bài giảng kinh tế lượng - gv. lê khắc bộ

TRUdNGDAT Hec lrduc NGrrrEp nA Ner KHOA KINII TN C, PUAT TRIEN N.6NC rrrbN r,txnAc so , ' iii' : 'ln ''"*" '";,,*' 7 ar:i.:! :l tt BAI GIANG 1i}' ': .: -, ,::,:. ) HANOI_2011 };. cHrIoNG 2. 6N rAp vi xic suAr vA rnONG Id* t?,,* 2.1 xic su6t 'i' T'.g '" 2.2 Th6ns k6 m6 ta ;11 Z.: rnrlnl rc suy di6n-Vdn tld u6c luong -'*"- : 18 z.+ rh6ni ke suy di6n - Ki6m dinh gia thiilt th6ng k6 ,. '-\r, "**,"n 22 ",j:r. _lq&. CHTIONG 3. H6I QTIY HAI BIEN . .q'; : 3.1 Gi6i thiQu '11 29 3.2 Hem h6i quy t6ng th6 vi h6i quy m6, .,;. 30 3.3 tl6c luqni i6c h6 s5 cria m6 hinh hoi quy$eo phydiig phep OLS 33 3.4 Kloing tin ciy vd ki6m dinh gi6 thi6t ve deghe.S6 h6i quy 36 3.5 Dinh li Gauss-Marko ,, . ,,- 1 39 3.6DQthichhqpctahdmh6iquy-$f ,9::"q"." 39 3.7 Ds bio bing m6 hinh h6i quy trai bltigi F 40 3.8 Y nghia cria hdi quy tuyiin tinh vd m6.ry dqng hdm thulng tluoc st dpng 42 .n 1qn:! cHuoNG 4. u6 niNA HOI auYFuvEN riNH BQr 4.1 X6y dsng m6 hinh. -"Ji\"}i 4s 4.2 tl6c luqng tham s"6 c"trg frrfl hifih h6i quy b6i 45 4.3 R'z vir n' hi,eu chiLh- a; . 4'], 4.4 Ki6m tllnh niirc ;i nghia chung cua m6 hinh 48 4.5 Quan hQ giqgqR'z,v.a-f 48 a.6 Udc luqne iii[4ne ve ki6m dinh gia thitit thi5ng k€ cho hQ sti h6i quy 48 4.7 Bifi p-hin loai @i6n giA-Dummy variable) 49 MUCLUC CHTIONG 1. GIOI THIE,U 1.1 Kinh tii luqng li gi? I .2 Phuong ph6p luin cria Kinh t6 lugng 1.3 Nheng cnu h6i d{t ra cho mQt nhd kinh t6 luqng 1.4 Dt ligu cho nghiEn cr?u kinh ti5 luqng 1.5 Vai trd oia miy vi tinh vi phim m,im chuy6n dung :i] ",gJuoNe6,.rcror rHlpu l40r sO viN Di LItN QUAN DEN 'qi; ,;, Mo HINH HOI QUY 5.1 DF cong tuydn 5.2 Phuong sai cria sai s6 thay d6i 5.3 Tu tuong qua:r (tuong quan chuSi) 5.4 Lua chgn m6 hinh CHU0NG 6 DtlBAovol MO HiNH HOr QUY 6.1 Du b6o vdi m6 hinh h6i quy don gian 6.2 Tinh ch6t tr5 cta dt lieu;hu6i thoi gian vi hQ qud cua n6 diSn m6 hinh 6.3 M6 hinl t.u h6i quy 6.4 M6 hinl c6 tt6 tr6 phnn phili 6.5 t-ldc luong m6 hinh t.u h6i quy 6.6 Pb6t hiQn tu tuong quan trong m6 hinh t.u h6i quy Trang 3 J 4 7 9 53 56 59 60 6t 62 62 62 64 64 April 2011 Ld Khdc Bd - HUA Bat pianp kitth ti luotts cHI-roNG 7. cAc M0 HiNH DU BAo nr.4,Nc rirur rrl6Nc xB ^, ,:. i ,. /.1 uac mantr pnan cua du lrgu chuol tnfi glan 7.2 Du biio theo xu hu6ns dii han ,^, l ,, ^,, ,: . /.J Mot so l(y thu?t du bao don gran 7.4 Ti6u chu6n tldnh sii m6 hinh du bdo ./ 7.5 M6t vi du beng s6 7.6 Gioi thiQu m6 hinh ARIMA C6c bing tra Z, t ,F vir y2 Tii liQu tham khio 66 67 68 69 69 70 'r., ^14 :' '' 1!''1'' 'n -'rti;', liii' -, : .:.) ., iri 'i:,. '1; Apil 201 1 CHLTONG 1. GI6t rIrrEU l.l. Kinh ti5 luorrg lh gi? iil;; ttil,G1r 1'E"ono*"t i"r"."6 nghia li do lu.onc !hhf'' Th{t ra.ph4m vi cria Urf,^t6-f"frg iO"i t-, Ao luong kinh t6. Chring ta sE thAy di6u t16 qua mQt dlnh nghia v6 kinh t6 luone nhu sau: **';h;;;';,7;,i) ,na"g ka kinh # c6 nQi dung chinh td sd tiQu thiing ka' kinh tii trqng h mAt min26c"l4p vbi sv kA hqp cia lj' thuydt kinh #',c6ng c4 todn hoc vd phuong phdp lud,n- th,ins ki. N6i r6nz hon, kinh ti lwng liin quan ddn: ( l) U. 6c lttqng cac quan h€ kinh' ri, til XiZ* chilms li, rhuyir kinh t0 bing dft liQu.thqrc i.vd.kidm dinh gid thidi'cia t'inh t6 hoc vi hdnh vi, vi 13) Dtr bdo hdnh vi cia biin s6 kinh ft "' Sau tlAy lir mQt s6 vi du v6 ung dung kinh t6 lucrnC' : vi hdnh vi, vd (3) Dr bdo hdnh vi cia bian sd hnh te. - Sau dAv lir mOt s6 vi du v6 ung dung kinh t6 lucrnC' tl6c luqng quan hf kinh t6 . : , , (l) D"lu}ll; mric d6ldc d6ng crla vi6c ha I6i su6r 16n tang trutog kig[]^g,. . ., . . (2) Udc lugng nhu ciu cria m6t mAt heng cp th6. vi du.ghu c{{1e hoi t4r thl truong Vi6tNam. 'q,,' , ), i:t pnan tich tec d6ng ctra qudng c6o vi khuy6n mii l€n doaffir s6 crla m6t c6ng ry' / Ki6m itlnh giA thiiit iii'ililil;ia iuia ra t6c dQng cira chuong trinh $firviln n6ng ldm trng ndng su6t lfa. (2) KiCm chimg nhdn dinh d0 co ddn theo e- __- ,qu "w . .{i{*," ciu vil c6 basa dang fillet d thi trudng nQi <lia. Dr; bio izi ci,irr, prli au b6o muc 13) Dq b6o chi s5 t+I 1.2. Phuong p t6 luqng Theo phucrng p! cftu sri dung kinhit6 th6ng, cdrigqi ld phuong phrip tuan cO tli6n, m6t nghiBn giim c6cludc n}u sau3: (1) Ph6t bi gin thi6t. (z) x4gdinh dad (3) Xric,.diph dac ",iu ,ia ni*, toan kinh ti5 cho lli thuyi5t hoac gie thiiit. cria m6 hinh kinh t6 luong cho 11i thuy6t noic gla titrit. i li6u. tham s6 cria m6 hinh kinh tt5 lucrng. dinh gin thii5t. riii k6t ouA giAi k6t quA Du b6o ve sri dpng m6 hinh d6 quy6t dinh chinh srich l.A.KoutsoyiaDnis, Theory ofEconometrics-Second Edition, ELBS with Macmillan-1996, trang 3 2. Ramu Ramanaiha4 Introductory Econometrics with ApPlications, Harcourt College Publish€rs_2oo2, tang 2. r Theo Ramu Ramanathan, Introductory Econometrics with APplications, Harcourt College Publistrers-2oo2 s6ch, tham hut thuong mqi, l4m ph6t lo+i cd phi6u cu th6 *u n-rE. U6c (6) (1) (8) April 201I L1i thuyt5t holc gii thirit LAp m6 hinh to6n kinh ti! L{p m6 hinh kinh ti5 iuorg LI6c luqng th6ng si5 -,.: ." 1 Krem Opn gra tnlet Xiy dmg lai m6 hinh La Khdc B6 - HUA Bdi siAns Ki h ti llrcrns Hinh 1.1 Phucmg ph6p . . Vi dp i: C6c bu6c ti(5n <16 tdi nghi6n ctu xu hugnl tQ luqng lduu mQt vAn de kinh te sri dpng kinh t6 luong v6i 3n cria n6n kinh t6 Vi6t Nam. (t) Ph6t bi6u l,i Keynes cho Qui luAt tlin 6ng (t1in bi) mu5n, nhu m6t qui tic vd vd trung binh, ting ti6u ding ilu ntr4p cria hg ting l6n, nhung kh6ng nhidu nhu ld gia tlng xu hu6ng tieu ding bi6n(marginal propensity to consume-MPC), l6n khi thu nhfp tdng 1 d<rn v! ti6n t6 l6n h<rn 0 nhrmg nh6 hon I . m6 hinh todn cho li thuyiit ho4c gia thi6t don gian nh6t th€ hiQn j tudng cria Keynes ld dang him tuy6n tinh. +F,GNP (1.1) Trongtl6:0< p, <1. Biiiu di6n du6i dang dd thi cta d4ng him niy nhu sau: a Joha Maynard Keynes, 1936, theo DN.Gujarati, Basic Economics, 3'a , 1995, trang 3. a" trong thu vOy x tuc ti6u d April 201I il ,';;6'.;fi;rO5'niiia" u"n" gini thich cNr: u6n a$'l4phav, pii5n giei thich Hinh l. 2. Him ti6u dirng theo thu nh{p. .ra M6 hinh to6n v6i d4ng him (1.1) the hiQn m6i quan h!- .tit dinh(determrnistic relationshrp) gita ti6u drirng vd,thu,nhip trong khi quan hQ gria cric bi6n s6 kinh te thuong mang tinh kh6ng chinh xiic. D6 bi6u dien m6i quan hQ khffig chinh x5c gita ti6u dirng vd thu Jrfp chung Ia dua vio thinh phAn sai s6: !.'.",q1* TD = Br + prcNP + s (1.2) _,*" &" '1 Trong d6 e ld sai sii, e ti mQt birin +dfu Siege ti€n cho c6c nhan ti5 kh6c cflng tiic dQng l€n ti6u dirng mi chua ilugc dua vio}{hilE Phu<rng trinh (1.2) ln mot m6 hinh kinl tdtydhg M6 hinh tr€n dugc goi li m6 hinh h6i qoy ruy6n tirt . H6j Cuv tuv6n tinh llfQi duqt'chinh cua hgc phAn niy. (4) Thuthepsi5 lieu ' 3"- \,." j quy tuy6n tinh. H6: quy tuyqn tjnh llfQi "dun$ chinh cua hgc ph6n niy (4) ThuthapsSlieu -i 1 1 i6 uOu ud iie" au"g va trrurfiir?B-&i-'n,in khh t6 ViQt Nam ru i986 di5n 1998 tinh theo tlon vi tiAn te hiQn hanh;Ehu sq;' i .I]' , ro , ei6; prri thuQt hay bi6n duoc giii thich GNP: Biiln dd.Cl4p'hav, bfi5n giei thich t.1*5'irtori!6 t6ng ti6u ding vir GNP cria ViQt Nam s53.099.984.896 526.442.004.480 2.530.537 .897 .984 2.667 .299.99s.648 13.285.535.514.624 14.33t .699.189.824 26 .849 .899 .9'l 0 .560 28.092.999.401.412 39.446.699.311.104 4t.954.997 .960.704 64.036.997 .693.440 16.707 .000.22t .696 245.t8 1 10.535.001.505.792 88.203.000.283.136 114.704.00s.464.064 t36.57 t.000.979.4s6 371;77 4 139.822.006.009.856 170.258.006.540.288 186.418.693.406.720 222.839.999.299.s 222.439.040.614.400 258.609.007.034.368 250.394.999.521.280 313.623.008.247 .808 36r .468 .004 .401 .t52 April 2011 Ngudn : World Development Indicator CD-ROM 2000, WorldBank. 5 TD: Tiing rieu dtng cria nen kini 16 Vi6r Nam, d6ne hi6n hdni. CN P: Thu nhnp qudc n6i cLia Vidr Nam. d6ne hi6n ian}r . - D9. trong thoi h) khao srit c6 lam ph6t rdt cao n6n chring ta cin chuyiin dang s6 li6u ve ti6u dirng vd thu nhnp thuc v6i nIm g6c Li 1989. Bingl.Z. Ti6u dring vi thu nhlp cria ViQt Nam, gin cd dinh 1989 1\ am Ti6u dirng. TD, tlong-giri c6 dinh 1989 Tdng thu nh6p GNr, dOng-gtd cd ainh 1989 1986 22.868.960.3C)2.145 24.025.999.156.721 1987 23.611.903.339.s1s 24.888.000.975.950 1988 24.255.972.111.640 26.16s.999.171.92 1989 26.849.899.970.560 28.092.999:401.472 1990 27.760.775.225.362 29.526.AA0.611:153 1991 26.118.36s.11A.rc3 31.2.8s.998,882.8t 3 1992 27 .123.609.120.80r .33 .990.:9.99 :913:67 9 1993 30.853.195 .807 .661 ' 3:6,1 3 5.4 A,L, 69 2. 5 I 1 1994 32.834.660.781.138 :s.9ez.oo:.187.889 1995 36.638.7 54.378.646 43.19V .n02.601.354 1996 41.190.217 .461.419 . :,, 47 .888.002.0 69.3 33 1991 41.349.567 .191.335, 51.790.873.128.79s 1998 43.126.144.904.439:, '!'i: 54.794.'746.182.076 tic luong m6 hinlr (-J,- oc luonl ng phumrg phrip t6ng binh chring ta thu du<rc.t6t qua ti .' 'ii -_ . if, ,".,. ,o,h-e.'S6'iata m6 hinh) 'rfuS,"t6i thi6u ttrdng ry nhir sau: thudng (or dinary Least (s) u Xu hu6ng (6) Ki6m dinh Irl so ll6c luong .6 F, ; =0,68 r'cria niSn kinh t6 ViCt Narn la MpC : 0,6g. th6ng k6 Keynes. chring ta cdn x6c dinh MPC tinh to6n nhu tr6n c6 lon hon'0 vd nh6 hsn ; k6 hay kh6ng. Ph6p kidm tlinh niy ctng duoc trinh bdy rrong chuong 1 v.9,, j 2. (7) giii kiit qu6 5 Se duoc gi6i thieu trong chuong 2. Dua theo 1i nghia kinh t6 cria MpC chung ta diQn giai k6t qua h6i quy nhu sau: !6u-d]Ic tdng.0,68 ne.an ty d6ng n5u GNp ting i ngdn rj.d6ng. (6) Su dung ker quri h6i quy . Dga vdo. k6t que h6i quy ChGg ta c6 th6 du beo hoic ph6n tich t6c d6ng cia chinh s6ch. vf du n€u d, brio dugc GNP cta vi6r Nam nim 2004 thi chrrne ta c6 thd iu brio tieu dims clta Vj€l N1m.rrong nam 20O4. Ngorii ra khi bi6r MpC chfng ta c6 th6 udc luong s6 nh6i c0a n6n kinfi t€ theo lf thuy6t kinh t6 vi m6 nhu sau: M: 1(1-MPC) - 1(1-0,68):3,125 )pril 201I La Khdc 86 - HUA Bdi sidns Kinh ti luortg Vay kiit qua h6i quy niy hfiu ich cho phin tich chinh srlch tliu tu, chinh sich kich ciu- 1.3. Nhtng ciu h6i il{t ra cho mQt nhir kinh tA luqng 1. M6 hinh c6 f nghia kinh tii kh6ng? 2. Dt liPu c6 ding tin cAY kh6ng? 3. Phucrng pbrip u6c luqng c6 phir hqp kh6ng? 4. Kiit qui thu dugc so vcri k6t qui ttr m6 hinh khdc hay phuong phdp khric nhu th6 ndo? 1.4. Dfr liQu cho nghiGn c.ri'u kinh t6 luqng cri ha danq dir li6u kinh tE crv bin: dri li6u c C6 ba dang dt fieu kinh t6 co bin: dt li-6u ch6o, dt lieuchu6i thdi gian vi dt liQu bing Dir ti6n ch 6o hro oAm orran s6t cho nhidu don vi kinh ti5 d m6t thdi tliiim cho tru6c. C6r Dft liQu chlo bao gdm quan s6t cho nhidu don vi kinh ti5 d mQt thdi tliiim cho tru6c. CdLc tlcrn vi kinh t5 bao gdm cic c6c nhdn, c6c hQ gia dinh, c6c c6ng ty, c6c tinh cac quoc 9n Dtr lifu chuSi thoi gian bao g6m c6c quan s6t h6n m6t don vi nhidu thoi tlii.m. Vi du ta quan s6t doanh thu, chi phi quang c5o, dO ddi m6i c6ng nghp d m6t c6ng ty trong khoing thoi gian 1 Dir liQu bing li su k6t hqp gita dt liQu ch6o vd dt li€u du v6i cing b0 bi6n s5 vd c6ng ty nhu o vi du trdn, chLing ta thu thfp spfi cdng ty trong cirng mQt khoang thdi gian. tai ttic Bi6n rci rac hav li6n tuc 'r"d" ;ffi i}i;il ia ilOi'i;i; "o tap.hqp c6c k6t qua c6 tr,6 a$yi auoc.vidu biiin Quy m6 hQ gia dinh 6 vi iu *u" i.z la m6t bi6n ;;i r?c. .r : Y." ". ^r , ,1 Bi6n [6n tgc lA biiin nhan k6t qua mQt s6 vd h4nrqac kilt qui. Vi ds luong luong mua ftong mQt nem d m6t tlia di6m. .r{*a q- '} . .r\ '\1 , ,-','A ' ,_ Dt li-6u c6 thii thu thip tu mQt thi ngSQ_m*tpg[i6m sp6t, n6i cich khric chring ta c6 the thay d6i mQt titin sii trong diAu kiQn cii git kh6ng d6i. Eay chinh ld c6ch b6 khoa hoc tu nhi6n. tri thi nghi€m kong n6ng hoc, y khoa vi D6i v6i kinh t6 hoc n6i ri€ns var .kho ,"&a tol noi chung, chring ta r6t kh6 b6 tri thi tdt ci moi thir d6u thav d6i n6n chrine ta chi c6 D6i v6i kinh tti hoc n6i r-i nghiQm c6 ki6m sodt, vd su itrgb -dufog alru tit ca mqi thir d6u thay di5i n6n chring ta chi c6 th6 quan s6t hay didu tra d6 1.5. Vai trd-cria m,1y.vi.ftff&Ff,im mdm chuy6n dgng . vi.kinh t6 luo-ngJi'efrdjafrffiviQc xri l;y' mQt ktrt5i tuqng sii liQu r6t l6n n6n chring ta cin d6n su trg giri6E;cua .n}'y*ri tiot vi mQt chucrng trinh h6 tro tinh to6n kinh ti5 luqng. Hiqn nay c6 r6t'ibiiup haq .riidm chuy6n dirng cho kinh tt5 luqng ho{c h5 trg xu li kinh tii luqng. Excel i1"' N6i chufr'gfiep phin m6m bang tinh(spreadsheet) dAu c6 mQt s6 chric ning tinh torn inh t6 m6m bing tinh th6ng dung nhdt hign nay li Excel nim trong b6 Office ft. Do tinh th6ng dpng cria Excel n6n mdc dir c6 mdt sii han chtl trong vlec tinh to6n kinh ti5 luong, gi6o trinh niy c6 sri dung Excel trong tinh toen d vi du minh'hoa vi huong dAn gini bii tip. cich nhanh ch6ng vi hiQu qu6 chring ta phdi quen thuQc v6i it nh6t m6t phin mAm chuyEn dung cho kinh tii lugng. HiQn nay c6 r6t nhidu phin m6m kinh t6 lucrng nhu: PhAn mdmC6ng ty ph6t tri€n AREMOS/PC Whartop Econometric Forcasting Associate BASSTALBASS Institute lnc BMDP/PCBMDP Statistics Software Inc DATA-FITOxford Electronic Publishing i ECONOMIST WORKSTATIONDaTa Resources, MC Graw- April 2011 ESPEconomic Software Package ETNew York University EVIEWSQuantitative Micro Software \CaUSSeptech System lnc ,\-IMDEPNew York Uni versiry ( MATLABMathWorks Inc YC-TSPTSP Intemational /P-STA-tp-stat Inc \SA S/STATVAR Econometrics /bCA SYSTEMSAS Instifute ]nc I SUeZelfUniversiry olBritish Columbia \sontrfcrne Soritec Group Inc ,,t,.,,,, $rsssRss rn. $TATPRoPenton Sofuare Inc . Trong si5 nriy c6 hai phin mdm. d_uqc sri dlmg hrcrng d6i ph6. bie; d cdc truong dai hoc vi viQn nghidn cuu o Viet Nam ld spSS vd EvIEws. sns-s r6t iinu ii0p ot6 ,giic" ",* th6ng kd vi, ctng tuong d6i thu6n tiQn cho tinh to6n kinh,t0.lugt,rB.,, trong tdri "eVmWS 'ti "t.ja April 201I .8 cI{t/oNG 2. 6N rAP vE xAc suAr vA ru6Nc rd Bi5n nsiu nhi6n. MQt bi6n md gi5 tri ctla n6 duoc x6c dinh boi m6t ph6p thri ng6u nhi6n tluoc gqi lA m6t biiln nsiu nli6n."N6i cach kh6c ta chua thd x6c dinh gi6 tri cia biiln ng6u nhi6n n6u ph6p thn chia di6n ra. Bi6n ngiu nhi6n duqc lcy hiQu bing ky t.u hoa X, Y , Z " Cic gi6 tri cia bi6n ngiu nli6n ruong img dugc bi6u thi blng lci tu thudng x, y. 2 Bitii neau nhi6n co thE rdi rac hay lidn tUc. M6t bii5n ngiu nhi6n rtri rac nlrin mQt s6 f,i., 5r"O-oa" v6 han d6m dugc) c6c gia t i. ft't6t bi6n ngiu ot iCn li6n tuc nhin v6 s5 gi6 tri trong khoing giri tri cua n6. . .:ir , - vi ar; z.f . Gqi X li s5 chdm xu6t hi6n khi tung mQt con sfc sic 1xi ngiu). X\ajrilt'Uien ngdu nhi6n roi rac vi n6 chi c6 th6 nhfln cdc k6t qud 1,2,3,4,5 vit 6. \. 2.1. X6c suAt 3s 2.1.1 X{c suAt biiin ng6u nhi6n nhfln.rtuqc pQt gin tr-l-cq th6 Ch{ng ta tbunng quan tim diin xric sudt.Uiiin:igffil-i6n nh4n dugc mQt gie tri xric dinh. Vi du khi ta sip tung mQt sric sac,vnta mptrQiet &igyffit xuit hj9n Xi :4.ld bao nhi6u. - du tu 160 cm tli5n irhi6n li6n tuc. Do con sric-sic * 6 -At ra o6r, khor&co"€ru,1ffiffi khi ning xudt hiQn cua m6i m6t tldu nhu nhau n6n ching ta c6 th€ suy ra Nguy6n tic lf do kh6ng tIAy tln(the p iiy ra mQt kiSt qui ld 1/K. kh6ng gian mAu. Vi dg 2.3. Gqi phdp thu tung hai con stc sic. Kh6ng gian F:CvdD:CnD:{4;5;6} Cric tinh chdt cria xic suit P(s):1 0<P(A)<1 P(E) = P(A uB) = P(A) +P(B)-P(AnB) I an sltat Khlo srit bii5n X li sii aliim khi tung sric sic. Gii su chring ta tung n lin thi sii lin xu6t hiQn gi6 tri xi ti ni. TAn suft xu6t hien k6t qua xi li April 2011 om. Con s6 niy kh6ng phai thc, ,6t dii x: + la: P(x.4) = tt6. of insufficient reason): Nriu c6 K kiit qui c6 khi nlng xiy ra nhr Kh6ng gian miu: MQt it xiy ra mQt k6t qui ld 1/K. r ld m6t tip hqp tit cd cric khA nlng xiy ra cta h S. M6i kha neng xiy ra ld m6t tti6m miu. mQt plrdp thu, h.i hiQu cho Bi6n c6 : Bi6n c6 liimi [...]... 2 sr3 Chung-ta co X6t gin thi6t Ho : of = o] = H1 i.< oo "2 l):; > X,i"_,.",,), thi bdc bo H6 6; Ntiu 1f ,-, ,",r, < n - l) "'l;, -" "niq i"* 1r 6'z t :o!+ol ,' s"' 'ti { Chringtadi c6 (n-Uj ;- " , fi" ,".:., 1 (n, Quy - / u.'"' 5 : , r)1 //*\,t-*Lr:r,'*/ tic quyiit ainh F Nilu ) Ni5u April 2011 $ {. ,-, ,. ,-, ,,,, t oa { !," ,-, ,, ,-, *,, 5 s q $ > r,, -, ,",-r,r-,14 thi ta b6c b6 Ho -, ,,,-r,r-"rzy thi ki6ng... quy (3.5) Tt hAm h6i vi p, sao cho t6ng binh tj -i =Y, -F, -prx, I"i = IF, -8 , -p,x,) (3.6) =Y, ", n vav ' Ir i=! nl ^ ,2 i=l Di€u ki6n d6 (3.6) tl4tcuc ols-ordinary Least April2011 ^ ili ld: squarE 33 La Khic 86 - HUA al (l) !"' Bdi "idns Kinh i tuons I \";i' ) =-2 L(v,-p B,x,)=-zie, =o(3.2) OPt i-r i=r ,li"r') (2) *3=-zl(v, -0 , -P,x,F, =-2 Ie,Xr -o(3 8t ,i-:i' AQ, i.r Tir f3 ta rtt ra g) i=l 3.3.3.Tinh... Ph61 tl6 r(X - z ,-. ,, t Nguy6n + 2,",, *lu ' r/n' = r,l =, - o ") tfc ra quydt ainh \ ,,r Neu ' ] < t, < x /o _ xt-L,.",2 Cf i- Ji , _ >po hoic i; X,+2,_o,, cr N5u X ,-2 ,_,,,* \i V6i mric n r/n 6 J;= U, thi ta b6c bo He vdi d6 '-. '' tntat Z 1-" p thi ta bic bd H6 vdi d6 tin ciy >N 1-cr ha thi ta kh6ng thii b6c b6 Hs V . s6 nh6i c0a n6n kinfi t€ theo lf thuy6t kinh t6 vi m6 nhu sau: M: 1(1-MPC) - 1( 1-0 ,68):3,125 )pril 201I La Khdc 86 - HUA Bdi sidns Kinh ti luortg Vay kiit qua h6i quy niy. bitin ngiu nh-i6n rdi rac cov(X, y) = II G - p, Xy - p, )f(x, y) yx = !)xvr(x, y) - p,p, OOi vcri Ui6n ngiu nhi€n fi6n tuc 11 cov(X,Y) = J J fx-u_Xv-p,)f(x,y)dxdy =. = { {xvr1x,yyaxdy_p,t-r, I,:h "I-1, *fiep phuong sai (1) - N6u X vn Y d6c ldp th5ng k6 thi hi6p phuo,ng sai cria chtng bing 0. cov(X,Y) - E(XY) -p-pr, ?) cov.(a rbx,c