LOGO Ths. Phm Anh Tun Bi ging Kinh t lng LOGO Ths. Phm Anh Tun Chng 1: M hnh hi quy hai bin LOGO 1.4 Cc gi thuyt c bn ca phng php OLS i vi MHHQ c in c cc gi thit sau: Ths. Phm Anh Tun Gi thit 1: Bin gii thch X v sai s tc ng n khng tng quan, do nu X l phi ngu nhin tc gi tr c nh th s t ng tha mn iu kin trn. Gi thit 2: Gi thit k vng ca sai s tc ng hay yu t ngu nhin U l bng khng. Tc l: ( )| 0i iE U X =Gi thit 3: Phng sai bng nhau ( phng sai thun nht: Homoscedastic).Tc l ( )( )2| | ,i i j jEU X EU X i j o = = =LOGO Ths. Phm Anh Tun LOGO Ths. Phm Anh Tun Gi thit 4: Khng c s tng quan gia cc iU , tc l( ), 0,i jCov UU i j = =Gi thit 5:,i iU Xkhng tng quan vi nhau: ( ), 0i iCov UX =LOGO 1.5 Tnh cht c lng OLS Ta c mt s tnh cht nh sau: Ths. Phm Anh Tun - 1 2, | |c xc nh mt cch duy nht ng vi n cp quan st ( ),i iXY- 1 2, | |lccclngimca 1 2, | |vlccilngngunhinviccmu khc nhau chng c gi tr khc nhau - SRF i qua trung bnh mu ( ), XY- Y Y =LOGO Ths. Phm Anh Tun - 10niie== - Cc phn d ie khng tng quan vi iY :10ni iiYe== - Cc phn d iekhng tng quan vi iXtc l 10ni iie X== LOGO 1.6 chnh xc ca c lng OLS Vi cc gi thit ca PP OLS, phng sai v lch chun cacc c lng c xc nh bi: Ths. Phm Anh Tun ( ) ( ) ( ) ( )2 2221 12 2 1 12 2 221 1 11ar , , ar ,n ni ii in n nni i iii i iiX XV se V sex n x n xxo o| | | o | o= == = === = = = Trong ( )2ar ,i i iV U x X X o = = Se: sai s tiu chun (Standard Erros) 2oc c lng khng chch ca n l : 2 221 1;2 2n ni ii ie en no o= == = LOGO 1.7 ph hp ca hm HQ mu TSS:Total Sum of Squares ESS: Explained Sum of Squares RSS: Residual Sum of Squares Ths. Phm Anh Tun ( )221 1n ni ii iTSS y Y Y= == = ( )( )222 2221 1 1 1ESn n n ni i ii i i iS Y Y Y Y y x |= = = == = = = ( )221 1 n ni i ii iRSS e Y Y= == = LOGO Khi ta c : TSS=ESS+RSS v suy ra c Ths. Phm Anh Tun 22221 122 21 1ES ES1 1n ni ii in ni ii iy xS RSS S RSSrTSS TSS TSS TSSy y|= == == + = = = = 2122 222 222111niiXnYiixSnrSyn| |== = = LOGO Ths. Phm Anh Tun Trong 2 2,X YS Sl phng sai mu ca X v Y Mt khc22 1122 2 21 1 1nni ii iiin n ni i ii i ix yx yrx x y|=== = =| | |\ .= = 1 1 112 22 22 21 11 1 1 1n n nni i i ii ii i iin nn n n ni ii i i ii ii i i iX Y X Yx yrx yn X X n Y Y= = === == = = =| || | | |\ .\ .= = ((| | | | (( ||\ . \ . (( LOGO Nhn xt: Ths. Phm Anh Tun 2ro t l hay s phn trm ca ton b sai lch ca Y vi gi tr trung bnh ca chng c gii thch bng m hnh c s dng o thch hp ca hm hi quy. r chnh lhstngquanmu,tuynhinducarphthucvoquanhcngchiuhay ngc chiu gia Y v X LOGO Tnh cht: Ths. Phm Anh Tun -rcthmhocdng,ducarphthucvoducats,chnhlduca Cov(X,Y) hay l du ca h s gc -1 1 r s s- ( ) ( ), , r X Y rYX =- Nu * *aX ; X x Y bY a = + = +Nu a,b >0 th ( )( )* *, , r X Y r XY =LOGO Ths. Phm Anh Tun - Nu X,Y c lp vi nhau th ( ), 0 r X Y = . iu ngc li khng ng -rosphthuctuyntnhnhngkhngcnghatrongvicnhrtnhchtcc quan h phi tuyn - r o ph thuc tuyn tnh gia X v Y, vy khng i hi X,Y c mi quan hnhn qu - 2rcng c th tnh bng cng thc: ( )( )( ) ( )2 21 122 221 1 1 1n ni i i ii in n n ni i i ii i i iY Y Y Y y yrY Y Y Y y y= == = = = ( | | |( \ .= = LOGO 1.8 Khong tin cy v kim nh gi thuyt Ths. Phm Anh Tun Githit6: ( )20,iU N oKhiclngbnhphngnhnht 21 2, , | | octnh cht sau: - Chng l c lng khng chch - C phng sai cc tiu - Khi s quan st ln th cc c lng ny xp x vi gi tr thc ca phn b - ( )( )1122 21 1, 0,1 N Z N||| || | oo=- ( )( )2222 22 2, 0,1 N Z N||| || | oo=LOGO Ths. Phm Anh Tun - ( )( )22222nno_o-Trongccclngkhngchchca 1 2, | |btkltuyntnhhayphituynth 1 2, | |c phng sai nh nht - ( )21 2,i iY N X | | o +LOGO Ths. Phm Anh Tun - Khong tin cy ca 1| : Vi h s tin cy 1 o ta c khong tin cy ca i|l: ( )( )( )( )2 22 , 2i i i it n se t n seo o| | | || | + |\ . Trong 2 1222 2 22 21 1;inn ni ii iXx x| |oo oo= == = LOGO Ths. Phm Anh Tun - Kim nh gi thit i vi i| : Vi tin cy ota c: ( )i iitse| ||=Gi thit * *0 1: ; :i i i iH H | | | | = =th min bc b l ( )22 t t no> Gi thit * *0 1: ; :i i i iH H | | | | s >th min bc b l ( )2 t t no> Gi thit * *0 1: ; :i i i iH H | | | | > < 2 2 2 20 0 1 0: ; : H H o o o o s > th min bc b: ( )2 22 no_ _ > 2 2 2 20 0 1 0: ; : H H o o o o > < th min bc b: ( )2 212 no_ _< LOGO 1.9 Kim nh s ph hp ca MHHQ Ths. Phm Anh Tun Ta c: ( )2 2; 1 ESS r TSSRSS r TSS = = Do ( ) ( )( )222 22 2 22 22 222, 0,1 ; 1i iiN x N xx| |o | || | _o o| | | | | |\ . Nn ( )( )222 221, 2ixF F n| |o= LOGO Ths. Phm Anh Tun Chngtakimnhgithit 0 2 1 2: 0; : 0 H H | | = =thvitincy othngthng nh hn 0.1 ta c min bc b ( )22221, 2ixF F no|o= > Hay ta c 222.1 1r nFr= LOGO Ths. Phm Anh Tun T ta c th a ra qu trnh phn tch phng sai nh sau: Ngun bin thinTng bnh phngBc t doPhng sai Thmhiquy (ESS) 2 222 i iy x | = 1222 ix | Tccyutngu nhin (RSS) 2ie n-2 ( )222ieno = TSS 2iy n-1 LOGO 1.10 D bo t MHHQ Ths. Phm Anh Tun C th s dng hm hi quy d bo: - D bo trung bnh c iu kin ca Y vi mt gi tr 0X X =- D bo gi tr c bit ca Y vi 0X X =LOGO D bo trung bnh Ths. Phm Anh Tun Gi s 0X X =ng hi quy mu cho c lng im ca ( )0 0 1 2 0| : EY X Y X | | = +Trong Yc phn phi chun vi k vng 1 2 0X | | + , nn ( )( )202021iX XVYnxo( (= +( ( ( LOGO Ths. Phm Anh Tun Do 2ocha bit nn ta s dng c lng khng chch ca 2ol 2okhi vi tin cy 1 o th khong tin cy ca ( )0| EY Xl : ( )( )( )( )0 0 0 02 22 , 2 Y t n se Y Y t n se Yo o| | + |\ .LOGO D bo gi tr c bit Ths. Phm Anh Tun Nu chng ta mun d bo gi tr c bit 0Y Y =vi 0X X =khi c lng ca 0Yl ( )( )2020 1 2 0 021; 1iX XY X VYnx| | o( (= + = + +( ( ( Vi tin cy 1 o khong tin cy ca 0Yl: ( ) ( ) ( ) ( )0 0 0 02 22 , 2 Y t n se Y Y t n se Yo o| | + |\ . LOGO Ths. Phm Anh Tun V d:Cho s liu sau y v nng sut (t/ha) ca mt loi cy trng v mc phn bn (t/ha)choloicynytnhtrnmthatrong10nm1988-1997.Hyclngm hnh hi quy ca nng sut ph thuc mc phn bn v tr li cc cu hi sau y: a)Hy gii thch ngha kinh t ca cc h s nhn c b)Hy tnh lch chun ca cc|c)Vi mc ngha 5% hy cho bit mc phn bn c nh hng n nng sut loi cy ny hay khng? d)Hy tm khong tin cy 95% cho cc h s hi quy e)Hy tnh 2rv gii thch ngha ca kt qu nhn c f)Vi mc phn bn l 20 t/ha, hy d bo gi tr trung bnh v gi tr c bit ca nng sut vi h s tin cy 95% LOGO Ths. Phm Anh Tun NmPhn bn(X)Nng sut(Y) NmPhn bn(X) Nngsut (Y) 198864019931858 1989104419942260 1990124619952468 1991144819962674 1992165219973280 LOGO Ths. Phm Anh Tun LOGO Ths. Phm Anh Tun Hm hi quy tng th c dng ( )1 2|i iEY X X | | = +Hm hi quy mu 1 2 i iY X | | = +LOGO Ths. Phm Anh Tun iYiXiy2iyix2ixi iy xiY ie2ie2iX406-17289-1214420437.082.928.526436 4410-13169-86410443.720.280.0784100 4612-11121-6366647.04-1.041.0816144 4814-981-4163650.36-2.365.5696196 5216-525-241053.68-1.682.8224256 LOGO Ths. Phm Anh Tun 5818110005711324 6022394161263.64-3.6413.2496484 6824111216366666.961.041.0816576 74261728986413670.283.7213.8384676 8032235291419632280.24-0.240.05761024 5701801634575956570047.30563816 LOGO Ths. Phm Anh Tun a) ngha kinh t ca h s|Theo l thuyt th tng lng phn bn cho mt ha th nng sut cy trng s tng. 21.66 0 | = >kt qu ny ph hp vi l thuyt c ngha tng 1 t/ha th sn lng trung bnh tng 1.66 t/ha 127.12 | =c ngha l khi khng bn phn th nng sut trung bnh ca loi cy trn l 27.12 t/ha LOGO Ths. Phm Anh Tun a) lch chun ca cc| : ( ) ( )221 22 21;ii iXV Vn x x| | o = = c lng ca 2o :225.9132 2.4322ieno o = = = ( ) ( )1 238162.432 1.98; 0.10110 576se se | | = = = LOGO Ths. Phm Anh Tun a)Mc phn bn /ha c nh hng n nng sut ca loi cy hay khng? Kim nh gi thit 0 2 1 2: 0; : 0 H H | | = =( )2 22216.43 tse| ||= =Vi mc ngha 5% ta c ( )0.0258 2.306 t =Do gi thit H0 bbc b.iuny c ngha rngmc phn bn cnh hng n nng sut LOGO Ths. Phm Anh Tun a)Khong tin cy 95% cho cc h s hi quy Khong tin cy ca cc h s hi quy: ( )( )( )( )( ) ( )2 21 22 , 2: 22.55,31.69 ; : 1.43,1.89i i i it n se t n seo o| | | || || | + |\ . b)H s 2r2ES 1 1 47.30560.9711634S RSSrTSS TSS = = = =LOGO Ths. Phm Anh Tun a)D bo gi tr trung bnh v c bit khi mc phn bn l 020 X =t/ha ( )( )( )( )( )( )( )220202020202020 181 15.9132 0.6323810 5760.79511 6.545582.558iiX XVYnxSeYX XVYnxseYoo ( ( | | = + = + =(| | (\ . ( = ( (= + + =( ( ( = Vy khong tin cy 95% cho mc sn lng trung bnh l :( )58.468,62.153Cho mc sn lng c bit ( )54.421,66.218LOGO Ths. Phm Anh Tun Ordinary Least Squares Estimation ************************************************************************ Dependent Variable is Y 10 Observations used for Estimation from 1 to 10 ************************************************************************ Regressor Coefficient Standard Error T-Ratio[Prob] INPT27.1250 1.9793 13.7046[.000] X1.6597 0.10132 16.3808[.000] LOGO Ths. Phm Anh Tun ************************************************************************ R-Squared.97105F-Statistic F(1,8)268.3312[.000] R-Bar-Squared.96743S.E. of Regression2.4317 Residual Sum of Squared 43.3056Mean of Dependent Variable57.0000 S.D. of Dependent Variable 13.4743Maximum of Log-likehood -21.9596 DW-statistic1.7836 *********************************************************************** LOGO www.themegallery.com Dependent Variable: Bin ph thuc Regressor: Bin c lp Coefficient = H s - gi tr cc|tng ng vi b s liu dng c lng T- ratio [Prob]= T s t[xc sut]= ( )Se||[Prob] [Prob]=p-value= ( )( )2 P t nSe||| | | > | |\ . cthdavogitrnykimnhgi thit 0 1: 0; : 0i iH H | | = =LOGO Ths. Phm Anh Tun Nu nh 2 2,2 2ppp t tooo > > th so snh ovi p/2 sau kt lun tng t R-Squared=2rR-bar-Squared=2r hiu chnh, c k hiu l 2rS.D. of Dependent Variable = lch chun ca bin ph thuc = ( )21iY Yn LOGO Ths. Phm Anh Tun F- Statistic F(1,8)=268.3312[0.000]. Gi tr F(1,8) c tnh bng cng thc ( )2221,10 .1 1r nFr n= . Trong hm hi quy hai bin , gi tr ny cng bng bnh phng catstngvihsgc.KimnhFylkimnhmtphav 2 20 1: 0; : 0 H r H r = > . Do gi tr p-value c so snh trc tip vi oS.E. of Regression = lch tiu chun ca hm hi quy 2oMean of Dependent Variable = Trung bnh ca bin ph thuc LOGO Ths. Phm Anh Tun Bi4:ChoktquclngsauybngMFIT3trongYltngchitiu;X-thu nhp sau thu sau khong thi gian (1986-1997) v cho 2145, 4817 X x = = Ordinary Least Squares Estimation ************************************************************************ Dependent Variable is Y 12 Observations used for Estimation from 1986 to 1997 ************************************************************************ Regressor Coefficient Standard Error T-Ratio[Prob] INPT2.1288 7.1641 .29715[.772] X.86118 .048943 17.5955[.000] LOGO Ths. Phm Anh Tun ************************************************************************ R-Squared.96871F-Statistic F(1,10)309.6016[.000] R-Bar-Squared.96558S.E. of Regression3.3951 Residual Sum of Squared 115.2685Mean of Dependent Variable127.0000 S.D. of Dependent Variable 18.3005Maximum of Log-likehood -30.6014 DW-statistic1.7822 *********************************************************************** LOGO Ths. Phm Anh Tun a)Hy vit hm hi quy mu v cho bit kt qu c lng c ph hp vi l thuyt kinh t khng? V sao? b)Vimcngha5%,phntiudngkhngphthucvothunhpckhc khng hay khng? c)Vimcngha5%,thunhpsauthucnhhngnmctiudnghay khng? d)Hy tm khong tin cy 95% cho h s gc e)Cho mc thu nhp sau thu l 150, hy d bo gi tr trung bnh v gi tr c bit ca mc tiu dng vi h s tin cy 95%. f)Hy cho bit ngha ca con s .96871 g)Hy cho bit ngha ca con s .86118 LOGO