da cong tuyen trong kinh te luong
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8/12/2019 Da Cong Tuyen Trong Kinh Te Luong
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I. Bn cht ca a cng tuyna cng tuyn l tn ti mi quan h
tuyn tnh gia mt s hoc tt ccc bin c lp trong m hnh.Xt hm hi qui k bin :
Yi = 1+ 2X2i + + kXki + Ui-Nu tn ti cc s 2, 3,,kkhng
ng thi bng 0 sao cho :
Chng 6
a cng tuyn
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2X2i + 3X3i ++ kXki + a = 0
(a : hng s)Th gia cc bin c lp xy ra hintng a cng tuyn hon ho.
-Nu tn ti cc s 2, 3,,kkhngng thi bng 0 sao cho :
2X2i + 3X3i ++ kXki + Vi = 0
(Vi : sai s ngu nhin)
Th gia cc bin c lp xy ra hin
tng a cng tuyn khng hon ho.
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Ta c : X3i = 5X2i c hin tng cngtuyn hon ho gia X2 v X3 v r23 =1
X4i = 5X2i + Vi c hin tngcng tuyn khng hon ho gia X2 vX3 , c th tnh c r24 = 0.9959.
X2 10 15 18 24 30
X3 50 75 90 120 150
X4 52 75 97 129 152
V d : Yi = 1+2X2i+3X3i+ 4X4i + UiVi s liu ca cc bin c lp :
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II. c lng trong trng hp c acng tuyn
1.Trng hp c a cng tuyn hon hoXt m hnh :Yi = 1+2X2i+3X3i+ Ui (1)
Gi s : X3i = X2i
x3i = x2i. Theo OLS:
2
3i2i
2
3i
2
2i
i2i3i2i
2
2ii3i
2
3i2i
2
3i
2
2i
i3i3i2i
2
3ii2i
)xx(xx
yxxxxyx)xx(xx
yxxxxyx
3
2
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Tuy nhin nu thay X3i = X2i vo hmhi qui (1), ta c :
Yi = 1+2X2i+3 X2i + Ui
Hay Yi = 1+ (2+ 3) X2i + Ui (2)
c lng (2), ta c :
00
)(
))(()(
22
2
2
22
2i
2
2i
2
2i
i2i
2
2i
2
2ii2i
)x(xxyxxxyx
0
0
3
3201
,
Thay x3i = 2x2i vo cng thc :
Tng t :
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Tm li, khi c a cng tuyn honho th khng th c lng c cc
h s trong m hnh m ch c th clng c mt t hp tuyn tnh cacc h s .
2. Trng hp c a cng tuyn khnghon ho
Thc hin tng t nh trong trng hp
c a cng tuyn hon ho nhng viX3i = X2i +Vi Vn c th clng c cc h s trong m hnh.
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III. Hu qu ca a cng tuyn
1. Phng sai v hip phng sai ca ccc lng OLS ln.
2. Khong tin cy rng hn3. Thng k t nh nn tng kh nng cch s c lng khng c ngha
4. R2 cao nhng thng k t nh.5. Du ca cc c lng c th sai.
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6. Cc c lng OLS v sai s chun
ca chng tr nn rt nhy vi nhngthay i nh trong d liu.
7. Thm vo hay bt i cc bin cngtuyn vi cc bin khc, m hnh sthay i v du hoc ln ca ccc lng.
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8/12/2019 Da Cong Tuyen Trong Kinh Te Luong
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Xt : Yi = 1+2X2i+3X3i+ 4X4i + UiCch s dng m hnh hi qui ph nh sau :- Hi qui mi bin c lp theo cc bin c
lp cn li. Tnh R2 cho mi hi qui ph :22R23R
24R
4...2j0R2j
Hi qui X2i = 1+2X3i+3X4i+u2i Hi qui X3i = 1+ 2X2i+ 3X4i+u3i Hi qui X4i = 1+ 2X2i+ 3X3i+u4i
- Kim nh cc gi thitH0 :
-Nu chp nhn cc gi thit trn th khng
c a cng tuyn gia cc bin c lp.
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