3.4.2. Parabolik empirik bog’liqlik qurish (parabolik regressiya funksiyasi koeffisiyentlarini aniqlash)
Olingan natijalar asosida sistema quyidagi ko’rinishda bo’ladi:
Bu sistemani yechib quyidagi ildizlarga ega bo’lamiz:
B0=- 63,333; b1= 52,827; b2=-9,3265
Demak, X2 va Y2 uchun parabolik regression bo’gliqlik funksiyasi quyidagi ko’rinishda bo’ladi:
y = - 63,333+52,827xi-9,3265xi2
3.5. X3 – kirish omili va Y1 – chiqish o’rtasidagi empirik bog’liqlik ifodasini topish
3.5.1. Chiziqli empirik bog’liqlik qurish (chiziqli regressiya funksiyasi koeffisiyentlarini aniqlash)
Hisoblashlarni yuqoridagi X1 va Y1 uchun bajarilgani kabi olib boramiz.
X3 va Y1 uchun quyidagi jadvalni tuzamiz (2.6-jadval):
2.6-jadval.
№
|
x3
|
y1
|
x3^2
|
x3y1
|
x3^3
|
x3^4
|
x3^2y1
|
1
|
83,98161
|
33,90532
|
7052,911
|
2847,423
|
592314,8
|
49743549
|
239131,2
|
2
|
84,55794
|
33,58244
|
7150,045
|
2839,662
|
604593
|
51123141
|
240115,9
|
3
|
84,67297
|
33,51405
|
7169,512
|
2837,734
|
607063,9
|
51401902
|
240279,4
|
4
|
86,11213
|
34,11232
|
7415,299
|
2937,484
|
638547,1
|
54986654
|
252953
|
5
|
85,30272
|
33,66283
|
7276,554
|
2871,531
|
620709,8
|
52948234
|
244949,4
|
6
|
86,26653
|
33,98334
|
7441,914
|
2931,625
|
641988,1
|
55382085
|
252901,1
|
7
|
85,75703
|
34,26062
|
7354,267
|
2938,089
|
630680,1
|
54085249
|
251961,8
|
8
|
85,16032
|
33,65661
|
7252,281
|
2866,208
|
617606,6
|
52595577
|
244087,2
|
9
|
87,27727
|
34,06488
|
7617,323
|
2973,09
|
664819,2
|
58023603
|
259483,2
|
10
|
87,05368
|
33,92456
|
7578,344
|
2953,258
|
659722,8
|
57431297
|
257092
|
11
|
85,57703
|
33,84605
|
7323,427
|
2896,444
|
626717,2
|
53632590
|
247869,1
|
12
|
89,3191
|
34,21423
|
7977,902
|
3055,984
|
712579,1
|
63646926
|
272957,8
|
summa
|
1031,038
|
406,7272
|
88609,78
|
34948,53
|
7617342
|
655000807
|
3003781
|
o'rtacha
|
85,91986
|
33,89394
|
7384,148
|
2912,378
|
634778,5
|
54583401
|
250315,1
|
Olingan natijalar asosida sistema quyidagi ko’rinishda bo’ladi:
Bu sistemani yechib ildizlarga ega bo’lamiz:
B0=24,287; b1=0,1118
Demak, X3 va Y1 o’rtasidagi chiziqli regression bo’gliqlik funksiyasi quyidagi ko’rinishda bo’ladi:
y = 24,287+0,1118xi
3.5.2. Parabolik empirik bog’liqlik qurish (parabolik regressiya funksiyasi koeffisiyentlarini aniqlash)
Olingan natijalar asosida sistema quyidagi ko’rinishda bo’ladi:
Bu sistemani yechib quyidagi ildizlarga ega bo’lamiz:
B0=- 49,071; b1=1,8068; b2=-0,0098;
Demak, X3 va Y1 uchun parabolik regression bo’gliqlik funksiyasi quyidagi ko’rinishda bo’ladi:
y = -49,071+1,8068xi-0,0098xi2
3.6. X3 – kirish omili va Y2 – chiqish o’rtasidagi empirik bog’liqlik ifodasini topish
3.6.1. Chiziqli empirik bog’liqlik qurish (chiziqli regressiya funksiyasi koeffisiyentlarini aniqlash)
Hisoblashlarni yuqoridagi X1 va Y1 uchun bajarilgani kabi olib boramiz.
X3 va Y2 uchun quyidagi jadvalni tuzamiz (2.7-jadval):
2.7-jadval.
№
|
x3
|
y2
|
x3^2
|
x3y2
|
x3^3
|
x3^4
|
x3^2y2
|
1
|
83,98161
|
10,64869
|
7052,911
|
894,2941
|
592314,8
|
49743549
|
75104,26
|
2
|
84,55794
|
10,94456
|
7150,045
|
925,4492
|
604593
|
51123141
|
78254,08
|
3
|
84,67297
|
11,37678
|
7169,512
|
963,3054
|
607063,9
|
51401902
|
81565,93
|
4
|
86,11213
|
11,51029
|
7415,299
|
991,1754
|
638547,1
|
54986654
|
85352,22
|
5
|
85,30272
|
10,65859
|
7276,554
|
909,2069
|
620709,8
|
52948234
|
77557,82
|
6
|
86,26653
|
11,27352
|
7441,914
|
972,5277
|
641988,1
|
55382085
|
83896,59
|
7
|
85,75703
|
10,96483
|
7354,267
|
940,3112
|
630680,1
|
54085249
|
80638,29
|
8
|
85,16032
|
10,88966
|
7252,281
|
927,3673
|
617606,6
|
52595577
|
78974,9
|
9
|
87,27727
|
11,9723
|
7617,323
|
1044,91
|
664819,2
|
58023603
|
91196,87
|
10
|
87,05368
|
12,05893
|
7578,344
|
1049,774
|
659722,8
|
57431297
|
91386,7
|
11
|
85,57703
|
10,81117
|
7323,427
|
925,1881
|
626717,2
|
53632590
|
79174,85
|
12
|
89,3191
|
13,06317
|
7977,902
|
1166,791
|
712579,1
|
63646926
|
104216,7
|
summa
|
1031,038
|
136,1725
|
88609,78
|
11710,3
|
7617342
|
655000807
|
1007319
|
urtacha
|
85,91986
|
11,34771
|
7384,148
|
975,8583
|
634778,5
|
54583401
|
83943,27
|
Olingan natijalar asosida sistema quyidagi ko’rinishda bo’ladi:
Bu sistemani yechib ildizlarga ega bo’lamiz:
B0= -27,24; b1=0,4491
Demak, X3 va Y2 o’rtasidagi chiziqli regression bo’gliqlik funksiyasi quyidagi ko’rinishda bo’ladi:
y = - 27,24+0,4491xi
3.6.2. Parabolik empirik bog’liqlik qurish (parabolik regressiya funksiyasi koeffisiyentlarini aniqlash)
Olingan natijalar asosida sistema quyidagi ko’rinishda bo’ladi:
Bu sistemani yechib quyidagi ildizlarga ega bo’lamiz:
B0=392,6; b1=- 9,2515; b2=0,056
Demak, X3 va Y2 uchun parabolik regression bo’gliqlik funksiyasi quyidagi ko’rinishda bo’ladi:
y = 392,6 - 9,2515xi+0,056xi2
3.7. Tajriba natijalari (tanlanmalar) asosida juft (bir omilli) regression bog’liqlik holati
3.7.1. Olingan natijalar bo’yicha jadval
2.8-jadval.
№
|
Kirish va chiqish
|
Regressiya funksiyasi
| |
X
|
Y
|
Chiziqli
|
Parabolik
| |
1
|
|
|
y = 25,381+0,1887xi
|
y = - 43,773+ 3,2395xi -0,0336xi2
| |
2
|
|
|
y = - 8,3102+ 0,4356xi
|
y i= 358,4 - 15,742xi+0,1783xi2
| |
3
|
|
|
y = 35,142-0,4456xi
|
y = 47,083-8,9768xi+1,5213xi2
| |
4
|
|
|
y = 9,8699+0,5276xi
|
y = - 63,333+52,827xi-9,3265xi2
| |
5
|
|
|
y = 24,287+0,1118xi
|
y = -49,071+1,8068xi-0,0098xi2
| |
6
|
|
|
y = - 27,24+0,4491xi
|
y = 392,6 - 9,2515xi+0,056xi2
|
3.7.2. Korrelyatsiya koeffisiyentlarini hisoblash jadvali
2.9-jadval.
|
|
|
|
|
|
| |
|
45,12401125
|
45,12401
|
2,801203
|
2,801203
|
85,91986
|
85,91986
| |
|
33,89394
|
11,34771
|
33,89394
|
11,34771
|
33,89394
|
11,34771
| |
|
2037,478
|
2037,478
|
7,859269
|
7,859269
|
7384,148
|
7384,148
| |
|
1529,676
|
512,6213
|
94,9382
|
31,79384
|
2912,378
|
975,8583
| |
|
1148,855
|
129,2406
|
1148,855
|
129,2406
|
1148,855
|
129,2406
| |
|
2036,176391
|
2036,176
|
7,846737
|
7,846737
|
7382,223
|
7382,223
| |
|
1148,799
|
128,7705
|
1148,799
|
128,7705
|
1148,799
|
128,7705
| |
| |
|
0,9462
|
0,7843
|
0,0426
|
0,1449
|
0,8854
|
0,8527
|
|
