Mgwirizano mu kupambana: Zitsanzo aone kuti pali. liniya mgwirizano

Mgwirizano kusanthula - ndi zowerengera kuphunzira njira kusonyeza kudalira kwa chizindikiro chimodzi kapena zinthu pawokha zosintha. Masiku chisanadze computer, ntchito zake wakhala m'malo ovuta, makamaka pamene zinafika mabuku lalikulu deta. Lero, kuphunzira m'mene tingamangire ndi mgwirizano mu kupambana, mungathe kuthetsa mavuto zovuta zowerengera mu maminiti pang'ono chabe. M'munsimu muli zitsanzo za zachuma.

mitundu mgwirizano

Mfundo imeneyi anadziŵa Masamu ndi Francis Galton mu 1886. Mgwirizano ndi:

• liniya;
• parabolic;
• mphamvu;
• kwakukulu kwambiri;
• hyperbolic;
• kwakukulu kwambiri;
• logarithmic.

CHITSANZO 1

Taganizani vuto kudziŵa kudalira chiwerengero cha Kusiya zinchito a anthu ogwira ntchito za malipiro ambiri ku 6 mabizinezi mafakitale.

Ntchito. Six makampani kusanthula pafupifupi malipiro apamwezi ndi chiwerengero cha ogwira ntchito amene amasiya mwaufulu. Mu mawonekedwe tabular tili:

	A	B	C
1	X	Chiwerengero cha Kusiya zinchito	malipiro
2		Y	30000 rubles
3	1	60	35000 rubles
4	2	35	40000 rubles
5	3	20	45000 rubles
6	4	20	rubles 50,000
7	5	15	55000 rubles
8	6	15	60000 rubles

Pakuti kudziŵa kudalira la ogwira kuchuluka Kulekanitsidwa kwa malipiro pafupifupi 6 mabizinezi mgwirizano chitsanzo ali mawonekedwe a aone kuti pali Y = munthu ₀ + ₁ × ₁ + ... + ndi _K × _K, kumene × _ine - kumamukopa zosintha, ndi _ine - mgwirizano koefishienti, AK - chiwerengero cha zinthu.

Y ntchito anapatsidwa - ndi chizindikiro moto wantchito, ndi zikuthandiza chinthu - malipiro, amene amaimira X.

Zitheke mphamvu ya "kupambana" spreadsheet

Mgwirizano kusanthula mu kupambana ayenera yoyamba yofunsira kuti deta zilipo tebulo anamanga-mu ntchito. Komabe, zolinga izi ndi bwino ntchito kwambiri pokha-mu "paketi kusanthula". Ndi zimenezi, muyenera:

• ndi tsamba "Buku" kupita "Zikhazikiko";
• pawindo kuti atsegula, kusankha 'Add-mvu;
• alemba pa batani "Pita", yomwe ili kumanja pansi pa mzere "kasamalidwe";
• kuika Chongani kuti "Analysis ToolPak" n'kutsimikizira kanthu anu ndi kukanikiza "Chabwino".

Ngati mwachita bwino, kumanja kwa "Data" tabu, inali pamwamba pa pepala ntchito "kupambana", zikusonyeza batani ankafuna.

Liniya mgwirizano mu kupambana

Tsopano muli pa dzanja zofunika zipangizo zonse pafupifupi kwa kuwerengetsera econometric Tikhoza vuto lathu. Kuchita izi:

• batani ndi kutsamba pa "Data Analysis";
• alemba pa batani "mgwirizano" mu zenera lotseguka;
• ndi tsamba limene limapezeka kuti atchule osiyanasiyana mfundo Y (chiwerengero cha anthu ogwira ntchito amapatukana) ndi X (malipiro awo);
• Tsimikizirani zochita zawo ndi kukanikiza «Chabwino» batani.

Motero, dongosolo adzakhala basi mudzaze dziko latsopano pepala spreadsheet deta mgwirizano kusanthula. Samalani! Mu kupambana, pali mwayi kukhazikitsa malo amene mungakonde kwa cholinga ichi. Mwachitsanzo, kungakhale pepala chomwecho, kumene mfundo Y ndi X, kapena ngakhale buku latsopano mwapadera kwa kusungiramo deta amenewa.

Zotsatira mgwirizano kusanthula kwa R lalikulu

Deta kupambana zopezera deta ankaona Mwachitsanzo nawo mawonekedwe:

Choyamba, tiyenera kulabadira kufunika R-mbali zonse. Akuimira koyefishienti wa mtima. Mu chitsanzo ichi R lalikulu = 0.755 (75.5%), m. E. The magawo masamu chitsanzo kufotokoza ubale magawo kuonedwa ndi 75.5%. The apamwamba mtengo wa koyefishienti wa mtima, chitsanzo anasankha imatengedwa kuti azithandiza kwambiri pochita makamaka. Akukhulupirira kuti molondola pofotokoza mwaimvetsa pa mtengo R lalikulu pamwamba 0,8. Ngati R lalikulu <0.5, ndiye kuwunika mgwirizano mu kupambana sangatengedwe kukhala wololera.

kusanthula chiŵerengero

Number 64,1428 limasonyeza kodi mtengo wa Y, ngati zosintha zonse XI mu chitsanzo chathu chidzakhala Yambitsaninso. M'mawu ena, akhoza amanena kuti mtengo wa chizindikiro kusanthula zimakhudza zinthu zina kuposa amene anafotokozedwa chitsanzo yeniyeni.

Chinanso -0,16285 ili mu B18 selo, chimasonyeza zofunika za variable X kuti Y. Izi zikutanthauza kuti malipiro pafupifupi antchito mwa chitsanzo amakhudza chiwerengero cha Kusiya zinchito kulemera kwa -0,16285, T. E. The digiri mmene iye konse ang'ono. Chizindikiro "-" akusonyeza kuti koyefishienti ndi negative. N'zoonekeratu popeza tonse tikudziwa kuti malipiro zambiri kumalo a ntchito, anthu zochepa kuti anasonyeza kuti akufuna kutsirizitsa mgwirizanowo ntchito kapena kuganiza.

mgwirizano angapo

Mu mawu akunena kuti anthu aone kuti pali kulankhulana ndi zosintha angapo palokha wa mawonekedwe:

Y = f (× ₁ + × ₂ + ... × _m) + ε, kumene Y - bokosi mphambu (a yozungulira variable), ndipo × _1, × _2, ... × _mamita - ndi zizindikiro zinthu (palokha zosintha).

chizindikiro kuyesa

Pakuti angapo mgwirizano (MR) ndi chinagwira ntchito osachepera mabwalo njira (LSM). Pakuti maikwezhoni liniya wa mawonekedwe Y = munthu + b ₁ × _{1 + ... + b mamita × mamita +} ε kumanga ka maikwezhoni yachibadwa (cm. Pansipa)

Kumvetsa mfundo ya njira, ife taganizirani ziwiri zimenezi. Ndiye ife zimene anafotokoza mfundo

Choncho, timapeza:

kumene σ - ndi masiyanidwe a mbali ziwalo, m'mawu index lapansi.

MNC ntchito kuti anthu aone kuti pali MR kuti standartiziruemom lonse. Pankhaniyi, timachotsa aone kuti pali:

momwe T _Y, T _{× 1, ...} T _xm - standartiziruemye zosintha zimene mfundo pafupifupi ali 0; β _ine - yovomerezeka mgwirizano koefishienti ndi kupatuka muyezo - 1.

Chonde dziwani kuti onse β _ine Pankhaniyi amatanthauziridwa kuti dekhetsa ndi tsentraliziruemye Choncho fanizo pakati pa ankaona chomveka ndi zovomerezeka. Komanso, alandirika kuchita mosamala zinthu, kutaya amene ali ndi makhalidwe wotsikitsitsa βi.

Vuto ndi ntchito liniya mgwirizano aone kuti pali

Tiyerekeze muli ndi tebulo la mphamvu ya mtengo wa makamaka mankhwala N kwa miyezi 8. M'pofunika kusankha kupeza chipani chake pa mtengo wa 1850 rubles. / T.

	A	B	C
1	m'mwezi	Dzina la mwezi	Price N
2	1	January	1750 rubles pa tani
3	2	February	1755 rubles pa tani
4	3	March	1767 rubles pa tani
5	4	April	1760 rubles pa tani
6	5	mulole	1770 rubles pa tani
7	6	June	1790 rubles pa tani
8	7	July	1810 rubles pa tani
9	8	August	1840 rubles pa tani

Kuti athetse vutoli mu tabular purosesa "kupambana" chofunika ntchito kale Mwachitsanzo chida "Data Analysis" anapereka pamwamba. Kenako, kusankha "mgwirizano" gawo ndipo anapereka magawo. Tiyenera kukumbukira kuti "Lowetsani osiyanasiyana Y» ayenera kuyamba kugwiritsa osiyanasiyana mfundo za variable yozungulira (mu nkhani iyi mtengo wa katundu mu miyezi yeniyeni pachaka) ndi "Lowetsani imeneyi X» - chifukwa wodziimira (mwezi). Kutsimikiza kanthu mwa kuwonekera «Chabwino». Mu fomu watsopano (ngati anasonyeza) timapeza deta kwa mgwirizano wa.

Tingamangire pa iwo liniya aone kuti pali mawonekedwe Y = nkhwangwa + b, kumene monga magawo ndi b ndi koefishienti ku mzere nambala ya mwezi ndi dzina la koefishienti ndi «Y-mphambano" mzere wa pepala ndi zotsatira za kuwunika mgwirizano. Choncho, liniya mgwirizano aone kuti pali (Eq) 3 vuto akhoza kulembedwa monga:

Mtengo wa katundu N = 11,714 * 1727.54 mwezi chiwerengero +.

kapena kalembedwe algebraic

Y = 11.714 × + 1727,54

Kupenda Zotsatira

Angasankhe analandira mokwanira liniya mgwirizano aone kuti pali ntchito koefishienti angapo malumikizanidwe (CMC) ndi mtima komanso mayesero Fisher ndi t-mayeso. Mu tebulo "kupambana" mgwirizano ndi zotsatira iwo amachita pansi mayina angapo R, R-Square, F-t-ziwerengero ndi ziwerengero motero.

KMC R chimathandiza chaka cha ubwenzi ubwenzi probabilistic pakati zosintha palokha ndipo yozungulira. Mtengo wake mkulu limasonyeza amphamvu kugwirizana zokwanira pakati pa variable "Number la mwezi" ndipo "N mtengo Mafotokozedwe mu rubles pa matani 1." Komabe, chikhalidwe cha ubwenzi ndi losadziwika.

Khwalala la koyefishienti wa mtima R ² (RI) ndi khalidwe M'ndandanda wa chiwerengero cha okwana kuwanditsa ndipo amasonyeza kuwanditsa gawo experimental deta i.e., mfundo za variable yozungulira lolingana ndi liniya mgwirizano aone kuti pali. Mu vutoli, mtengo uwu 84,8%, mp. E. Kafukufuku ndi digiri yapamwamba molondola analandira akufotokozedwa Sd.

F-ziwerengero amatchedwanso Fisher muyezo ntchito kuwunika tanthauzo la kudalira liniya kapena kutsutsa kungoganizira kutsimikizira linakhalapo.

Mtengo wa t-kuwirikiza kawiri (Wophunzira ndi T mayeso) amathandiza kuunikira tanthauzo la koyefishienti pa ufulu osadziwika liniya aliyense chidakwa. Ngati mtengo wa t-mayeso> T _Kr, ndi kungoganizira ya liniya aone kuti pali kwachabechabe ufulu akuti ali wokanidwa.

Mu vutoli kwa ufulu akuti kudzera zida "kupambana" chinapezeka kuti T = 169,20903, ndipo tsa = 2,89E-12, T. E. Kodi ziro n'kutheka kuti wokhulupirika adzakanidwa ndi ganizo loperekedwa kwa kwachabechabe a mfulu yaitali. Pakuti koyefishienti osadziwika pa T = 5,79405, ndipo tsa = 0,001158. M'mawu ena, n'kutheka kuti yokanidwa zolondola kungoganizira adzakhala kwachabechabe wa koyefishienti kwa zosadziwika, ndi 0,12%.

Choncho, akhoza amanena kuti analandira liniya mgwirizano aone kuti pali mokwanira.

Vuto la anaiyamba kugula magawo

Angapo mgwirizano unkachitika mu kupambana ntchito chimodzimodzi "Data Analysis" chida. Taganizirani ntchito yeniyeni.

Guide kampani «NNN» angasankhe kugula 20% ya magawo a JSC «mmm». Phukusi mtengo (SP) ndi 70 miliyoni madola US. Akatswiri a «NNN» adziŵe za wotuluka ofanana. Anaganiza kuti aone ubwino magawo pa magawo amenewa, m'kukoma mamilioni a madola US, monga:

• payables (VK);
• zolowa pachaka buku (VO);
• receivables (VD);
• Mtengo wa katundu atathana (SOF).

Komanso, ntchito mangawa malipiro amakampani (V3 U) mu ndalama zambiri US.

Chisankho tebulo purosesa kupambana njira

Choyamba muyenera jambulani tebulo deta athandizira. Icho chiri motere:

chotsatira:

• kuitana bokosi "kusanthulidwe ka deta";
• anasankha "mgwirizano" gawo;
• zenera "Lowetsani imeneyi Y» kutumikiridwa osiyanasiyana yozungulira variable mfundo ku ndime G;
• alemba pa mafano ndi muvi wofiira lamanja la zenera "Lowetsani imeneyi X» mosavuta pa pepala osiyanasiyana makhalidwe onse a mzati B, C, D, F.

Mark mfundo "New fomu" ndi kudina "Chabwino".

Pezani mgwirizano kusanthula ntchito imeneyi.

Zotsatira kuphunzira ndi mfundo

"Sungani" anamaliza pazimene zokambidwa pamwamba pa pepala tebulo kupambana purosesa mgwirizano aone kuti pali:

Sd = 0,103 * SOF + 0,541 * VO - 0.031 * VK + 0,405 * VD + 0,691 * VZP - 265.844.

Mu zambiri mwachizolowezi mawonekedwe masamu akhoza kulemba monga:

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

Data kwa «mmm» JSC kuperekedwa mu tebulo pansipa:

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

M'malo iwo mu mgwirizano aone kuti pali Mulungu, anapeza chithunzi cha madola US miliyoni 64,72. Izi zikutanthauza kuti magawo a JSC «mmm» ayenera kugula, chifukwa mtengo wawo ndithu overpriced pa US madola 70 miliyoni.

Monga mukuonera, ntchito spreadsheet "kupambana" ndi mgwirizano aone kuti pali analola kuti zochita zambiri zokhudzana ndi anaiyamba ndikupeleka achindunji kwambiri.

Tsopano inu mukudziwa chimene mgwirizano. Zitsanzo kupambana, kukambirana pamwamba, kudzakuthandizani kuthetsa mavuto ntchito econometrics.