5 Da cong tuyen

8/3/2019 5 Da cong tuyen

1/34

Econometrics

Chng 5A CNG TUYN

(Multicollinearity)Ths. Trn Vn Hong


2/34

E

conometrics

Ths. Tran Van Hoang

NI DUNG

1. Bn cht ca a cng tuyn2. c lng OLS khi c a cng tuyn

3. Hu qu ca a cng tuyn

4. Pht hin s tn ti ca a cng tuyn.

5. Bin php khc phc.


3/34

E

conometrics

Ths. Tran Van Hoang

Trong m hnh hi quy bi, gi thuyt cc bin giithch (Xi) ca m hnh khng c tng quan vi nhau.Nu gi thuyt ny b vi phm th s c hin tng acng tuyn

Nh vy , a cng tuyn l hin tng cc bin c lptrong m hnh ph thuc ln nhau v th hin c didng hm sV d: Y: Nhu cu go

X1: Gi goX2: Thu nhp ngi nng dn

1. Bn cht a cng tuyn


4/34

E

conometrics

Ths. Tran Van Hoang

a cng tuyn hoan hoxy ra khi gia cc bin clp c mi quan h chnh xc theo dng

2 2 3 3... 0

k ka X a X a X + + + =

1 2 2 3 3...

i i i k ki iY X X X U

Xt m hnh hi quy tuyn tnh k bin vi hm PRF :

a cng tuyn khng hon hoxy ra khi gia cc

bin c lp c mi quan h theo dng

2 2 3 3... 0

k ka X a X a X V + + + + =



5/34

E

conometrics

Ths. Tran Van Hoang

V d acngtuyn hon ho:

X2 X3 X410 50 52

15 75 52

18 90 97

24 120 129

11 55 63

X3 = 5X2 => Trnghp ny c acngtuyn hon ho

X4 = 5X2 + v => acngtuyn khng hon ho



6/34

E

conometrics

Vd:

Chi tiu (Y)

Thu nhp (X2)

S giu c (X3)

Thu nhp v s giu c l hai bin thng c

tng quan rt cao, nn d pht sinh hintngacngtuyngia cc bin ny.



7/34

E

conometrics

- Phng php thu thpsliu: mu khng

ctrng cho tngth- Do bnchtcami quan hgia cc bin ngm cha hin tng a cng tuyn, v

dnhgiabin thu nhp v s giu c.- c trngca m hnh: khi b sung nhngbin c lythabc cao vo m hnh, cbit

khi phm vi dliucabinclp l nh.- Mt m hnh xc nh qu mc: sbingiithch nhiuhncmu

Nguon goc cua a cong tuyen


8/34

E

conometrics

Ths. Tran Van Hoang

Khi c acngtuyn hon hoXt vd hm hi quy tuyn tnh 3bin

iiiiUXXY

33221

V gis c acngtuyn hon ho : X3i=aX2i

2322322

332232

2

iiii

iiiiiii

xxxx

xyxxxxyTa c :

V : X3i=aX2i

0

02

22

2

2

22

2

232

2

2

2

2

2

iiii

iiiiiii

xxaxax

xyaxxaxaxy

2. c lng OLS khi c a cng tuyn


9/34

E

conometrics

Ths. Tran Van Hoang

Nh vy trong trng hp a cng tuyn hon hoth s khng xy dng c m hnh hi quy

y l dng v nh => Vy khng xc nhc 2

Tngt => Vy khng xc nhc 3


Khi c acngtuyn hon ho


10/34

E

conometrics

Ths. Tran Van Hoang

Vnc lngc cc tham s v xy dngc m hnh hi quy nhng hy xt n huqu ca a cng tuyn khng hon ho trong

ccphntip theo


Khi c acngtuyn khng hon ho


11/34

E

conometrics

3.1. nhhngn chnh xc ca cc clng

Phng sai v hipphng sai ca cc clng:

Phng sai v hipphng sai gia cc c lng

tinti v r tinn 1. Khong tin cyca cc c

lngrnghn, hay c ngha l gi tr cc c lng

thay inhiu tmu ny sang mu khc mc

chnh xc ca cc clnggim.

2

23

2

2

2

21

1)var(

rx i

2

23

2

3

2

31

1)var(

rx i

23

2

2

2

23

2

23

32)1()

,

cov(

ii xxr

r



12/34

E

conometrics

3.2. nh hngnkim nh cc hs hi quy

Khi kimnhgithuyt:

Ta sdngtrsthng k

Khi a cngtuyn, phng sai ca cc hsclngln, sai schunln gi trthng k nh,

dnnvic chng ta c xu hngchpnhngi

thuyt khngthng c xu hng cho rnghs

hi quy c nghathng k.

*0 : jjH

)(

*

j

jj

set



13/34

E

conometrics

3.3.Hs R2 cao nhng t t c ngha

Khi acngtuyn, ta c xu hngchpnhn cc

githuyt H0i = 0 vhshi quy

Ngcli, hs xc nh R2 cao, nn bngkim

nh F, chng ta c th bc bgithuyt H0i = 0

Mu thun ny l mt tn hiucahin tngacngtuyn.



14/34

E

conometrics

3.4. Duca cc hshi quy c th sai


Xem ktquclng hm tiu dng: Y = 24.77 + 0.94X2 - 0.04X3

R2=0.96, F = 92.40

X2 : thu nhpX3 : caciR2 rt cao gii thch 96% binica hm

tiu dng.

Sai st :C mtbin sai du.Bin thu nhp v cacitng quan rtmnhvi nhau do khng th no c lngc tc ng bin chnh xccho thu nhphoccaci ln tiu dng


15/34

E

conometrics

H s xc nh R2 cao (R2>0.8), m tr s t thp

Tng quan cp gia cc bin gii thch cao

Phng php hi quy ph

Nhn t phng i phng sai VIF

Xem xt tng quan ring

o Theil

4. Nhan biet a cong tuyen


16/34

E

conometrics

-Khi h s xc nh cao, th thng gi thuyt v

cc hshi quy bng 0 b bc bthanhn t

nhtmthshi quy ring khc 0.

-Tuy nhin trs |t| thp c xu hngchpnhnhshi quy ring bng 0.

-Khi c hin tngnghch l ny xy ra nguyn

nhn l do c acngtuyn. Tuy nhin quy tc ny

ch thhin r khi c hin tngacng tuyn

mc cao.

4.1. H s R2 cao (R2>0.8), tr s t thp


17/34

E

conometrics

Nu hstng quan cpgia cc binclp cao

(>0.8), th c khnngtntihintngacngtuyn.

Tuy nhin tiu chun ny thng khng chnh xc

V d: X1 = (1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0)X2= (0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0)

X3= (1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0)

Hstng quan gia cc cp: r12= -0.333, r13=r23= 0.59

khng cao, nhng X1 + X2= X3acngtuyn hon ho

4.2. Tng quan cp gia cc bin Xi cao


18/34

E

conometrics

4.3. Phng php hi quy ph

Thc hin hi quy mt bin X no theo ccbin cn li, tnh R2 v F cho m hnh

Thc hin kim nh gi thuyt H0 : R2= 0, nugi thuyt Ho c chp nhn th khng c a

cng tuyn

)1)(1(

)(

2

2

kR

knRF

Nh t h i h i


19/34

E

conometrics

Nu c cng tuyn th VIF => v cc

Nu khng c cng tuyn th VIF = 1

Phng sai ca cc c lng trong m hnh hi

quy hai bin c lp:

21

1

jj RVIF

j

jijji

j VIFxRx

2

2

22

2

1

1)var(

4.4. Nhn t phng i phng saiVIF Variance inflation factor


20/34

E

conometrics

o Theil

Trong R2l hs xc nh trong m hnh hi quy bi:

l hs xc nh trong m hnh hi quy cabin Y

ivi cc bin

Nu khng tngquan th m = 0. Cn trong cc trnghp khc th m c

thnhn gi tr m hocdngln.

1

1

222 )(k

i

iRRRm

UXXXY kk 1122110 ...

2

iR

11121,...,,,....,,

kiiXXXXX

11121 ,...,,,....,, kii XXXXX

4.5.o Theil


21/34

Econometrics

S dng thng tin tin nghim

Thu thp thm s liu hoc ly thm mu mi

B bin

S dng sai phn cp mt

5. Khac phuc a cong tuyen


22/34

Econometrics

VD: Kho st hm snxutca Cobb Douglas

Hay:

- Gis K v L c tng quan rt cao, iu ny sdn

tiphng sai rtlnca cc clng.

- Gisktqu nghin cuthcnghim no rt

ra rngnnsnxutcaquc gia ta ang nghin cu csnlng khng i theo quy m, tc l + = 1.

Utttt eKALQ tttt UKLAQ lnlnlnln

tttt UKLAQ ****

5.1. S dng thng tin tin nghim


23/34

Econometrics

Cch x l ca chng ta l thay = 1-, v thu c:

t

Gim bt s bin c lp trong m hnh. Sau khi

c lng c t m hnh, chng ta tnh

tttt UKLAQ

****

)1(

ttttt UKLAKQ )(*****

ttt UZAY ***

***

ttt KQY

***ttt KLZ

1

5.1. S dng thng tin tin nghim


24/34

Econometrics

iu ny chcchpnhn khi chi ph lymu

micchpnhn.

Ngoi ra vic tngcmu (thm s liu) cng c

th lm gim tnh nghim trngcaacngtuyn.

5.2. Thu thp thm s liu hoc ly mu mi

i


25/34

Econometrics

M hnh hi quy:

- Trong X1 v X2tng quan chtchvi nhau.

Nhiu thng tin v Y cha trong X1 th cngcha

trong X2, nhvy ta c thbmt trong hai bin

ny.

- Bng cch so snh hs xc nh v hs xc

nh iu chnh ca m hnh c hai bin, v mhnh khng c mt trong hai bin, chng ta s

quytnh nn bbin no.

UXXXY kk 1122110 ...

5.3. B bin

5 4 S d i h 1


26/34

Econometrics

Hm hi quy

Hm ngvithiim (t-1):

M hnh sai phn cp 1 c lm gimcnhnghuqu nghim trngcaacngtuyn.

tttt UXXY 22110

11,221,1101 tttt UXXY

11,221,111 )()( tttttttt UUXXXXYY

5.4. S dng sai phn cp 1


27/34

Econometrics

Vi hm athc trn, c khnngxy ra hintnga

cngtuyngia cc binclptngngvi cc bc

lytha.gimnhhngcaacngtuyn, chng

ta c thsdng hm hi quy lch theo gi tr trung

bnh:

UZZZY

UXXXY

3322110

332210

iVZZZZZZY )()()( 3332221110

5.5. Gim a cng tuyn trong hi quy a thc


28/34

Econometrics

Kho st v lng tiu dng tht g tnh theo u ngi(Y), vi thu nhp kh dng theo u ngi (X1), gi bn

l ca tht g (X2), gi bn l ca tht heo (X3), gi bn lca tht b (X4):

Variable Coefficient Std. Error t-Statistic Prob.

C 2.189792 0.155715 14.06283 0.0000LNX1 0.342555 0.083266 4.113970 0.0007LNX2 -0.504592 0.110894 -4.550212 0.0002LNX3 0.148545 0.099673 1.490334 0.1535LNX4 0.091105 0.100716 0.904568 0.3776

R-squared 0.982313 Mean dependent var 3.663887Adjusted R-squared 0.978383 S.D. dependent var 0.187659S.E. of regression 0.027591 Akaike info criterion -4.152987Sum squared resid 0.013703 Schwarz criterion -3.906140Log likelihood 52.75935 F-statistic 249.9282Durbin-Watson stat 1.826069 Prob(F-statistic) 0.000000

V d


29/34

Econometrics

Ths. Tran Van Hoang

Kho st chi tiu cho tiu dng (Y), thu nhp (X2) v quy

m ti sn (X3) ta c s liu sau :Y 70 65 90 95 110 115 120 140 155 150

X2 80 100 120 140 160 180 200 220 240 260

X3 810 1009 1273 1425 1633 1876 2052 2201 2435 2686

V du


30/34

Econometrics

Ths. Tran Van Hoang

V du

Hi quy phX2 theo X1 ta thu c kt qu sau:12 19.1054.7

XX 997.02 R ,

p-value = (0.8044) (0.0000); F=3847, p-value =0.000

Nhn thy p-value ca kim nh F rt nh,C mi quan hcng tuyn gia X2 v X1.

Nhn t phng i: VIF(X2) = 1/(1-0.997) = 482 cao

C a cng tuyn cao gia X1 v X2.


31/34

Econometrics

Ths. Tran Van Hoang

V duTin hnh hi quy Y theo X1 ta thu c kt qu sau:

1509091.045455.24 XY 962062.02 R ,

p-value = (0.0051) (0.0000); F=202.8679 ,

p-value =0.0001Cc h s hi quy c ngha thng k, h s xc nh

ca m hnh cao, p-value ca kim nh F thp chng

t m hnh hi quy ph hp.


32/34

Econometrics

Ths. Tran Van Hoang

Tin hnh hi quy Y theo X2 ta thu c kt qu sau:

2049764.041104.24 XY 956679.02 R ,

p-value = (0.0075) (0.0000); F=176.6681

p-value =0.000001

Cc h s hi quy c ngha thng k, h s xc nh

ca m hnh cao, p-value ca kim nh F thp chng

t m hnh hi quy ph hp.Tuy nhin, X2 khng c ngha thng k nhiu hn X1

m hnh hi quy ca Y theo X1 c h s xc nh cao hn

Ta chn m hnh th nht.

BI TP


33/34

Econometrics

Ths. Tran Van Hoang

Cho tiu dng (Y), thu nhp (X2) v Phc li x hi (X3)

Vit phng trnh hi quyM hnh c xy ra a cng tuyn khng

Khc phc a cng tuyn

Y 32 11 15 17 16 13 18 20 14 17

X2 36 32 16 18 17 14 20 23 15 18

X3 144 47 63 70 67 52 79 90 58 70

BI TP


34/34

Econometrics

Ths. Trn Vn Hong

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5 Da cong tuyen