Tsu-2011 - ieeetsu

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gayidvis moculoba korelaciis koeficientis es mniSvneloba gvaewmunebs, rom arsebobs sustad gamoxatuli pozitiuri wrfivi kavSiri A da B trestebis amonagebs Soris, rasac gabnevis diagramac adasturebs. magaliTi 6. axali produqciis fasis dasadgenad kompaniam SearCia 10 qalaqi, romelTac arsebiTad erTi da igive yidvis potenciali gaaCnia da gamoitana produqcia bazarze yovel maTganSi sxvadasxva fasad. kompaniis mier miRebuli Sedegebi moyvanilia cxrilSi: qalaqis nomeri 1 2 3 4 5 6 7 8 9 10 fasi, x 15. 15. 16. 16. 17. 17. 18. 18. 19. 19. 0 5 0 5 0 5 0 5 0 5 gayidvis moculoba, y 15 14 16 9 12 10 8 9 6 5 davadginoT gayidvis moculobis fasze damokidebulebis saxe. amoxsna. avagoT gabnevis diagrama gabnevis diagrama 20 15 10 5 0 12 14 16 18 20 22 rogorc diagrama gviCvenebs, Cvens winaSea uaryofiTi wrfivi kavSiris tendencia: monacemebi Tavmoyrili arian uaryofiTi daxrilobis mqone wrfis midamoSi. radganac korelaciis koeficienti zomavs or sidides Soris arsebuli wrfivi kavSiris siZlieres, unda movelodeT, rom korelaciis koeficienti sakmaod axlos iqneba -1-TTan. gamovTvaloT korelaciis koeficienti. gvaqvs: x 17.25 , sx 1.44 , y 10.4 , sy 3.56 , cov( xy , ) 4.75 da cov( xy , ) 4.75 r 0.93 . ss x y 5.13 korelaciis koeficientis es mniSvneloba adasturebs gabnevis diagramis daxmarebiT miRebul daskvnas. wrfes, romlis midamoSiac Tavmoyrilia dakvirvebuli wyvilebi aqvs saxe: y ax b , sadac cov( xy , ) 4.75 a 2.29 da b yax 10.4 2.29 17.25 49.90 2 2 s 1.44 , x fasi 213
anu y 2.29 x 49.9 . es gantoleba kompanias saSualebas aZlevs axali produqciis fasis mixedviT gaakeTos prognozi gayidvis SesaZlo moculobis Sesaxeb. amrigad, korelaciis koeficientis mniSvneloba moTavsebulia -1-sa da 1-s Soris. Tu or sidides Soris adgili aqvs mkacrad dadebiT wrfiv damokidebulebas, maSin r -is mniSvneloba axlosaa +1-Tan. Tu or sidides Soris adgili aqvs mkacrad uaryofiT wrfiv damokidebulebas, maSin r -is mniSvneloba axlosaa -1-Tan. rodesac or sidides Soris ara gvaqvs wrfivi damokidebuleba, an am sidideebs Soris susti kavSiria, maSin r -is mni- Svneloba axlosaa 0-Tan. qvemoT moyvanilia korelaciis xarisxis sityvieri daxasiaTebisaTvis miRebuli terminologia da Sesabamisi diagramebi: srulyofili uaryofiTi korelacia Zlieri uaryofiTi korelacia saSualo uaryofiTi korelacia saSualo dadebiTi korelacia ar aris korelacia susti susti Zlieri uaryofiTi dadebiTi dadebiTi korelacia korelacia korelacia -1 -0.5 0 0.5 1 uaryofiTi korelacia dadebiTi korelacia Y Y srulyofili dadebiTi korelacia r=–1 r=1 srulyofili uaryofiTi korelacia Y X X . . . . . . . . . . . . . . . . . . ar aris korelacia srulyofili dadebiTi korelacia X Y . . . . . . . . . . . . . . . X Y . . . . . . . . . . . . . . X 214
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omar furTuxia albaToba da statistik
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statistikuri hipoTezis Semowmeba no
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. Tu P( ) aTobebi. P( A): P( ) A
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I. kursze, romelzec sami jgufia, jg
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magaliTi 4. vipovoT albaToba imisa,
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3 10! 8910 С 10 120. 3!7! 6 mag
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C 2 4 6 2 496 C32 0,012 . davaleb
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sa, rom: a). orive nomeri iqneba er
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Tu A ,..., 1 , A2 An xdomilebaTa sr
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1 1 1 1 1 . * * m m1 m 1 m1 sauke
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kamaTelze movida kenti qula, C -- o
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amocanis pirobebSi cxadia agreTve,
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is SemTxvevaSi ukanaskneli Sedegi S
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Sesabamisad, saZiebeli albaToba alb
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oba aris wina cdaze CaWris albaTobi
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22. ( A B) , P( A| B) 1/3, PA ( )
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42. albaToba imisa, rom oTx damouki
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5). P{ xk} F( xk 0) F( xk ) (Se
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E( | B) xiP( xi | B) . 1 cxadia,
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{ ggg,ggs,gsg,sgg,gss,sgs,ssg, sss}
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magaliTi 6. mocemulia SemTxveviTi s
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P{ 2} P{ 0} P{ 2} 0.1 0.4
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aqedan gamomdinare, korelaciis koef
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17. kompiuteri daprogramebulia 0-da
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37. samSeneblo kompanias sTavazoben
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Tavi IV diskretul ganawilebaTa gamo
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ualod drois mocemul intervalSi xidz
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9. universitetis studentTa 30%-is a
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27. martis TveSi Semosuli satelefon
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43. umaRlesi ligis fexburTis matCeb
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va arcerT kamaTelze, maSin is arafe
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2 2 2 () D x f x dx . asimet
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gavixsenoT, rom ( MA) . meore mxri
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x amoxsna. visargebloT formuliT: F(
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a). ipoveT c ; b). gamoTvaleT moda;
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Tavi VI normaluri ganawileba SemTxv
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magaliTi 4. vipovoT albaToba imisa,
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X -s Soris mdebare aris farTobi 0.5
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amitom 12 a 16a 0.407 da 0.900 .
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cali SuSis sawmendidan ramdenis sig
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obili 56 mili/sT siCqariT moZraobis
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52. uwyveti SemTxveviTi sididis ga
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Tavi VII albaTobis Teoriis zRvariTi
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Tu axla gavixsenebT, rom ( x) ( x)
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amoxsna. SemoviRoT xdomilebebi: A {
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n n 2(0.005 ) 1 0.95, anu ( 0.005 )
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18. detalebis 80% I xarisxisaa. ram
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s t a t i s t i k a Tavi I wertilov
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ucnobi parametris maqsimaluri dasaj
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magaliTi 2. cnobilia, rom garkveuli
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ndobis intervali mexuTe klaselebis
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tervalisaTvis, roca n 10 ; e). 95%
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Tavi II ndobis intervali bernulis s
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4. gamokiTxuli 1015 axalgazrdidan 1
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Tavi III ndobis intervali dispersii
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18.6 19.5 20.2 20.4 19.3 21 20.3 19
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26. 22 balaxis sakreWi manqanis mie
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Tavi IV 2 hipoTezaTa Semowmeba saSu
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xE 43260 42000 z 1.32 . / n 523
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2. CamoayalibeT ZiriTadi da alterna
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15. miuTiTeT unda ukuvagdoT Tu ara
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pasuxebi: 1. 2.58 ; 1.65; -2.58; -
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X E gamoiyene T , T.x. n 1 * ' S
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Seesabameba 0.025 -sa da 0.01 -
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mniSvnelovnebis doniT gvaqvs Tu ara
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gadawyvetileba: Tu T.V.C.R., maSin
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magaliTi 5. vipovoT P -mniSvneloba,
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8. plastikatis boTlSi moTavsebuli 1
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hipoTezis Semowmeba puasonis popula
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3. samSobiaro saxlis warsuli Canawe
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Tavi VIII ndobis intervali da hipoT
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3. uZravi qonebis agentis mtkicebiT
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finansur daxmarebas. imis gasarkvev
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pasuxebi: 1. H0 : E 1800 , H1 : E
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( xn y ) z / n / m a a ( x y )
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P{ T t | H0}, Tu H1 : a1 a2 0; P
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(sadac z aris N(0,1) -is zeda -kr
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amerika evropa 729 329 450 330 481
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TiToeuli jgufidan SemTxveviT SerCeu
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SeniSvna: saSualoTa Sesaxeb tolobis
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gadavideT saSualoebis Sesaxeb hipoT
Page 163 and 164: 4. mkvlevaris SefasebiT studenti go
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Page 169 and 170: 5. sagadasaxado inspeqtoris mtkiceb
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Page 173 and 174: s n s n ' ' D D d n tn 1, /2 aD d
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Page 177 and 178: 4. mkvlevars ainteresebs axali diet
Page 179 and 180: Tavi XIII oramokrefiani amocanebi b
Page 181 and 182: ( 0.36 0.242, 0.36 0.242) , ( 0.60
Page 183 and 184: 11. 200 gamokiTxuli mozardidan 50-s
Page 185 and 186: 23. dedaqalaqis SemTxveviT SerCeuli
Page 187 and 188: Tavi XIV Tanxmobis kriteriumebi xi-
Page 189 and 190: nabiji 4. gadawyvetilebis miReba: r
Page 191 and 192: e 26.7 55.1 66.64 38.96 12.6 i (aq
Page 193 and 194: programebs. SemTxveviT SerCeul myid
Page 195 and 196: nabiji 2. SevadginoT niSanTa SeuRle
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Page 199 and 200: nebis doniT, aris Tu ara avtomobili
Page 201 and 202: hipoTeza imis Sesaxeb, rom arCeuli
Page 203 and 204: proporcia, romlebic institutSi dadi
Page 205 and 206: is Sesaxeb, rom im momxmareblebis p
Page 207 and 208: fatalur avariaTa ricxvi Tavi XVII d
Page 209 and 210: uaryofi Ti wrfi vi kavSi ri 400 300
Page 211 and 212: ' ' ' 2 x i y i y i yi yi ( yi yi)
Page 213: B trestis monacemebi 5. rac ufro ko
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Page 219 and 220: 218 amocanebi 1. gamoTvaleT korelac
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Page 223 and 224: Tavi XVIII regresia da korelacia 1.
Page 225 and 226: wrfiT (regression sum of squares).
Page 227 and 228: saxlis gayidvis fasi a). ormxrivi a
Page 229 and 230: 2 SSE 21995.88 S 168.91 . n2 13
Page 231 and 232: determinaciis koeficienti. davweroT
Page 233 and 234: 2 va damakmayofilebel Sedegs (deter
Page 235 and 236: x1 (b 1 ) 4.146 0.751 5.520 0.000 2
Page 237 and 238: spirmenis rangobrivi korelaciis koe
Page 239 and 240: Tavi XIX dispersiuli analizi (ANOVA
Page 241 and 242: Cven gvaqvs sakmarisi safuZveli dav
Page 243 and 244: fexburTi kalaTburTi xelburTi ------
Page 245 and 246: gazze benzinze eleqtronuli meqaniku
Page 247 and 248: sakredito baraTiT sargeblobisas pro
Page 249 and 250: pasuxebi: 1. H 0 : a 1 a 2 a 3 , H
Page 251 and 252: varianti # 2007.1.1 1. Ada B damouk
Page 253 and 254: ( XY , ) (0.5q.); cov(5 X, 4Y 7) (0
Page 255 and 256: danarTi (statistikuri cxrilebi) k
Page 257 and 258: 1 x N(0.1) -is ganawilebis funqcii
Page 259 and 260: t (stiudentis) ganawilebis zeda -k
Page 261 and 262: 2 (xi kvadrat) ganawilebis zeda -
Page 263 and 264: F( n, m ) (fiSeris) ganawilebis zed
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14. studentma unda Caabaros 4 gamoc
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44. saTamaSo kamaTels agoreben samj
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). A -- pirveli agdebisas movida 1
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81. msrolelis mier samiznis daziane
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literatura 1. g. mania. albaTobis T
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