(y, x2) |
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r(y, x |
x |
) = 1 |
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1 − R2(y, x1, x2) |
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0 ( ' (
' &
r(y, x |
1| |
x |
) = |
r(y, x1) − r(y, x2)r(x1, x2) |
. |
.7/ |
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1 − r2(x1, x2) 1 − r2(y, x2) |
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% )
- ( ( . /
# ( # #
< m
yi = b0 + b1xi1 + · · · + bmxim + εi
y xj
1 − R2(y, x1, . . . , xj , . . . , xm) r(y, xj |x1, . . . , xj−1, xj+1, . . . , xm) = 1 − 1 − R2(y, x1, . . . , xj−1, xj+1, . . . , xm) ,
R2(y, x1, . . . , xj , . . . , xm) ! m
( R2(y, x1, . . . , xj−1, xj+1, . . . , xm) !
xj m−1
? #
#
r(y, x |
j | |
x |
, . . . , x |
j−1 |
, x |
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, . . . , x |
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) = |
r(y, xj |x1, . . . , xm−1) − r(y, xm|x1, . . . , xm−1)r(xj , xm|x1, . . . , xm−1) |
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(1 − r2(y, xm|x1, . . . , xm−1))(1 − r2(xj , xm|x1, . . . , xm−1)) |
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. xj / % (
y x1 # # x2( x3 &
r(y, x |
1| |
x |
, x |
) = |
r(y, x1|x2) − r(y, x3|x2)r(x1, x3|x2) |
. |
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2 |
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1 − r2 |
(y, x3|x2)(1 − r2(x1, x3|x2)) |
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t |
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H0& r=0 6 & |
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√ |
r |
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√ |
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t = |
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n − l − 2 |
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1− r2
n ! ( l ! #
t = tα(n − l − 2) 1 t < t ( α
.H0/(
=' # '
( ' # ( - -
% # ( -
# . # #/(
(
# ' -
& (
"- # ( '
0 @ ' # # X % -
. / ( ' -
y
- # - % #( (
- #( 3'
xs( - -
; F
F .
( / 1 F <F ( xs
- #
' # # 3' xp -
. AB CC # /
F
F 1 F >F ( xp
" F < F - # (
#
)
F &
Fxj = |
Ryx2 |
1...xj ...xk − Ryx2 |
1...xj−1xj+1 |
...xk |
· (n − m). |
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1 − Ryx2 |
1...xj ...xk |
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= F F =Fα(1, n−m)(
xj ( F <F
? ( -#
% -