2.3.2. X1 – kirish omili va Y2 chiqish o`rtasidagi empiric bog`liqlik ifodasini toppish.
2.3.2.1. Chiziqli empiric bo`liqlik qurish (chiziqli regressiya funksiyasi koeffisiyentlarini aniqlash)
Hisoblashlarni yuqoridagi X1 va Y1 uchun bajarilgan kabi olib boramiz
X1 va Y2 uchun quyidagi jadvalni tuzamiz (2.3) jadval
№
|
X1=
|
Y2=
|
X2=
|
X3=
|
X4=
|
X*Y=
|
X2*Y=
|
1
|
42,64913962
|
10,97126417
|
1818,94911
|
77576,61457
|
3308575,866
|
467,9149776
|
19956,17121
|
2
|
43,21873937
|
10,59998312
|
1867,859432
|
80726,52998
|
3488898,859
|
458,1179077
|
19799,27845
|
3
|
43,63332194
|
10,10008528
|
1903,866784
|
83072,03231
|
3624708,73
|
440,7002725
|
19229,21687
|
4
|
44,24625093
|
10,43894034
|
1957,730722
|
86622,24478
|
3832709,579
|
461,8839736
|
20436,6342
|
5
|
44,72577178
|
10,99834316
|
2000,394661
|
89469,19507
|
4001578,799
|
491,9093861
|
22001,02694
|
6
|
45,18535759
|
11,18422164
|
2041,71654
|
92255,69196
|
4168606,431
|
505,363054
|
22835,01031
|
7
|
45,68600628
|
11,73447538
|
2087,21117
|
95356,34262
|
4356450,468
|
536,1013159
|
24492,32809
|
8
|
46,20583563
|
12,05481218
|
2134,979246
|
98648,50013
|
4558136,382
|
557,0026702
|
25736,77383
|
9
|
46,51743321
|
11,63450166
|
2163,871592
|
100657,7523
|
4682340,267
|
541,2071539
|
25175,56763
|
10
|
47,24083537
|
11,80849863
|
2231,696526
|
105427,2082
|
4980469,385
|
557,8433398
|
26352,98538
|
11
|
47,99509964
|
11,53118779
|
2303,529589
|
110558,1322
|
5306248,568
|
553,4405067
|
26562,43226
|
12
|
48,37794683
|
11,99124292
|
2340,425739
|
113224,992
|
5477592,64
|
580,1117122
|
28064,61357
|
13
|
48,54555964
|
15,47280899
|
2356,671361
|
114405,9301
|
5553899,902
|
751,1361714
|
36464,3258
|
Yig`indisi
|
594,2272978
|
150,5203652
|
27208,90247
|
1248001,166
|
57340215,88
|
6902,732442
|
317106,3645
|
O`rtachasi
|
45,70979214
|
11,57848963
|
2092,992498
|
96000,0897
|
4410785,837
|
530,9794186
|
24392,79727
|
Bizning holda n = 13 va jadvalda hisoblashlarga ko`ra:
;
Olingan natijalar asosida yuqoridagi Sistema quyidagi ko`rinishda bo`ladi:
Bu sistemani yechib quyidagi ildizlarga ega bo`lamiz:
b0 = -10,3306834; b1 = 0,479310275
Demak, X1 va Y2 o`rtasidagi chiziqli regression bog`liqlik funksiya quyidagi ko`rinishda bo`ladi:
Y2 = -10,3306834+ 0,479310275* X1
2.3.2.2. Parabolik empirik bo`liqlik qurish (parabolik regressiya funksiyasi koeffisiyentlarini aniqlash)
Yuqoridagilarga qo`shimcha ravishda yozamiz:
U holda quyidagi ko`rinishdagi tenglamalar sistemasiga ega bo`lamiz:
Bu sistemani yechib quyidagi ildizlarga ega bo`lamiz:
b0 = 200,7610615; b1 = -8,77141117; b2 = 0,101174185
Demak, X1 va Y2 o`rtasidagi chiziqli regression bog`liqlik funksiya quyidagi ko`rinishda bo`ladi:
Y2 = 200,7610615 - 8,77141117* X1 + 0,101174185* X12
2.3.3. X2 – kirish omili va Y1 chiqish o`rtasidagi empiric bog`liqlik ifodasini toppish.
2.3.3.1. Chiziqli empiric bo`liqlik qurish (chiziqli regressiya funksiyasi koeffisiyentlarini aniqlash)
Hisoblashlarni yuqoridagi X1 va Y1 uchun bajarilgan kabi olib boramiz
X2 va Y1 uchun quyidagi jadvalni tuzamiz (2.3) jadval
№
|
X2=
|
Y1=
|
X2=
|
X3=
|
X4=
|
X*Y=
|
X2*Y=
|
1
|
2,447613292
|
33,89349259
|
5,990810827
|
14,66318821
|
35,88981436
|
82,95816297
|
203,0495024
|
2
|
2,488010788
|
33,66104902
|
6,190197679
|
15,4012786
|
38,3185473
|
83,74905309
|
208,3685475
|
3
|
2,523075007
|
33,69190926
|
6,365907493
|
16,06166209
|
40,52477821
|
85,00721421
|
214,4795776
|
4
|
2,575154771
|
33,63755312
|
6,631422095
|
17,07693825
|
43,975759
|
86,6219054
|
223,064813
|
5
|
2,627196277
|
34,00607004
|
6,902160279
|
18,13332979
|
47,63981652
|
89,34062062
|
234,7153459
|
6
|
2,673433993
|
34,17545455
|
7,147249314
|
19,10769927
|
51,08317276
|
91,36582192
|
244,2604941
|
7
|
2,72726582
|
33,75366147
|
7,437978855
|
20,2853455
|
55,32352945
|
92,05520725
|
251,0590203
|
8
|
2,773492442
|
34,18910417
|
7,692260326
|
21,33442588
|
59,17086892
|
94,82322201
|
262,9914896
|
9
|
2,829095117
|
34,02079681
|
8,003779179
|
22,64345259
|
64,06048115
|
96,24807012
|
272,2949451
|
10
|
2,891588311
|
33,92525756
|
8,361282958
|
24,17738806
|
69,9110527
|
98,09787819
|
283,6586779
|
11
|
2,936258469
|
33,78307896
|
8,621613796
|
25,31528653
|
74,33222446
|
99,19585171
|
291,2646597
|
12
|
2,975733541
|
34,06070268
|
8,854990105
|
26,35009106
|
78,41084976
|
101,3555754
|
301,6071852
|
13
|
3,018596043
|
33,3415926
|
9,111922068
|
27,5052119
|
83,02712378
|
100,6447995
|
303,8059934
|
14
|
3,058459429
|
33,52230814
|
9,354174076
|
28,6093619
|
87,50057265
|
102,5266194
|
313,5735058
|
Yig`indisi
|
38,5449733
|
473,662031
|
106,6657491
|
296,6646596
|
829,168591
|
1303,990002
|
3608,193757
|
O`rtachasi
|
2,753212378
|
33,83300221
|
7,618982075
|
21,19033283
|
59,22632793
|
93,14214298
|
257,7281255
|
Bizning holda n = 14 va jadvalda hisoblashlarga ko`ra:
;
Olingan natijalar asosida yuqoridagi Sistema quyidagi ko`rinishda bo`ladi:
Bu sistemani yechib quyidagi ildizlarga ega bo`lamiz:
b0 = 34,35077786; b1 = -0,18806237
Demak, X2 va Y1 o`rtasidagi chiziqli regression bog`liqlik funksiya quyidagi ko`rinishda bo`ladi:
Y1 = 34,35077786 - 0,18806237* X2
2.3.3.2. Parabolik empirik bo`liqlik qurish (parabolik regressiya funksiyasi koeffisiyentlarini aniqlash)
Yuqoridagilarga qo`shimcha ravishda yozamiz:
U holda quyidagi ko`rinishdagi tenglamalar sistemasiga ega bo`lamiz:
Bu sistemani yechib quyidagi ildizlarga ega bo`lamiz:
b0 = -0,55565095; b1 = 25,30078277; b2 = -4,62919781
Demak, X2 va Y1 o`rtasidagi chiziqli regression bog`liqlik funksiya quyidagi ko`rinishda bo`ladi:
Y1 = -0,55565095 + 25,30078277 * X2 - 4,62919781 * X22
2.3.4. X2 – kirish omili va Y2 chiqish o`rtasidagi empiric bog`liqlik ifodasini toppish.
2.3.4.1. Chiziqli empiric bo`liqlik qurish (chiziqli regressiya funksiyasi koeffisiyentlarini aniqlash)
Hisoblashlarni yuqoridagi X1 va Y1 uchun bajarilgan kabi olib boramiz
X2 va Y2 uchun quyidagi jadvalni tuzamiz (2.3) jadval
№
|
X2=
|
Y2=
|
X2=
|
X3=
|
X4=
|
X*Y=
|
X2*Y=
|
1
|
2,447613292
|
10,61117198
|
5,990810827
|
14,66318821
|
35,88981436
|
25,97204559
|
63,569524
|
2
|
2,488010788
|
10,31118779
|
6,190197679
|
15,4012786
|
38,3185473
|
25,65434644
|
63,82829069
|
3
|
2,523075007
|
10,48016322
|
6,365907493
|
16,06166209
|
40,52477821
|
26,4422379
|
66,71574959
|
4
|
2,575154771
|
10,26113679
|
6,631422095
|
17,07693825
|
43,975759
|
26,42401535
|
68,0459292
|
5
|
2,627196277
|
11,45000201
|
6,902160279
|
18,13332979
|
47,63981652
|
30,08140266
|
79,02974908
|
6
|
2,673433993
|
11,55363696
|
7,147249314
|
19,10769927
|
51,08317276
|
30,88788579
|
82,57672385
|
7
|
2,72726582
|
11,10854321
|
7,437978855
|
20,2853455
|
55,32352945
|
30,29595022
|
82,62510953
|
8
|
2,773492442
|
11,52831211
|
7,692260326
|
21,33442588
|
59,17086892
|
31,9736865
|
88,67877785
|
9
|
2,829095117
|
11,59470117
|
8,003779179
|
22,64345259
|
64,06048115
|
32,80251245
|
92,8014278
|
10
|
2,891588311
|
11,33068483
|
8,361282958
|
24,17738806
|
69,9110527
|
32,7636758
|
94,73906195
|
11
|
2,936258469
|
10,85025333
|
8,621613796
|
25,31528653
|
74,33222446
|
31,85914824
|
93,54669383
|
12
|
2,975733541
|
11,54949497
|
8,854990105
|
26,35009106
|
78,41084976
|
34,36821956
|
102,2706637
|
13
|
3,018596043
|
11,30973896
|
9,111922068
|
27,5052119
|
83,02712378
|
34,13953326
|
103,05346
|
14
|
3,058459429
|
10,64050171
|
9,354174076
|
28,6093619
|
87,50057265
|
32,54354279
|
99,53310527
|
Yig`indisi
|
38,5449733
|
154,579529
|
106,6657491
|
296,6646596
|
829,168591
|
426,2082025
|
1181,014266
|
O`rtachasi
|
|
|
