Berilishi
|
Kirish yoki chiqish
|
Sartli belgilanishi
|
1
|
Gkir [m3/soat]
|
1-kirish faktori
|
X1
|
2
|
Рkir[atm]
|
2-kirish faktori
|
X2
|
3
|
Lkir [%]
|
3-kirish faktori
|
X3
|
4
|
GNchiqх[m3/soat]
|
1-chiqish faktori
|
Y1
|
5
|
GGchiqх[m3/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
Keyingi bosqich jarayonida tanlanma qiymatlardan foydalanish mumkin, chumki olingan tanlanma qiymatlar kirish faktorlari va chiqish kattaliklari o`rtasidagi munosabatlar o`zgarishiga sabab bo`lmaydi;
Qurilgan regressiya chiziqlari masalani chiziqlashtirish mumkinligini va chiziqli model yordamida kamida bitta factor va chiqish kattaliklari o`rtasida kuchli korelyatsion bog`liqlik mavjudligini kafolatlaydi;
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 b0,b1 – regressiya koefitsiyentlari.
Regressiya xatoligi quyidagiga teng:
bu yerda n – tejribalar soni.
Regressiya funsksiyasining b0,b1 – koefitsiyentlarini aniqlaymiz. Ularni en kichik kvadratlar usulidan foydalanib, b0,b1 – koefitsiyentlarni hisoblash uchun olingan tenglamalar sistemasining ildizlari sifatida topamiz. U holda X1 va Y1 uchun quyidagi jadvalni tuzamiz (2.2-jadval)
№
|
X1=
|
Y1=
|
X2=
|
X3=
|
X4=
|
X*Y=
|
X2*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
|
|
|
