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

X3=	Y1=	X^2=	X^3=	X^4=	X*Y=
X^2*Y=
1	83,2078482	33,42302563	6923,546002	576093,3647	47935489,24	2781,058043	231405,8555
2	83,7835442	33,5022472	7019,682279	588133,8605	49275939,29	2806,937009	235175,131
3	84,26648295	33,73915254	7100,840149	598362,8253	50421930,82	2843,079722	239576,3289
4	84,7695862	33,70354264	7185,882745	609144,3067	51636910,82	2857,035363	242189,7055
5	85,25642563	33,70180509	7268,658111	619699,8097	52833390,73	2873,295439	244966,8989
6	85,82376395	33,891141	7365,718459	632153,6823	54253808,41	2908,665285	249632,6029
7	86,24332483	34,279083	7437,911077	641470,181	55322521,19	2956,34209	254964,7712
8	86,7316592	33,97955306	7522,380708	652428,5599	56586211,51	2947,103016	255607,1344
9	87,18696753	34,27624851	7601,567308	662757,6021	57783825,53	2988,442166	260553,2101
10	87,8332017	34,19103246	7714,671321	677604,2822	59516153,59	3003,10785	263772,5775
11	88,2589732	34,21899715	7789,64635	687506,1885	60678590,26	3020,133552	266553,8863
12	88,7723842	34,07882237	7880,536197	699573,9869	62102850,75	3025,258313	268559,3933
13	89,1893142	35,17276389	7954,733767	709477,2494	63277789,31	3137,03469	279789,9726
14	89,7293242	34,38195689	8051,351621	722442,3399	64824262,93	3085,069756	276821,2243
Yig`indisi	1211,0528	476,5393714	104817,1261	9076848,239	786449674,4	41232,5623	3569568,692
O`rtachasi	86,50377144	34,03852653	7486,937578	648346,3028	56174976,74	2945,183021	254969,1923

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> 18,55824963; b<sub>1</sub> = 0,178954936
Demak, X3 va Y1 o`rtasidagi chiziqli regression bog`liqlik funksiya quyidagi ko`rinishda bo`ladi:
Y<sub>1</sub> = 0,178954936 + 0,178954936 * X<sub>3</sub>
2.3.5.2. 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> = -1,95701646; b<sub>1</sub> = 0,653625361; b<sub>2</sub> = -0,00274418
Demak, X3 va Y1 o`rtasidagi chiziqli regression bog`liqlik funksiya quyidagi ko`rinishda bo`ladi:
Y₁ = -1,95701646 + 0,653625361 * X₃ - 0,00274418 * X₃²


2.3.6. X3 – kirish omili va Y1 chiqish o`rtasidagi empiric bog`liqlik ifodasini toppish.
2.3.6.1. Chiziqli empiric bo`liqlik qurish (chiziqli regressiya funksiyasi koeffisiyentlarini aniqlash)
Hisoblashlarni yuqoridagi X1 va Y1 uchun bajarilgan kabi olib boramiz
X3 va Y1 uchun quyidagi jadvalni tuzamiz (2.3) jadval

№	X3=	Y2=	X^2=	X^3=	X^4=	X*Y=	X^2*Y=
1	83,2078482	10,33648991	6923,546002	576093,3647	47935489,24	860,0770836	71565,16342
2	83,7835442	10,41017757	7019,682279	588133,8605	49275939,29	872,2015722	73076,13897
3	84,26648295	10,4833266	7100,840149	598362,8253	50421930,82	883,3930619	74440,42639
4	84,7695862	10,88710419	7185,882745	609144,3067	51636910,82	922,8953171	78233,45414
5	85,25642563	10,84474724	7268,658111	619699,8097	52833390,73	924,5843867	78826,76
6	85,82376395	11,39478197	7365,718459	632153,6823	54253808,41	977,9430781	83930,75589
7	86,24332483	11,24169147	7437,911077	641470,181	55322521,19	969,5208494	83614,70154
8	86,7316592	11,68141492	7522,380708	652428,5599	56586211,51	1013,148497	87872,0502
9	87,18696753	11,77515444	7601,567308	662757,6021	57783825,53	1026,640008	89509,62906
10	87,8332017	11,8056305	7714,671321	677604,2822	59516153,59	1036,926325	91076,55903
11	88,2589732	11,14319419	7789,64635	687506,1885	60678590,26	983,486877	86801,54192
12	88,7723842	12,4709349	7880,536197	699573,9869	62102850,75	1107,074624	98277,65389
13	89,1893142	15,47280899	7954,733767	709477,2494	63277789,31	1380,009222	123082,0761
14	89,7293242	13,31072425	8051,351621	722442,3399	64824262,93	1194,362291	107169,3212
Yig`indisi	1211,0528	163,2581811	104817,1261	9076848,239	786449674,4	14152,26319	1227476,232
O`rtachasi	86,50377144	11,66129865	7486,937578	648346,3028	56174976,74	1010,875942	87676,8737

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> = -33,9932708; b<sub>1</sub> = 0,527775479
Demak, X3 va Y2 o`rtasidagi chiziqli regression bog`liqlik funksiya quyidagi ko`rinishda bo`ladi:
Y<sub>2</sub> = -33,9932708 + 0,527775479 * X<sub>3</sub>
2.3.6.2. 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> = 595,71218; b<sub>1</sub> = -14,041987; b<sub>2</sub> = -0,00274418
Demak, X3 va Y2 o`rtasidagi chiziqli regression bog`liqlik funksiya quyidagi ko`rinishda bo`ladi:
Y₂ = 595,71218 - 14,041987* X₃ + 0,084231228 * X₃²

2.3.7. Tajriba natijalari (tanlanmalar) asosida juft (biro milli) regression bog`liqlik hollari
2.3.7.1. Olingan natijalar bo`yicha jadval

№	Kirish va chiqish		Regressiya funksiyasi
	X	Y	Chiziqli
1	X1	Y1	Y=	20,99816715	+	0,285403134	*X
2	X1	Y2	Y=	-10,3306834	+	0,479310275	*X
3	X2	Y1	Y=	34,35077786	-	0,188062373	*X
4	X2	Y2	Y=	7,909710957	+	1,137465456	*X
5	X3	Y1	Y=	18,55824963	+	0,178954936	*X
6	X3	Y2	Y=	-33,99327078	+	0,527775479	*X

№	Kirish va chiqish		Regressiya funksiyasi