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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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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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