Reja: Kirish 1-§ Nazariy qism. Jarayon tavsifi. Eksperimental-statistik modellashtirish usullari

Berilishi	Kirish yoki chiqish
Sartli belgilanishi
1	Gkir [m^3/soat]	1-kirish faktori	X1
2	Рkir[atm]	2-kirish faktori	X2
3	Lkir [%]	3-kirish faktori	X3
4	GNchiqх[m^3/soat]	1-chiqish faktori	Y1
5	GGchiqх[m^3/soat]	2-chiqish faktori	Y2

2.1.2 Tajriba natijalarining dekart sistemasida tasvirlanishi







2.2 Juft regressiyaning emperik chizig`ini qurish
X1 ning qiymatlarini teng intervallarda bo`lib chiqamiz. Bunda X1 qiymatlari ichidagi minimum va maksimim qiymatlarini bilish zarur: min{X1}=42,57925221; mak{X1}= 48,54555964.
Har bir interval uzunligini 0,5ga teng deb olsak u holda X1 ning qiymatlari uchun quyidagi intervallarni olishimiz mumkin:
(42,5;43), (43;43,5), (43,5;44), (44;44,5), (44,5;45), (45;45,5), (45,5;46), (46;46,5), (46,5;47), (47;47,5), (47,5;48), (48;48,5) va (48,5;48)
Y ning qiymatlari uchun har bir intervalga mos keluvchi Y lar o`rtachasi olinadi.
Jadval tuzamiz. Bunda tajriba natijalarining 60 ta qiymatini Excel dasturiga kiritib, X1 bo`yicha usbu (СРЗНАЧЕСЛИМН) formula yordamida tartiblaymiz.

X1	Y1	Y2
42,64913962	33,16192837	10,97126417
43,21873937	33,30826649	10,59998312
43,63332194	33,54083974	10,10008528
44,24625093	33,71206488	10,43894034
44,72577178	33,72254116	10,99834316
45,18535759	33,94322841	11,18422164
45,68600628	34,0477923	11,73447538
46,20583563	34,08938259	12,05481218
46,51743321	34,19126248	11,63450166
47,24083537	34,29777512	11,80849863
47,99509964	34,65279176	11,53118779
48,37794683	34,72986899	11,99124292
48,54555964	35,17276389	15,47280899

X2 ning qiymatlarini teng intervallarda bo`lib chiqamiz. Bunda X2 qiymatlari ichidagi minimum va maksimim qiymatlarini bilish zarur: min{X2}=2,447315784; mak{X2}= 3,058904617.
Har bir interval uzunligini 0,05ga teng deb olsak u holda X2 ning qiymatlari uchun quyidagi intervallarni olishimiz mumkin:
(2,4;2,45), (2,45;2,5), (2,5;2,55), (2,55;2,6), (2,6;2,65), (2,65;2,7), (2,7;2,75), (2,75;2,8), (2,8;2,85), (2,85;2,9), (2,9;2,95), (2,95;3), (3;3,05), (3,05;3,1)
Y ning qiymatlari uchun har bir intervalga mos keluvchi Y lar o`rtachasi olinadi.

X2	Y1	Y2
2,447613292	33,89349259	10,61117198
2,488010788	33,66104902	10,31118779
2,523075007	33,69190926	10,48016322
2,575154771	33,63755312	10,26113679
2,627196277	34,00607004	11,45000201
2,673433993	34,17545455	11,55363696
2,72726582	33,75366147	11,10854321
2,773492442	34,18910417	11,52831211
2,829095117	34,02079681	11,59470117
2,891588311	33,92525756	11,33068483
2,936258469	33,78307896	10,85025333
2,975733541	34,06070268	11,54949497
3,018596043	33,3415926	11,30973896
3,058459429	33,52230814	10,64050171

X3 ning qiymatlarini teng intervallarda bo`lib chiqamiz. Bunda X3 qiymatlari ichidagi minimum va maksimim qiymatlarini bilish zarur: min{X3}=83,0793142; mak{X3}= 89,7293242.

Har bir interval uzunligini 0,5ga teng deb olsak u holda X3 ning qiymatlari uchun quyidagi intervallarni olishimiz mumkin:
(83;83,5), (83,5;84), (84;84,5), (84,5;85), (85;85,5), (85,5;86), (86;86,5), (86,5;87), (87;87,5), (87,5;88), (88;88,5), (88,5;89), (89;89,5), (89,5;90)
Y ning qiymatlari uchun har bir intervalga mos keluvchi Y lar o`rtachasi olinadi.

X3	Y1	Y2
83,2078482	33,42302563	10,33648991
83,7835442	33,5022472	10,41017757
84,26648295	33,73915254	10,4833266
84,7695862	33,70354264	10,88710419
85,25642563	33,70180509	10,84474724
85,82376395	33,891141	11,39478197
86,24332483	34,279083	11,24169147
86,7316592	33,97955306	11,68141492
87,18696753	34,27624851	11,77515444
87,8332017	34,19103246	11,8056305
88,2589732	34,21899715	11,14319419
88,7723842	34,07882237	12,4709349
89,1893142	35,17276389	15,47280899
89,7293242	34,38195689	13,31072425

1-bosqichda tanlanmalar asosida regressiyaning chizig`ini tasvirladik. Bu ekspremental-statik modellashtirishning dastlabki bosqichi bo`lib, odatda kirish qismi ham deyiladi. Shuningdek, empirik modelni qurishda dastlabki ma`lumotlar tahlili hamdir.

1-bosqich bo`yicha xulosalar

1. 
   Keyingi bosqich jarayonida tanlanma qiymatlardan foydalanish mumkin, chumki olingan tanlanma qiymatlar kirish faktorlari va chiqish kattaliklari o`rtasidagi munosabatlar o`zgarishiga sabab bo`lmaydi;
   
2. 
   Qurilgan regressiya chiziqlari masalani chiziqlashtirish mumkinligini va chiziqli model yordamida kamida bitta factor va chiqish kattaliklari o`rtasida kuchli korelyatsion bog`liqlik mavjudligini kafolatlaydi;
   
3. 
   Olingan regressiya chiziqlari tanlanma qiymatlari bo`yicha umumiy chetlanishlar holati to`g`risida dastlabki visual ma`lumotlarga ega bo`lishga imkon beradi.
   

2.3. Juft regressiyanig empirik funksiyasini qurish
(2-bosqich: parametrik identifikatsiyalash masalasini yechish)
2.3.1. X1 – kirish omili va Y1 chiqish o`rtasidagi empiric bog`liqlik ifodasini toppish.
2.3.1.1. Chiziqli empiric bo`liqlik qurish (chiziqli regressiya funksiyasi koeffisiyentlarini aniqlash)
Chiziqli empiric tenglama ko`rinishi (regressiyaning nazariy tenglamasi o`rnini bosuvchi funksiya):

Chiziqli regressiya funksiyasi quyidagi ko`rimishga ega, ya`ni

bu yerda b_0,b₁ – regressiya koefitsiyentlari.
Regressiya xatoligi quyidagiga teng:

bu yerda n – tejribalar soni.
Regressiya funsksiyasining b_0,b₁ – koefitsiyentlarini aniqlaymiz. Ularni en kichik kvadratlar usulidan foydalanib, b_0,b₁ – koefitsiyentlarni hisoblash uchun olingan tenglamalar sistemasining ildizlari sifatida topamiz. U holda X1 va Y1 uchun quyidagi jadvalni tuzamiz (2.2-jadval)

№	X1=	Y1=	X^2=	X^3=	X^4=	X*Y=	X^2*Y=
1	42,64913962	33,16192837	1818,94911	77576,61457	3308575,866	1414,327713	60319,8601
2	43,21873937	33,30826649	1867,859432	80726,52998	3488898,859	1439,541288	62215,15973
3	43,63332194	33,54083974	1903,866784	83072,03231	3624708,73	1463,498258	63857,29067
4	44,24625093	33,71206488	1957,730722	86622,24478	3832709,579	1491,632482	65999,14512
5	44,72577178	33,72254116	2000,394661	89469,19507	4001578,799	1508,266679	67458,39128
6	45,18535759	33,94322841	2041,71654	92255,69196	4168606,431	1533,736913	69302,45087
7	45,68600628	34,0477923	2087,21117	95356,34262	4356450,468	1555,507653	71064,93241
8	46,20583563	34,08938259	2134,979246	98648,50013	4558136,382	1575,128409	72780,12434
9	46,51743321	34,19126248	2163,871592	100657,7523	4682340,267	1590,489769	73985,50158
10	47,24083537	34,29777512	2231,696526	105427,2082	4980469,385	1620,255548	76542,22558
11	47,99509964	34,65279176	2303,529589	110558,1322	5306248,568	1663,164193	79823,73117
12	48,37794683	34,72986899	2340,425739	113224,992	5477592,64	1680,159755	81282,67931
13	48,54555964	35,17276389	2356,671361	114405,9301	5553899,902	1707,481507	82890,64533