
parasparsanvad (aakadevari)

sankhyikimadhye, teen kinwa adhik chalanmadhil sambandhancha vichar kartana parasparkriya udbhavu shakate aanee asha paristhitiche varnan karate jyamadhye eka karanatmak chalcha parinam nikalavar dusya karanatmak chull sthitivar avalambun asato (mhanje, jevha done karananche parinam yojak nasatat). jaree samanyatah karanatmak sambandhanchya sandarbhat vichar keela jaat asala, taree parasparsanvadachi sankalpana karanaheen sambandhanche varnan dekhil karoo shakate (nantar tyala 'sanyam' kinwa 'parinam badal' asehi mhanatat). parasparsanvadancha vichar anekada pratigaman vishleshan kinwa factorial prayoganchya sandarbhat keela jaato.
parasparsanvadachya upasthitiche sankhyikeey pratimanchya vyakhyesathi mahattvache parinam houu shakatat. jarr swarsyache done chull parasparsanvad sadhat asateel, tarr parasparsanvadi chull aanee tisra "aashrit chull" yanchyatil sambandh itar parasparsanvadi chalanchya mulyavar avalambun asato. vyavharat, yamule chalche moolya badalanyachya parinamancha andaj lavane adhik katheen hote, visheshtah jarr teey jyaa chalanshi sanvad sadhatat teey mojane katheen asel kinwa niyantrit karane katheen asel.
parasparsanvad" yaa kalpanecha samajik aanee aarogya vidnyan sanshodhanat samanya asalelya sanyamashi jawalcha sambandh aaheh spashtikaranatmak chull aanee paryavaraniy chull yanchyatil parasparsanvad asey soochit karato qee spashtikaranatmak chull prabhav paryavaraniy chaladware niyantrit kinwa sudharit keela gela aahe.
parichay.
parasparsanvad chull kinwa parasparsanvad vaishishtya heey eka asey chull aahe jeey upasthit asalelya serve parasparsanvadache kinwa tyateel kahee bhagache pratinidhitva karnyacha prayatna karnyasathi chalanchya mool sanchatoon tayar kele jaate. shodhatmak sankhyikeey vishleshananmadhye nantarchya tappyat itar adhik vastavadi parasparsanvad chalanchya jaagi badalanyachi shakyata asalelya parasparsanvadat aahe qee nahee yachee chachani karnyacha aadhar mhanoon mool chalanchi utpadane vaparane samanya aahe. jevha donpeksha jaast spashtikaranatmak chull asatat, tevha anek parasparsanvad chull tayar kele jaatat, jyat jodinusar utpadane jodinusar parasparsanvad darshavtat aanee uchch kram utpadane uchch kram parasparsanvad darshavtat.
asha prakare, "y" aanee done chull "x" 1 aanee "x" 2 yaa pratisadasathi eka "yojak" model asey aselah
yaulat,
x" 1 aanee "x" 2 yaa chalanmadhil "parasparsanvad" asalelya pratimanache heey eka udaharan aahe ("truti" mhanje yadruchchik chull jyache moolya "y" chya apekshit mulyapeksha vegale aahe; aakadevaritil truti aanee avashisht pahaa). anekada, parasparsanvadachya sandnya sootra _ 3shivay namune sadar kele jaatat, parantu yamule mukhya parinam aanee parasparsanvadacha parinam gondhalat padato (i.eae.parasparsanvadachi sandnya nirdisht naan karata, aadhalanara konatahi mukhya parinam pratyakshat parasparsanvadamule asanyachi shakyata aahe).
modelingmadhye.
anovamadhye.
parasparsanvad udbhavu shakato ashee eka sadhee mandani mhanje dvi-ghatak prayog, jyache vishleshan bhinnateche (enova) vishleshan karoon kele jaate. samaja, aaplyakade 'aaa' aanee 'buub' heey done dwaiti ghatak aahet. udaharanarth, heey ghatak soochit karoo shakatat qee donpaiki eka upchar rugnala denyat aale hote qee nahee, upchar ektar ektyane kinwa ektritpane lagoo kele gele. tyanantar aapan upcharanchya sarasari pratisadacha vichar karoo shakato (udaa.jee. upcharanantarchi lakshane patali) pratyek rugnasathi, upchar sanyojanache karya mhanoon. khaleel taktyat eka sambhavya paristhiti darshavili aaheh
yaa udaharanat, done upcharanmadhye konatahi parasparsanvad nahee-tyanche parinam mishrit aahet. yache kaaran asey qee, 'aaa' upchar ghenanya aanee 'aaa' upchar naan ghenanya vyaktinmadhye sarasari pratisadatil farak-2 aahe, mug 'buub' upchar deela jaato (-2 = 4-6) kinwa nahee (-2 = 5-7). lakshat ghya qee, 'aaa' varr upchar kele jaatat qee nahee yachee parva naan karata, 'buub' varr upchar ghenare aanee 'buub' varr upchar naan ghenare heey vyakti yanchyatil sarasari pratisadatil farak samaan aahe (7−6 = 5−4).
yaulat, jarr khaleel sarasari pratisad pahile gele tarr
mug upcharanmadhye parasparsanvad hoto-tyanche parinam yojak nasatat. adhik sankhya changlya pratisadashi sambandhit aahe asey samaja, yaa paristhitit jarr vishayavar 'aaa' upcharhi hott nasel tarr upchar 'buub' sarasarine upayukt tharato, parantu upchar 'aaa' chya sanyogane dilyas sarasari hanikarak tharato. buub' haah upcharhi deela jaato qee nahee yachee parva naan karata 'aaa' haah upchar sarasarine upayukt aahe, parantu 'buub' yaa upcharanchya sanyojanaivaji, ektyane dilyas too paripoorn aanee sapeksh asha donhi drushtine adhik upayukt aahe. pudhil vibhagat yaa vishisht udaharanasathi samaan nirikshane kelee aahet.
gunatmak aanee parimanatmak parasparsanvad.
anek upayoganmadhye gunatmak aanee parimanatmak parasparsanvadanmadhye farak karane upayukt aahe. aaa" aanee "buub" yanchyatil parimanatmak parasparkriya hii ashee paristhiti aahe jithe "buub" chya prabhavachi tivrata "aaa" chya mulyavar avalambun asate, parantu "buub" chya prabhavachi disha serve "aaa" sathee sthir asate. aaa" aanee "buub" yanchyatil gunatmak parasparsanvad mhanje ashee paristhiti jithe pratyek chull prabhavache pariman aanee disha donhi itar chalanchya mulyanvar avalambun asoo shakatat.
khalee davya bajula asalelya sadhananchya taktyat, eka parimanatmak parasparkriya darshavili aahe-jevha 'buub' deela jaato aanee jevha 'buub' deela jaat nahee, tevha upchar 'aaa' fayadeshir asato, parantu jevha 'buub' deela jaat nahee tevha fayda jaast asato (i.eae. jevha "aaa" ektyane dile jaate). ujavikadil sadhananchi sarani gunatmak parasparkriya darshavate. "aaa" "jevha" "buub" dile jaate tevha teey hanikarak asate, parantu jevha "" buub "dile jaat nahee tevha teey fayadeshir asate". lakshat ghya qee jarr aapan 'aaa' deela aahe qee nahee yachya aadhare 'buub' chya fayadhyacha vichar keela tarr toch arth lagoo hoil.
gunatmak aanee parimanatmak parasparsanvadanmadhil farak haah chalancha vichar konatya kramane keela jaato yavar avalambun asato (yaulat, jodanicha gunadharm chalanchya kramanusar aparivartaniy asato). pudhil taktyat, jarr aapan 'aaa' upcharachya parinamavar laksh kendrit kele tarr eka parimanatmak parasparkriya aahe-'aaa' upchar dilyas, 'buub' upchar aadhich deela jaat aahe qee nahee yachee parva naan karata sarasari parinam sudharel (jaree 'aaa' upchar ektyane dilyas fayda jaast aahe). tathapi, jarr aapan 'buub' upcharachya parinamavar laksh kendrit kele tarr eka gunatmak parasparkriya hote-aadhich 'aaa' upchar ghet asalelya vyaktila 'buub' upchar dilyas (sarasari) paristhiti bighadel, tarr jyaa vyaktila 'aaa' upchar milat naheet tyala 'buub' upchar dilyas sarasari parinam sudharel.
ekak upchar jodani.
tyachya sarvat sopya swarupat, upchar ekak sankalanachya gruhitkamadhye asey mhatale aahe qee upchar "jeey" prapt kartana prayogik ekak "aay" pasoon aadhalalela pratisad "vaay" "aayji" hii berries "vaay" "aayji" = "vaay" "aay" + "" tii "" jeey "mhanoon lihili jaau shakate. ekak upchar jodanichi dharana asey soochit karate qee pratyek upcharancha pratyek prayogik ghatkavar agadi samaan jodani prabhav asato. konatehi prayogik ekak keval eka upcharatoon jaau shakat asalyane, cocks aanee kempthorn yanchya matey, ekak upchar jodanichi dharana heey eka asey gruhitak aahe jeey thet khote nahee.
tathapi, upchar-ekkachya jodaniche anek parinam khote asoo shakatat. yadruchchik prayogasathi, upcharanchya jodanichi dharana soochit karate qee serve upcharansathi farak sthir aahe. mhanoon, pratirupanadvare, ekak upcharatil jodanisathi eka aavashyak aut mhanje farak sthir aahe.
ekak upchar jodanicha gunadharm pramanatil badalantargat aparivartaniy nasato, mhanoon sankhyikishastradnya sahasa ekak upchar jodani prapt karnyasathi parivartan vapartat. jarr pratisad chull sambhavyata vitaranachya parametric kutumbache anusaran karane apekshit asel, tarr sankhyikishastradnya (prayog kinwa nirikshan abhyasasathichya protocolmadhye) spasht karoo shakato qee farak sthir karnyasathi pratisadanmadhye badal keela jaeel. anek prakarananmadhye, sankhyikishastradnya heey nirdisht karoo shakato qee gunakar pratikrutiche anusaran karananya pratisadanvar laghuganak rupantaran lagoo kele jaave.
kempthorn aanee cocks yanni prayogik rachnet ekak upchar jodanichi dharana spasht kelee. kempthorncha ekak upchar jodani aanee yadruchchikatecha vapar haah maryadit loksankhya sarvekshan namunyanchya rachana-aadharit vishleshanasarkhach aahe.
alikadchya varshant, donald rubinchi shabdavali vaparane samanya jhaale aahe, jee prati-vastusthiti vaparte. samaja aapan kahee gunavishesh "y" chya sandarbhat lokanchya done gatanchi tulana karat aahot. udaharanarth, pahilya gatat asey lock asoo shakatat jyanna vaidyakeey sthitisathi manak upchar dile jaatat, tarr dusya gatat asey lock asatat jyanna adnyat parinamasah naveen upchar midatat. prati-vastusthiti" drushtikon ghetalyas, aapan asha vyakticha vichar karoo shakato jyachya gunavisheshache moolya "y" aahe, jarr tee vyakti pahilya gatachi asel aanee jyachya gunavisheshache moolya "τ" ("y") asel, jarr tee vyakti dusya gatachi asel. ekak upchar jodani" chee dharana ashee aahe qee "τ" ("y") = "τ", mhanje "upchar parinam" haah "y" varr avalambun nasato. aapan dilelya vyaktisathi 'y' aanee 'y' ('y') donhiche nirikshan karoo shakat naslyamule, heey vaiyaktik staravar tapasanyayogya nahee. tathapi, ekak upchar jodani mhanje done gatansathi sanchayi vitaran karye "f" 1 aanee "f" 2 purn karatat 
"f" "2 (" "y" ") =" "f" "1 (" "y−τ" "), joparyant 1 aanee 2 gatanna vyaktinchi nemanook" "y" "(i) varr prabhav takna itar serve ghatakanpasun swatantra aahe".eae. konatehi gondhal karnare naheet). ekak upchar jodanicha abhav haah upchar assignmentmadhil parasparsanvadacha eka prakar mhanoon pahila jaau shakato (udaa.jee. gut 1 kinwa 2), aanee "y" chey baseline kinwa upchar naan kelele moolya.
shrenibaddha chull.
kadhikadhi parasparsanvadi chull heey vastavik sankhyanaivaji shrenibaddha chull asatat aanee nantar abhyasala bhinnatechya samasyeche vishleshan mhanoon hatalale jaau shakate. udaharanarth, loksankhyechya sadasyanche dharm aanee vyavasayanusar vargikaran kele jaau shakate. jarr ekhadyala keval tyaa vyakticha dharm aanee vyavasay yavar aadharit ekhadya vyaktichya unchicha andaj lavayacha asel tarr eka sadhe 'yojak' model, mhanje.eae.parasparsanvad nasalele eka model, ekoon sarasari unchimadhye eka vishisht dharmasathi aanee dusya vishisht vyavasayasathi samayojan karel. parasparsanvad asalele eka pratirup, eka sanyoji pratirupachya ulat, too dharm aanee too vyavasay yanchyatil "parasparsanvadasathi" aanakhi samayojan karoo shakate. yaa udaharanamule ekhadyala sanshay yeu shakato qee 'parasparkriya' haah shabd kahitari chukiche naav aahe.
sankhyikiyadrushtya, shrenibaddha chalanmadhil parasparsanvadachya upasthitichi chachani samanyatah bhinnatechya vishleshanachya prakaracha (enova) vapar karoon kelee jaate. tathapi, jarr eka kinwa adhik chull satatche swarupache asateel, tarr samanyatah moderated multiple regression vaparoon tyachi chachani kelee jaeel. yala asey mhanatat kaaran madhyasth haah eka chull aahe joou itar done chalanmadhil sambandhanchya samarthyavar parinam karato.
prayoganchi rachana.
jenichi taguchi yanni assa yuktivad keela qee pratisad chull aanee parivartanachya yogya nivadidvare parasparsanvad pranalitoon kadhoon takale jaau shakatat. tathapi, george boxes aanee itaranni assa yuktivad keela aahe qee sarvasadharanpane asey hott nahee.
model aakar.
aine" andajak dile tarr, resheey modelmadhil sandnyanchi sankhya jyamadhye sthirank, pratyek andajak aanee pratyek sambhavya parasparsanvadacha samavesh aahe teey sootra 4 aahe. heey praman vegane vadhat asalyane, teey sahajpane avyavaharikdrushtya mothe hote. pratimanacha aakar maryadit karanyachi eka paddhat mhanje parasparsanvadacha kram maryadit karane. udaharanarth, jarr keval dwimukh parasparsanvadas parvanagi asel tarr sandnyanchi sankhya sootra 5 banate. khaleel taktyat pratyek sankhyechya andajkartyansathi sandnyanchi sankhya aanee parasparsanvadacha kamal kram darshavila aahe.
pratigaman.
parasparsanvadachya parinamanchya modelingchya sarvat samanya drushtikonat, varr dilelya prathamik aavruttipasun suru houn, pratigaman samavisht aaheh
jethe parasparsanvadache sootra _ 7 heey done (kinwa adhik) chalancha gunakar karoon kinwa statasarkhya aadhunik sankhyikeey sankulanmadhye apratyakshapane factorial notation vaparoon spashtapane tayar kele jaau shakate. x" 1 aanee "x" 2 heey ghatak mojmap kinwa konatyahi sanyogatil {0,1} dummy chull asoo shakatat. mapan chalane gunile dummy chull samavisht asalelya parasparsanvadanna 'slope dummy variables' mhanatat, kaaran teey 0 aanee 1 gatanmadhil utaranmadhil farkacha andaj lavtat aanee tyachi chachani ghetat.
jevha parasparsanvadamadhye mojmap chull vaparale jaatat, tevha kendrit aavrutyansah kaam karane bahutek vela isht asate, jethe chalchi sarasari (kinwa itar kahee vajvi kendriya moolya) shoonya mhanoon seet kelee jaate. parasparsanvadachya pratikrutinmadhil mukhya parinam kendrikaranamule adhik arth lavnyayogya houu shakatat, kaaran yamule parasparsanvadachi sandnya aanee mukhya parinam yanchyatil bahurekheeyata qamee hote. udaharanarth, vareel samikaranatil gunank 'aaa', jevha 'x' 2 haah shoonyachya barobaricha asato tevha 'x' 1 chaa parinam darshavito.
parasparsanvad modelingsathi pratigaman drushtikon khoop samanya aahet kaaran teey atirikt bhavishyasuchak aanee samanya kiman chaurasanchya palikade anek paryayi vaishishtye kinwa andaj dhorane samavoon gheu shakatat. majboot, parimanatmak aanee mishra-parinam (bahustareey) models heey shakyatanpaiki aahet, tasech samanyikrut resheey modelingmadhye shrenibaddha, krambaddha, mojalele kinwa anyatha maryadit avalambun asalelya chalanchi vistrut shreni samavisht aahe. sarvekshan mahitichya sambhavyata-bharit loggit pratigaman vishleshanatun aalekh shaikshanik * rajkiy parasparsanvad darshavito.
parasparsanvadache plot.
parasparsanvadache bhukhand, jyanna sadhe-utaar bhukhand dekhil mhanatat, teey chalanmadhil sambhavya parasparsanvad darshavtat.
udaharaneh prajati aanee haveche tapman yancha parasparsanvad aanee sharirachya tapmanavar tyancha parinam.
vegvegalya prajatinchya sharirachya tapmanacha abhyas vegvegalya havechya tapmanat, degree fahrenheitmadhye vicharat ghya. hii mahitee khaleel taktyat darshavili aahe.
parasparsanvadacha aalekh ektar haveche tapman kinwa prajaticha x aksh mhanoon vapar karoo shakato. dusra ghatak parasparsanvadachya rachnevaril reshandvare darshavila jaato.
pratisadavar (sharirache tapman) honanya prabhavamadhye done ghatakanmadhye (haveche tapman aanee prajati) parasparsanvad aahe, kaaran havechya tapmanacha prabhav prajatinvar avalambun asato. parasparsanvad bhukhandavar darshavila jaato kaaran resha samantar nasatat.
udaharaneh mastishkaghatachya tivratecha aanee barey honyavar upcharancha parinam.
dusare udaharan mhanoon, strokechi tivrata aanee rugnachya astitvavar aushadhachi parinamkarakta yanchyatil parasparsanvadavar vaidyakeey chachanicha vichar qaraa. hii mahitee khaleel taktyat darshavili aahe.
parasparsanvadachya rachnet, saumya aanee madhyam stroke gatansathichya resha samantar asatat, jeey soochit karatat qee aushadhacha donhi gatanmadhye samaan parinam hoto, tyamule parasparsanvad hott nahee. tivra stroke gatachi resha itar reshanna samantar nasate, jee strokechi tivrata aanee jaganyavar aushadhancha parinam yanchyat parasparkriya asalyache soochit karate. gambhir stroke gatasathichi resha sapat aahe, jeey soochit karate qee, yaa rugnanmadhye, aushadh aanee placebo upcharanmadhye jaganyat konatahi farak nahee. yaulat, saumya aanee madhyam stroke gatansathichya resha ujavikade khalee sarakatat, jeey soochit karate qee, yaa rugnanmadhye, aushadh-upcharit gatapeksha placebo gut qamee tikato.
parasparsanvadasathi gruhitak chachanya.
bhinnateche vishleshan aanee pratigaman vishleshan heey lakshaniy parasparsanvadachi chachani karnyasathi vaparale jaate.
udaharaneh kuki beckingmadhe tapman aanee velecha parasparsanvad.
baking tapman aanee ovhanmadhil velemule changlya kukeejchya utpannavar parinam hoto qaa? table kukeejchya 8 batchessathi deta darshavite.
deta darshavito qee changlya kukijche utpadan tevha sarvottam asate jevha ektar (i) tapman jaast asate aanee ovhanmadhye vel qamee asato kinwa (ii) tapman qamee asate aanee ovhanmadhye vel jaast asato. jarr cookies jaast tapmanat ovhanmadhye barach vel thevalyas, tyaa jalalelya cookies asatat aanee utpadan qamee asate.
aalekh aanee mahitivarun heey spasht hote qee resha samantar naheet, jeey parasparsanvad asalyache darshavate. bhinnateche vishleshan (enova) vaparoon yachee chachani kelee jaau shakate. pahilya enova modelmadhye parasparsanvadachi sandnya samavisht kelee jaanar nahee. mhanje, pahile enova model sambhavya parasparsanvadakade durlaksh karate. dusya enova modelmadhye parasparsanvadachi sandnya samavisht asel. mhanjech, dusare enova model parasparsanvadasathi spashtapane gruhitak chachani karate.
enova model 1: parasparsanvadachi sandnya nahee; utpann ~ tapman + vel.
parasparsanvadakade durlaksh karananya enova modelmadhye, tapman kinwa velecha utpannavar lakshaniy parinam hott nahee (pii = 0.91), joou spashtapane chukicha nishkarsh aahe. adhik yogya annova modelane sambhavya parasparsanvadasathi chachani kelee pahije.
enova model 2: parasparsanvadachi sandnya samavisht qaraa; utpann ~ tapman * vel.
tapmanah velecha parasparsanvad hii sandnya lakshaniy aahe (pii = 0.000180). parasparsanvad chachani aanee parasparsanvadachya rachnevar aadharit asey disate qee velecha utpannavar honara parinam tapmanavar avalambun asato aanee ulat.
udaharane.
parasparsanvadachya vastavik jagachya udaharananmadhye khaleel goshtincha samavesh hotoh