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

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=	X^2=	X^3=	X^4=	X*Y=	X^2*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:
b<sub>0</sub> = -10,3306834; b<sub>1</sub> = 0,479310275
Demak, X1 va Y2 o`rtasidagi chiziqli regression bog`liqlik funksiya quyidagi ko`rinishda bo`ladi:
Y<sub>2</sub> = -10,3306834+ 0,479310275* X<sub>1</sub>
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:
b<sub>0</sub> = 200,7610615; b<sub>1</sub> = -8,77141117; b<sub>2</sub> = 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=	X^2=	X^3=	X^4=	X*Y=	X^2*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:
b<sub>0</sub> = 34,35077786; b<sub>1</sub> = -0,18806237
Demak, X2 va Y1 o`rtasidagi chiziqli regression bog`liqlik funksiya quyidagi ko`rinishda bo`ladi:
Y<sub>1</sub> = 34,35077786 - 0,18806237* X<sub>2</sub>
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:
b<sub>0</sub> = -0,55565095; b<sub>1</sub> = 25,30078277; b<sub>2</sub> = -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=	X^2=	X^3=	X^4=	X*Y=	X^2*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