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Khong tin cy v kim nhgi thit v cc h s hi quy

Bi:

Phm Tr Cao

Khong tin cy v kim nh gi thit v cc h s hi quy

Khong tin cy cho cc h s hi quy

Thc s chng ta khng bit 2 nn ta dng c lng khng chch ca n l

Sai s chun ca h s hi quy cho dc

T

vi

ta c


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(3.14)

T tnh cht ca phng sai mu ta c

(3.15)

T (3.14) v (3.15) Ta xy dng tr thng k

(3.16)

Bin i v tri chng ta c

Thay vo (3.16) ta c

(3.17)

Chng minh tng t ta c

(3.18)

c lng khong cho h s hi quy vi mc ngha nh sau


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(3.19)

(3.20)

Kim nh gi thit v h s hi quy

Chng ta quan tm nhiu n ngha thng k dc ( 2) ca phng trnh hi quyhn l tung gc ( 1). Cho nn t y n cui chng ch yu chng ta kim nhgi thit thng k v dc.

Gi thit

Pht biu mnh xc sut

Quy tc quyt nh

Nu

hoc

th bc b H0.

Nu

th ta khng th bc b H0.


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Quy tc thc hnh-Tr thng k t trong cc phn mm kinh t lng

Trong thc t chng ta thng xt xem bin c lp X c tc ng ln bin ph thuc Y

hay khng. Vy khi thc hin hi quy chng ta k vng 2 0. Mc ngha hay c

dng trong phn tch hi quy l =5%.

Gi thit

Tr thng k tr thnh

Quy tc quyt nh

Nu

th bc b H0.

Nu

th khng th bc b H0.

Tra bng phn phi Student chng ta thy khi bc t do n trn 20 th tr thng k t97,5%th xp x 2.

Quy tc thc hnh

Nu /t-stat/ > 2 th bc b gi thit 2 = 0.

Nu /t-stat/ 2 th ta khng th bc b gi thit 2=0.


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Trong cc phn mm bng tnh c tnh ton hi quy, ngi ta mc nh mc ngha=5% v gi thit H0: i=0. Th tc tnh ton hi quy ca Excel cung cp cho ta cc hs hi quy, tr thng k t, c lng khong ca h s hi quy v gi tr p

chng 2 chng ta bit c kim nh trn c lng khong, tr thng k v gitr p l tng ng nhau..Sau y l kt qu hi quy c tnh ton bng th tc hi quy ca mt vi phn mmthng dng.

Excel

Kt qu Regresstion cho d liu ca v d 3.1. (Ch trch phn h s hi quy)

Intercept: Tung gc

Coefficients : H s hi quy

Standard Error : Sai s chun ca c lng h s

t Stat : Tr thng k t(n-2)

P-value : Gi tr p

Lower95%: Gi tr ti hn di ca khong c lng vi tin cy 95%.

Upper95% : Gi tr ti hn trn ca khong c lng vi tin cy 95%.

Bc b H0 khi /t-stat/ > 2 hoc p-value < 0,05 hoc khong (Lower;Upper) khng cha0.

Nh trnh by chng 2, y thc ra l 3 cch din t t mt mnh xc sutnn kt lun t 3 tr thng k t, p v c lng khong l tng ng nhau.

Eviews

Th tc Make Equation cho kt qu nh sau(ch trch phn h s hi quy):


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C : Tung gc

Coefficient : H s hi quy

Std. Error : Sai s chun ca c lng h s

t Statistic : Tr thng k t(n-2)

Prob: Gi tr p.Bc b H0 khi /t-Statistic/ > 2 hoc Prob < 0,05.

SPSS

Th tc Regression->Linear. (Ch trch phn h s hi quy).

Constant: Tung gc

Unstandardized Coefficients: Cc h s hi quy

Standardized Coefficients: Cc h s hi quy chun ho

Khi nim ny nm ngoi khun kh ca gio trnh..

t: t-StatSig: Gi tr p.


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Bc b H0 khi /t/ >2 hoc Sig < 0,05

nh l Gauss-Markov

Vi cc gi nh ca m hnh hi quy tuyn tnh c in, hm hi quy tuyn tnh theophng php bnh phng ti thiu l c lng tuyn tnh khng thin lch tt nht.

Chng ta s khng chng minh inh l ny.

Phn chng minh cc tnh cht phn ny c Gujarati, Basic Econometrics-3rd

Edition, trang 97-98.

thch hp ca hm hi quy R 2

Lm th no chng ta o lng mc ph hp ca hm hi quy tm c cho d liumu. Thc o ph hp ca m hnh i vi d liu l R2. c ci nhn trc quanv R2, chng ta xem xt th sau

Hnh 3.5. Phn tch thch hp ca hi quy

Yi Y : bin thin ca bin ph thuc Y, o lng lch ca gi tr Yi so vi gi trtrung bnh Y .


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Y i Y : bin thin ca Y c gii thch bi hm hi quy

ei = Yi Y i: bin thin ca Y khng gii thch c bi hm hi quy hay sai s hi quy.

Trn mi Xi chng ta k vng ei nh nht, hay phn ln bin thin ca bin ph thucc gii thch bi bin c lp. Nhng mt hm hi quy tt phi c tnh cht mangtnh tng qut hn. Trong hi quy tuyn tnh c in, ngi ta chn tnh cht tng bnhphng bin thin khng gii thch c l nh nht.

Ta c

Vi yi = Yi Y v y i = Y Y

Vy

(3.21)

S hng cui cng ca (3.21) bng 0.

Vy

t

TSS(Total Sum of Squares): Tng bnh phng bin thin ca Y.

ESS(Explained Sum of Squares): Tng bnh phng phn bin thin gii thch cbng hm hi quy ca Y.


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RSS(Residual Sum of Squares) : Tng bnh phng phn bin thin khng gii thchc bng hm hi quy ca Y hay tng bnh phng phn d.Ta c:

TSS = ESS + RSS

t

Mt khc ta c

Vy

(3.22)

Vy i vi hi quy hai bin R2 l bnh phng ca h s tng quan.

Tnh cht ca R2

0 R2 1. Vi R2=0 th hin X v Y c lp thng k. R2 =1 th hin X v Y ph thuctuyn tnh hon ho.


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R2 khng xt n quan h nhn qu.

D bo bng m hnh hi quy hai bin

Da trn X0 xc nh chng ta d bo Y0.

c lng im cho Y0 l :

.

c lng khong chng ta phi tm phn phi xc sut ca Y i.

D bo gi tr trung bnh

T

Suy ra

(3.23)

Thay biu thc ca

mc 3.3.4 vo (3.23) v rt gn

D bo gi tr c th ca Y0


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T

Ta c

v

(3.25)

S hng cui cng

. Vy

(3.26)

Sai s chun ca d bo

Cho gi tr ca Y0

Khong tin cy cho d bo

Y o t(n 2,1 / 2)se( Y o)

Nhn xt: X 0 cng lch ra khi gi tr trung bnh th d sai s ca d bo cng ln.Chng ta s thy r iu ny qua th sau.


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c lng khong cho Y0 trung bnhY trung bnhc lng khong cho Y0X trungbnh

Hnh 3.6. c lng khong cho Y0.


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Khong tin cy v kim nh gi thit v cc h s hi quyKhong tin cy v kim nh gi thit v cc h s hi quyKhong tin cy cho cc h s hi quyKim nh gi thit v h s hi quy