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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
Khong tin cy v kim nh gi thit v cc h s hi quy
1/12
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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
Khong tin cy v kim nh gi thit v cc h s hi quy
2/12
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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.
Khong tin cy v kim nh gi thit v cc h s hi quy
3/12
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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.
Khong tin cy v kim nh gi thit v cc h s hi quy
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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):
Khong tin cy v kim nh gi thit v cc 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.
Khong tin cy v kim nh gi thit v cc h s hi quy
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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 .
Khong tin cy v kim nh gi thit v cc h s hi quy
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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.
Khong tin cy v kim nh gi thit v cc h s hi quy
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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.
Khong tin cy v kim nh gi thit v cc h s hi quy
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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
Khong tin cy v kim nh gi thit v cc h s hi quy
10/12
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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.
Khong tin cy v kim nh gi thit v cc h s hi quy
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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.
Khong tin cy v kim nh gi thit v cc h s hi quy
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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
