Bofokoli ka ipabola: mehlala abel. guttate bofokoli

Bofokoli and analysis - ya dipalopalo ho ithuta mokhoa ho bontša ho itšetleha ya paramethara ba le 'ngoe kapa ho feta ikemetseng divariabole. Ka ea puso ea pele ho mehla ea k'homphieutha, e sebelisa e bile ena thata, haholo-holo tabeng ea ho meqolo kgolo ya data. Kajeno, ho ithuta mokhoa oa ho haha ka bofokoli ka ipabola, o ka rarollang mathata a rarahaneng dipalopalo ka mor'a metsotso e seng mekae feela. Ka tlaase mona ho mehlala e itseng ea moruo.

mefuta bofokoli

khopolo ena ile tsebisoa mmetse ya motheo wa ka Francis Galton ka 1886. Bofokoli ke:

• guttate;
• parabola;
• matla;
• kholo;
• hyperbolic;
• kholo;
• logarithmic.

MOHLALA 1

Nahana ka bothata ba ho laola ho itšetleha ya palo ea tlogela tiro ya ditho tsa lere la moputso karolelano ka 6 likhoebo le liindasteri.

Mosebetsi. Tse tsheletseng lik'hamphani li hlahlobisisa ka karolelano moputso oa khoeli 'me palo ea basebetsi ba tlohela ka boithaopo. Foromo tafola re na:

	A	B	C
1	X	Palo ya tlogela tiro	moputso
2		featswan	30000 li-ruble
3	1	60	35000 li-ruble
4	2	35	40000 li-ruble
5	3	20	45000 li-ruble
6	4	20	li-ruble 50,000
7	5	15	55000 li-ruble
8	6	15	60000 li-ruble

Bakeng sa bothata ba ho laola ho itšetleha ya basebetsi chelete karohano ho tloha moputso karolelano ya 6 likhoebo bofokoli ea mohlala o na le sebōpeho sa abel Y = sa ₀ + sa _1: x ₁ + ... + e _K: x _K, moo x, _kea - susumetsa divariabole, e _kea - bofokoli coefficients, AK - nomoro ea lintlha.

Y bakeng sa mosebetsi o itseng - e ke pontshi ho mollo mosebeletsi, ka ho tlatsetsa ha ntlha e - sa moputso, e leng e denoted ke X.

Ho sebelisa matla a "ipabola" seporeteshiti

Bofokoli and analysis ka ipabola lokela ho etelloa pele ke kōpo ea ho ya data tse teng tafole a haha-ka mesebetsi. Leha ho le joalo, bakeng sa merero ea tsena ho molemo ho sebelisa ba molemo haholo agregar a-ka "pakete and analysis". Ho etsa hore ho, o lokela ho:

• le tab ya "File" ea "Settings";
• ka fensetere eo e qala, khetha 'Add-ons';
• tobetsa konopo "E-eang", teng ka ho le letona ka tlase ya mola "taolo ya";
• beha letšoao cheke e haufi le "Analysis ToolPak" le netefatse ketso ya hao ya ka phehella "OK".

Ha etsoa ka nepo, lehlakoreng le letona la "Data" tab ya, teng ka holimo ho lakane mosebetsi "ipabola", e bontša konopo batlang.

Guttate bofokoli ka ipabola

Hona joale hore u na le ka letsohong le hlokahala lisebelisoa tsohle ho ka thoeng ho dipalelo econometric, re ka qala ho rarolla bothata ba rōna. Ho etsa sena:

• konopo e tlanya ka "Data Analysis";
• tobetsa konopo "bofokoli" ka fensetere bulehileng;
• e tab ya le hlahang ho hlahisa mefuta e fapaneng ya makgabane Y (palo ea basebetsi ba karohano) le X (moputso bona);
• tiisa liketso tsa bona ka phehella le «Ok» konopo.

Ka lebaka leo, lenaneo lena le tla ka tsela e iketsang tlatsa e ncha lakane seporeteshiti ya data bofokoli hlahlojoe. Lefa a lebisa tlhokomelo! Ka ea fetisisang, ho na le monyetla oa ho beha sebaka hore u khetha bakeng sa morero ona. Ka mohlala, e ka 'na ea e-ba lakane e tšoanang, moo melemo Y le X, kapa esita le buka e ncha, ka ho toba etselitsoe bakeng sa polokelo ya data joalo.

diphetho bofokoli and analysis bakeng sa R-lisekoere

Ya data ipabola fumana ka ya data nkoa mohlala na mofuta o le:

Pele ho tsohle, re lokela ho ela hloko ho boleng ba R-disekwere. Ho emela coefficient la boikemisetso ba. Ka mohlala ona, R-lisekoere = 0.755 (75,5%), m. E. The entsprechen balwa ya ea mohlala oa ho hlalosa kamano pakeng tsa entsprechen ho nkoa ke 75,5%. A phahameng boleng ba coefficient la boikemisetso, ea mohlala kgethile e nkoa e le ea bohlokoa ho feta bakeng sa mesebetsi e itseng. Ho lumeloa hore ka nepo ho hlalosa boemo ba sebele ka boleng R-lisekoere holimo 0,8. Ha R-lisekoere <0.5, ka nako eo e and analysis bofokoli ka ipabola ka hore ho talingoe ho kahlolo e molemo.

and analysis karo-karolelano

Number 64,1428 bontša seo e tla ba bohlokoa ba Y, haeba divariabole tsohle XI ka ea mohlala oa rōna o tla ba le ho seta botjha. Ka mantsoe a mang, e ka pheha khang ea hore boleng ya paramethara hlahlobisisa e susumetsoa ke lintho tse ling tse ho feta a hlalositsoeng ka ea mohlala e itseng.

Ntlha latelang -0,16285 sebakeng B18 seleng, bontša tšusumetso ea bohlokoa ea polygonal X ho Y. Sena se bolela hore moputso oa karolelano ea basebetsi ka hare ho ea mohlala e amang palo ea tlogela tiro tloha boima ba -0,16285, 't. E. le tekanyo ea ho tshusumetso lona ho hang e nyenyane. pontšo "-" e bontša hore ho coefficient e mpe. Ho totobetse, kaha kaofela ha rōna re tsebe hore moputso ho feta ka kgwebo, e leng batho ba ka tlaase ho moo ba boletse hore o lakatsa ho a fedise ho le konteraka ea mosebetsi kapa leleka.

bofokoli multiple

Tlas'a lentsoe lena le bolela ho abel buisana le divariabole 'maloa e ikemetseng ea mokgwa:

featswan = o f (x, ₁ + x, ₂ + ...: x _limithara) + ε, moo featswan - ke tšobotsi lintlha (e itšetlehileng ka polygonal), 'me a x _1, x, _2, ...: x _m - ke matšoao lintlha (ikemetseng divariabole).

paramethara fopholetsa

Bakeng sa multiple bofokoli (Mr) e etsa e sebelisa bonyane dikwere mokhoa (LSM). Bakeng sa ditekanyo guttate ya foromo Y = ka + e b _1: x _{1 + ... + e b limithara: x limithara +} ε haha tsamaiso ea ditekanyo tloaelehile (cm,. Ka tlaase mona)

Ho utloisisa molao-motheo oa mokhoa, re nahane ka taba e 'meli-Ntlha e. Ka nako eo re boemo bo hlalositsoeng ke moralo wa

Kahoo, re fumana:

moo σ - ke fapanago ba tšobotsi e fapaneng, bonahatsoa-index ya.

MNC e sebetsa ho abel Mr ho standartiziruemom tekanyo e. Tabeng ena, re fumana abel:

moo t la _{featswan, 't: x 1, ...'} t _xm - standartiziruemye divariabole oo makgabane karolelano di 0; β _kea - ditekanyetos bofokoli coefficients le kheloha molao-motheo - 1.

Ka kopo ela hloko hore bohle β _kea tabeng ena ho hlalosoa e le ho boetse maemong le tsentraliziruemye hona ka papiso pakeng tsa nkoa e sebetsang le e amohelehang. Ho phaella moo, ho e amohela ho phetha screening mabaka, lahla tseo o nang le melemo e tlaase-tlaase tsa βi.

The bothata ba ho sebelisa guttate bofokoli abel

A re re u na le tafole ea dipharologanyo tsa theko ea ho khetheha sehlahisoa N bakeng sa likhoeli tse fetileng 8. Hoa hlokahala ho etsa qeto ea hore na fumana tsa mokha oa hae oa ka theko ea 1850 li-ruble. / T.

	A	B	C
1	khoeli	lebitso la khoeli	theko n
2	1	January	1750 li-ruble ka ton
3	2	February	1755 li-ruble ka ton
4	3	March	1767 li-ruble ka ton
5	4	Mmesa	1760 li-ruble ka ton
6	5	E se eka	1770 li-ruble ka ton
7	6	June	1790 li-ruble ka ton
8	7	July	1810 li-ruble ka ton
9	8	Phato	1840 li-ruble ka ton

Ho rarolla bothata bona ka tafola lab "ipabola" hlokahala ho sebelisa se tsebahala ka mohlala sesebelisoa "Data Analysis" hlahiswa mona ka hodimo. Ka mor'a moo, khetha "bofokoli" karolo le beha entsprechen. Re lokela ho hopola hore ba ka, "Keletso ho mefuta e fapaneng Y» lokela ho tsebisoa mefuta e fapaneng ya makgabane ea polygonal itšetlehileng ka (tabeng ena theko ea thepa e ka likhoeli tse itseng tsa selemo) le ka "Keletso ho karohano X» - tsa e ikemetseng (khoeli ea). Re tiisetsa bohato ka ho tobetsa «Ok». Ka pampiritiro e ncha (haeba e le ho bontšitsoe), re fumana ya data ho bofokoli ba.

Re haha ho tsona guttate abel ya foromo featswan = selepe + e b, moo e le entsprechen le b-ke coefficients tloha moleng nomoro la khoeli le lebitso la coefficients le «Y-motsoako" mocheng oa lakane le diphetho tsa and analysis bofokoli. Kahoo, guttate bofokoli abel (shishe ka) 3 bakeng sa bothata ka ho ngoloa e le:

Theko ea thepa N = 11,714 * 1727.54 khoeli palo +.

kapa notation aljebra

featswan = 11.714 x, + 1727,54

ho hlahloba sephetho

Ho etsa qeto ea hore na ba ile ba fumana ho lekaneng guttate bofokoli abel sebedisa coefficients multiple Correlation (de hat karaoke dc) le boikemisetso hammoho le teko 'me Fisher e t-teko. Ka tafole "ipabola" bofokoli ba le liphello tse sa ba ho sebetsa tlas'a mabitso a mangata R, R-Square, F-t-Lipalo-palo le lipalo-palo, ka ho latellana.

KMC R nolofalletsa ho hakanya ho katamelano kamano ea probabilistic pakeng divariabole ikemetseng le itšetlehileng ka eona. boleng lona phahameng e bontša e matla mabapi lekana pakeng tsa polygonal "Number la khoeli" 'me a "N theko Product ka li-ruble ka ton 1." Leha ho le joalo, sebōpeho sa kamano ena e sa tsejoeng.

The boholo ba lisekoere tsa coefficient la boikemisetso ba R ² (RI) ke tšobotsi e hlaheletseng sa dinomoro tsa palo ea palo yohle qhalakana 'me se bontša e hasanya la karolo liteko ya data, i.e., makgabane ea polygonal itšetlehileng ka ho ngollana ya guttate bofokoli abel. Ka bothata bona, boleng ena ke 84,8%, mp. E. Lipalo-palo ka tsela e itseng e phahameng ea ho nepahala fumana ba hlalosoa SD.

F-Lipalo-palo, tsejoang hape e le Fisher criterion sebelisoa ho hlahloba bohlokoa ba ho itšetleha guttate kapa disproving khopolo tiisang teng.

Boleng ba t-lipalo-palo (Seithuti sa e sa t teko) thusa ho hlahloba se boleloang ke coefficient le ka mahala e sa tsejoeng guttate setho sefe kapa sefe ho itšetleha. Ha boleng ba t-teko> sa t _thuong, le khopolo tsa guttate abel letho ea bolokolohi poleloana e reng e hana.

Ka bothata bona bakeng sa mahala poleloana e reng ka liletsa "ipabola" ho ile ha fumanoa hore 't = 169,20903, le leq = 2,89E-12,' t. E. ba le lefela kgonego hore ba tšepahalang ba tla hana khopolo ea letho ea mahala telele. Bakeng sa coefficient sa tsejoeng ho sa t = 5,79405, le leq = 0,001158. Ka mantsoe a mang, le kgonego ya hore a hana nepahetse khopolo tla letho tsa coefficient bakeng sa tsejoeng, ke 0,12%.

Kahoo, ho ka beha lebaka la hore o ile a fumana guttate bofokoli abel lekaneng.

The bothata ba advisability ho reka dishere

Multiple length bofokoli ile a etsa ka ho fetisisang ho sebelisa e tšoanang "Data Analysis" sesebelisoa. Nahana ka kopo e itseng.

Guide khampani «NNN» lokela ho etsa qeto hore na ho reka 20% ya dishere tsa JSC «MMM». Sephutheloana theko (sp,) e limilione tse 70 liranta US. Ditsebi ea «NNN» bokella ya data ka ditransekshene tšoanang. Ho ile ha etsoa qeto ea ho hlahloba boleng ba dishere ka entsprechen joalo, a bontša hore ka limilione tsa liranta US, tse kang:

• duelelwang (vk);
• letseno selemo le selemo ba modumo (Vo);
• amogetsweng (VD);
• boleng ba thepa e tsitsitseng (SOF).

Ho phaella moo, sebelisa melato moputso oa likhoebo (V3 U) ka liranta tse likete US.

Qeto tafole lab ipabola ho bolela

Pele u lokela ho bopa tafole ya data input. Ho ka tsela e latelang:

Next:

• pitso lebokose le reng "and analysis ya data";
• kgethile "bofokoli" karolo;
• fensetere "Keletso ho karohano Y» laolwa mefuta e fapaneng e itšetlehileng polygonal makgabane tswa lenaneng la G;
• tobetsa aekhoneng e ka motsu o mofubelu ho le letona la fensetere "Keletso ho karohano X» le ka thōko ka lakane fapaneng ya makgabane kaofela karolong e ngotsoeng B, C, D, F.

Mark ntlha "New pampiritiro" o tobetsa "Ok".

Fumana bofokoli and analysis bakeng sa mosebetsi ona.

Liphetho li ithuta le ho etsa liqeto

"Phuthehang" lekaneng ho tloha ya data hlahiswa ka holimo ho lakane tafole ipabola lab bofokoli abel:

SD = 0,103 * SOF + 0,541 * Vo - 0.031 * vk + 0,405 * VD + 0,691 * VZP - 265.844.

Ka ho feta e tloaelehileng foromo thuto ea lipalo e ka ngotsoe e le:

featswan = 0.103 * x1 + 0,541 * x2 - 0.031 * x3 + 0,405 * x4 + 0,691 * x5 - 265.844

Data ho «MMM» JSC fanoa ka tafole ka tlase:

SOF, USD	Vo, USD	Vk, USD	VD, USD	VZP, USD	JV, USD
102,5	535,5	45,2	41,5	21,55	64,72

A emeng ka bona bofokoli abel, o ile a fumana setšoantšo sa lidolara US milione 64,72. Sena se bolela hore o bolella ba JSC «MMM» lokela ho ke ke ea reka, hobane theko ea bona e haholo overpriced ho liranta US limilione tse 70.

Joalokaha u ka bona, ho sebelisa seporeteshiti "ipabola" le bofokoli abel lumelloa ho etsa qeto e tsebisoa eng mabapi le advisability kgwebisano itseng haholo.

Hona joale ua tseba hore na bofokoli. Mehlala hore li ipabole, tšohloa ka holimo, ho tla u thusa ho rarolla mathata a sebetsang oa econometrics.