2. KO'P FAKTORLI REGRESSION TAHLIL
2.1. Korrelyatsion matritsani hisoblash.
Biz quyidagi kirish va chiqish faktorlarni hisobga olgan holda otkazilgan tajriba ma’lumotlariga asosan, korrelyatsion regression tahlil usuludan foydalanib ushbu jarayon uchun matematik model tuzamiz va tuzilgan matematik modelni monandlikka tekshiramiz.
Jarayon uchun quyidagi faktorlar qaralayotgan bo’lsin.
X1 – qurilmaning ishlash vaqti (s);
X2 – qurilmaning quvvati (Vatt);
X3 – pamidor quritilshdan oldingi sarf(kg);
Y1 – pamidor quritilgandan keyingi harorati ;
Laboratoriya sharoitida olingan tajriba ma’lumotlari quyidagi 1.1 – jadvalda keltirilgan.
1.1 – jadval
№
|
T pos
|
Vaqt
|
Quvvat
|
Sarf do
|
№
|
T pos
|
Vaqt
|
Quvvat
|
Sarf do
|
Tpos y
|
|
|
|
Tpos y
|
|
|
|
1
|
30
|
485
|
202
|
88
|
21
|
698
|
126
|
182
|
24
|
2
|
60
|
452
|
302
|
84
|
22
|
321
|
125
|
169
|
25
|
3
|
25
|
420
|
502
|
55
|
23
|
45
|
124
|
124
|
22
|
4
|
101
|
460
|
602
|
63
|
24
|
69
|
123
|
174
|
30
|
5
|
123
|
410
|
102
|
59
|
25
|
210
|
256
|
178
|
31
|
6
|
145
|
400
|
160
|
50
|
26
|
654
|
546
|
256
|
63
|
7
|
126
|
390
|
170
|
58
|
27
|
147
|
210
|
342
|
25
|
8
|
147
|
380
|
140
|
57
|
28
|
106
|
510
|
452
|
87
|
9
|
152
|
370
|
150
|
56
|
29
|
444
|
524
|
510
|
89
|
10
|
103
|
369
|
130
|
54
|
30
|
550
|
514
|
530
|
84
|
11
|
147
|
365
|
145
|
24
|
31
|
33
|
522
|
578
|
54
|
12
|
159
|
400
|
162
|
50
|
32
|
210
|
516
|
590
|
61
|
13
|
250
|
363
|
153
|
20
|
33
|
148
|
512
|
300
|
13
|
14
|
214
|
218
|
188
|
21
|
34
|
841
|
521
|
400
|
12
|
15
|
256
|
336
|
163
|
23
|
35
|
269
|
511
|
410
|
54
|
16
|
236
|
158
|
190
|
29
|
36
|
654
|
520
|
420
|
97
|
17
|
254
|
159
|
132
|
26
|
37
|
325
|
510
|
430
|
85
|
18
|
145
|
127
|
152
|
26
|
38
|
258
|
509
|
440
|
45
|
19
|
30
|
485
|
202
|
88
|
39
|
158
|
508
|
450
|
35
|
20
|
60
|
452
|
302
|
84
|
40
|
156
|
503
|
480
|
25
|
Ushbu jadvaldan foydalanib jarayon uchun matematik model tuzamiz. Faktorlarning o’zaro bogliqliklarini inobatga olgan holda, ko’plik regressiya tenglamasini quyidagi formulaga asosan tuzamiz . Matematik modelni tuzishdan oldin kiruvchi va chiquvchi faktorlar orasidagi munosabatni korrelyatsion tahlil orqali tekshiramiz. Buning uchun biz Excel dasturidagi Analiz dannix bo’limidan foydalanib korrelyatsion matritsani hosil qilamiz.
Korrelyatsion matritsaninig umumiy ko’rinishi
2-jadval
Korrelyatsion matritsa
|
|
|
|
Y
|
X1
|
X2
|
X3
|
Y
|
1
|
|
|
|
X1
|
0,06808
|
1
|
|
|
X2
|
0, 418154
|
0, 128888
|
1
|
|
X3
|
-0, 304673
|
0, 548459
|
-0, 00776
|
1
|
|
|
|
|
|
1-rasm. Tajriba natijalarinig koorelyatsion maydoni
Hosil bolgan korrelyatsion matritsaga binoan faktorlar orasidagi bo’gliqliklarni korib chiqishimiz mumkun. Demak, orasidagi bogliqlik eng yuqori tog’ri boglanishni esa eng yuqori teskari bog’lanishni ko’rsatmoqda. Faktorlar orasida ning qolgan faktorlar bilan bog’liqligi judayam kichik miqdorni korsatmoqda.
Ko’lpik regressiya tenglamasini aniqlash uchun faktorlarning o’za’ro munosabatlarini inobatga olgan holda quyidagi modelni quyida funksiyalar yordamida quramiz va uni tahlil qilib ko’ramiz umuiy korinishga keltiramiz (2.1).
2.2. Regressiya tenglamasining koeffitsientlarini kichik kvadratlar usuli yordamida hisoblash.
Matematik model tuzish ikki hil usulda amalga oshiriladi birinchi teglama ko’rinishi chiziqli ikkinchisiniki esa ko’rsatkichli funksiya yordamida aniqlanadi (2.1). Demak, biz har ikkalla tenglamani tuzishni ko’rib chiqamiz.
Hosil bolgan tenlamani noma’lum koeffitsientlarni topish uchun kichik kvadratlar usuli yoki Excel dasturidagi mazsus bo’limlaridan foydalanamiz. Yuqoridagi shartga ko’ra pamidorning zararsizlantirilgandan keyingi harorati uchun matematik model (2.2) korinishga keltiramiz va noma’lum koeffitsientlarni topib birinchi chiziqli funksiyani hosil qilamiz. Quyidagi jadvalga muofiq regressiya tenglamasininig koeffitsientlari mos ravishda aniqlanadi.
b3
|
b2
|
b1
|
b0
|
-0,56514
|
0,129548
|
0,156353
|
163,9329
|
1,493373
|
0,259774
|
0,29653
|
93,25679
|
0,029648
|
199,7635
|
#Н/Д
|
#Н/Д
|
0,366649
|
36
|
#Н/Д
|
#Н/Д
|
43893,86
|
1436597
|
#Н/Д
|
#Н/Д
|
Chiziqli tenglama hosil qilingandan so’ng jarayon uchun ko’rsatkichli tenglama tuzib ikkalasidan jarayonga mosini ajratib olamiz. Buning uchun quyidagi matematik amalni bajaramiz. Tenlamani har ikki tomonini logorifmlab regressiya tenglamasini koeffitsientlarini aniqlaymiz (2.3).
-
№
|
T pos
|
Vaqt
|
Quvvat
|
Sarf do
|
|
T pos y
|
|
|
1
|
30
|
485
|
202
|
88
|
2
|
60
|
452
|
302
|
84
|
3
|
25
|
420
|
502
|
55
|
4
|
101
|
460
|
602
|
63
|
5
|
123
|
410
|
102
|
59
|
6
|
145
|
400
|
160
|
50
|
7
|
126
|
390
|
170
|
58
|
8
|
147
|
380
|
140
|
57
|
9
|
152
|
370
|
150
|
56
|
10
|
103
|
369
|
130
|
54
|
11
|
147
|
365
|
145
|
24
|
12
|
159
|
400
|
162
|
50
|
13
|
250
|
363
|
153
|
20
|
14
|
214
|
218
|
188
|
21
|
15
|
256
|
336
|
163
|
23
|
16
|
236
|
158
|
190
|
29
|
17
|
254
|
159
|
132
|
26
|
18
|
145
|
127
|
152
|
26
|
19
|
698
|
126
|
182
|
24
|
20
|
321
|
125
|
169
|
25
|
21
|
45
|
124
|
124
|
22
|
22
|
69
|
123
|
174
|
30
|
23
|
210
|
256
|
178
|
31
|
24
|
654
|
546
|
256
|
63
|
25
|
147
|
210
|
342
|
25
|
26
|
106
|
510
|
452
|
87
|
27
|
444
|
524
|
510
|
89
|
28
|
550
|
514
|
530
|
84
|
29
|
33
|
522
|
578
|
54
|
30
|
210
|
516
|
590
|
61
|
31
|
148
|
512
|
300
|
13
|
32
|
841
|
521
|
400
|
12
|
33
|
269
|
511
|
410
|
54
|
34
|
654
|
520
|
420
|
97
|
35
|
325
|
510
|
430
|
85
|
36
|
258
|
509
|
440
|
45
|
37
|
158
|
508
|
450
|
35
|
38
|
156
|
503
|
480
|
25
|
39
|
145
|
501
|
199
|
14
|
40
|
321
|
500
|
200
|
15
|
|
|
|
|
|
(2.3)
Quyidagi amallarni bajargandan so’ng yuqoridagi operatsiyani takrorlaymiz va ko’rsatkichli funksiyaning koeffitsientlarini topamiz.
b3
|
b2
|
b1
|
bo'
|
b0
|
-0,3104
|
0,175843
|
0,115465
|
4,643805
|
103,939
|
0,249333
|
0,30383
|
0,335411
|
1,697275
|
|
0,046857
|
0,845039
|
#Н/Д
|
#Н/Д
|
|
0,589929
|
36
|
#Н/Д
|
#Н/Д
|
|
1,263789
|
25,70725
|
#Н/Д
|
#Н/Д
|
|
Quyidagi amallarni bajarish orqali biz ushbu jarayon uchun ikkinchi tenglamani hosil qildik va u quyidagicha ko’rinishga ega
Y=103,939*X10,115465*X20,175843*X3-0,3104
Keyingi bisqichda ko’p faktorli tajriba ma’lumotlari asosida olingan tenglamalarga asosan biz tajriba natijasi va matematik model o’rtasidsagi bog’liqliklarni aniqlashimiz mumkun bo’ladi.
№
|
Vaqt
|
Quvvat
|
Sarf do
|
Y_chiziqli
|
Y_ko'rstkichli
|
|
|
|
|
1
|
85
|
100
|
53
|
160,2256203
|
113,7685194
|
2
|
90
|
145
|
53
|
166,8370596
|
122,2542098
|
3
|
152
|
156
|
53
|
177,9559931
|
131,5612254
|
4
|
136
|
147
|
53
|
174,2884063
|
128,5323327
|
5
|
123
|
856
|
53
|
264,10555
|
173,1895906
|
6
|
250
|
159
|
53
|
193,6672579
|
139,8086686
|
7
|
145
|
163
|
53
|
177,7683583
|
131,8608289
|
8
|
652
|
185
|
53
|
259,8895257
|
160,3869304
|
9
|
70
|
163
|
53
|
166,0418635
|
121,2265552
|
10
|
156
|
150
|
53
|
177,8041165
|
131,049471
|
11
|
145
|
129
|
53
|
173,3637165
|
126,546606
|
12
|
125
|
128
|
53
|
170,1071029
|
124,2263058
|
13
|
320
|
127
|
53
|
200,4664412
|
138,277633
|
14
|
52
|
124
|
53
|
158,1751215
|
111,6368812
|
15
|
50
|
149
|
53
|
161,1011222
|
114,7802073
|
16
|
77
|
148
|
53
|
165,193112
|
120,5049198
|
17
|
369
|
147
|
53
|
210,7187169
|
144,2330931
|
18
|
601
|
126
|
53
|
244,2721602
|
148,5093409
|
19
|
300
|
123
|
53
|
196,8211828
|
136,4808224
|
20
|
365
|
125
|
53
|
207,2432415
|
140,0031203
|
21
|
315
|
156
|
53
|
203,4415752
|
143,1095757
|
22
|
617
|
145
|
53
|
249,2352299
|
152,685323
|
23
|
581
|
654
|
53
|
309,546591
|
197,6154794
|
24
|
530
|
369
|
53
|
264,6513124
|
176,8104026
|
25
|
791
|
258
|
53
|
291,0796545
|
173,8841517
|
26
|
101
|
147
|
53
|
168,8160421
|
124,1916271
|
27
|
721
|
741
|
53
|
342,706749
|
207,1021718
|
28
|
400
|
852
|
53
|
306,8972111
|
198,2895987
|
29
|
503
|
753
|
53
|
310,1763168
|
199,2308368
|
30
|
400
|
951
|
53
|
319,7224916
|
202,159824
|
31
|
263
|
789
|
53
|
277,3152717
|
186,3831833
|
32
|
209
|
456
|
53
|
225,7326156
|
164,8207334
|
33
|
810
|
159
|
53
|
281,225086
|
160,1341873
|
34
|
430
|
147
|
53
|
220,2562661
|
146,8035769
|
35
|
517
|
258
|
53
|
248,23886
|
165,5523241
|
36
|
553
|
369
|
53
|
268,2474375
|
177,6797984
|
37
|
162
|
321
|
53
|
200,8949933
|
150,4626845
|
38
|
325
|
502
|
53
|
249,8288155
|
176,3966026
|
39
|
541
|
402
|
53
|
270,6462918
|
179,9199129
|
40
|
116
|
302
|
53
|
191,2413257
|
143,2254916
|
|
|
|
|
|
|
2-rasm. Tajriba natijasi va matematik model o’rtasidagi boglanish grafigi
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