Lim. Amaliy hisob qismi regression va korrelyatsion tahlil

x^4
x^2*y
1	42,65437	10,98937	1819,395634	468,7448686	77605,18208	3310200,472	19994,02
2	43,22397	10,61809	1868,311919	458,9561706	80755,8656	3490589,426	19837,91
3	43,63856	10,1182	1904,323611	441,5434267	83101,93341	3626448,414	19268,32
4	44,25149	10,45705	1958,193965	462,7400016	86652,99179	3834523,606	20476,93
5	44,73101	11,01645	2000,862925	492,7770263	89500,61209	4003452,444	22042,41
6	45,19059	11,20233	2042,189615	506,2399902	92287,75793	4170538,426	22877,28
7	45,69124	11,75259	2087,689486	536,9901991	95389,12306	4358447,392	24535,75
8	46,21107	12,07292	2135,463005	557,9026442	98682,03074	4560202,246	25781,28
9	46,52267	11,65261	2164,358613	542,1105707	100691,7366	4684448,206	25220,43
10	47,24607	11,82661	2232,19112	558,7607681	105462,2577	4982677,198	26399,25
11	48,00033	11,5493	2304,03208	554,3701429	110594,3098	5308563,825	26609,95
12	48,38318	12,00935	2340,932238	581,0506899	113261,749	5479963,742	28113,08
13	48,55079	15,49092	2357,179614	752,0964088	114442,9422	5556295,733	36514,88
Summa	594,2953	150,7558	27215,12383	6914,282908	1248428,492	57366351,13	317671,5
Urtacha	45,71503	11,5966	2093,471063	531,867916	96032,96092	4412796,241	24436,27

Olingan natijalar asosida sistema quyidagi ko’rinishda bo’ladi:

Bu sistemani yechib quyidagi ildizlarga ega bo’lamiz:

Demak, X1 va Y2 o’rtasidagi chiziqli regression bo’gliqlik funksiyasi quyidagi ko’rinishda bo’ladi:
y = 0,4793x - 10,315
3.2.2. 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:

Demak, X1 va Y2 uchun parabolik regression bo’gliqlik funksiyasi quyidagi ko’rinishda bo’ladi:

y = 0,1012x² - 8,7725x + 200,83

3.3. X2 – kirish omili va Y1 – chiqish o’rtasidagi empirik bog’liqlik ifodasini topish
3.3.1. Chiziqli empirik bog’liqlik qurish (chiziqli regressiya funksiyasi koeffisiyentlarini aniqlash)
Hisoblashlarni yuqoridagi X1 va Y1 uchun bajarilgani kabi olib boramiz.
X2 va Y1 uchun quyidagi jadvalni tuzamiz (2.4-jadval):
2.4-jadval.

№	x2	y1	x2^2	x2^3	x2^4	x2*y1	x2^2*y
1	2,718315	33,39134	7,389237	20,08628	54,60083	90,76818	246,7365
2	3,006297	33,31545	9,037824	27,17039	81,68227	100,1562	301,0992
3	3,055288	33,54803	9,334784	28,52045	87,13819	102,4989	313,1636
4	2,624334	33,79333	6,887131	18,07413	47,43257	88,68498	232,739
5	3,024335	33,84084	9,146601	27,66238	83,66031	102,346	309,5286
6	2,744328	33,95041	7,531335	20,66845	56,72101	93,17107	255,692
7	2,544345	34,05498	6,473693	16,47131	41,9087	86,64762	220,4615
8	2,763334	34,09657	7,636016	21,10087	58,30875	94,22022	260,362
9	2,924312	34,19845	8,551602	25,00756	73,1299	100,0069	292,4515
10	2,715344	34,30496	7,373091	20,02048	54,36248	93,14976	252,9336
11	2,974394	34,65998	8,84702	26,31452	78,26976	103,0924	306,6375
12	2,559344	34,73706	6,55024	16,76432	42,90565	88,90406	227,5361
13	2,744336	35,17995	7,531382	20,66864	56,72171	96,54561	264,9536
summa	36,39831	443,0713	102,29	288,5298	816,8421	1240,192	3484,295
urtachasi	2,79987	34,08241	7,868458	22,1946	62,83401	95,39938	268,0227

Olingan natijalar asosida sistema quyidagi ko’rinishda bo’ladi:

Bu sistemani yechib quyidagi ildizlarga ega bo’lamiz:

Demak, X2 va Y1 o’rtasidagi chiziqli regression bo’gliqlik funksiyasi quyidagi ko’rinishda bo’ladi:

y = -0,9227x + 36,666

3.3.2. 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:

Demak, X2 va Y1 uchun parabolik regression bo’gliqlik funksiyasi quyidagi ko’rinishda bo’ladi:

Y^ = -3,7416x² + 20,093x + 7,2651

3.4. X2 – kirish omili va Y2 – chiqish o’rtasidagi empirik bog’liqlik ifodasini topish
3.4.1. Chiziqli empirik bog’liqlik qurish (chiziqli regressiya funksiyasi koeffisiyentlarini aniqlash)
Hisoblashlarni yuqoridagi X1 va Y1 uchun bajarilgani kabi olib boramiz.
X2 va Y2 uchun quyidagi jadvalni tuzamiz (2.5-jadval):

№	x2	y2	x2^2	x2^3	x2^4	x2*y2	x2^2*y2
1	2,851059	10,98937	8,128536	23,17493	66,07309	31,33135	89,327518
2	2,771003	10,61809	7,678456	21,27702	58,95868	29,42276	81,530555
3	2,800997	10,1182	7,845583	21,97545	61,55317	28,34103	79,383137
4	2,709664	10,45705	7,342277	19,8951	53,90903	28,33509	76,778554
5	2,730717	11,01645	7,456817	20,36246	55,60411	30,08282	82,147668
6	2,837793	11,20233	8,053071	22,85295	64,85195	31,7899	90,213165
7	2,811408	11,75259	7,904014	22,22141	62,47344	33,04131	92,8926
8	2,747284	12,07292	7,54757	20,73532	56,96581	33,16775	91,121223
9	2,782971	11,65261	7,744929	21,55392	59,98393	32,42888	90,248651
10	2,87681	11,82661	8,276034	23,80857	68,49274	34,0229	97,877412
11	2,624254	11,5493	6,88671	18,07248	47,42678	30,30829	79,536668
12	2,809685	12,00935	7,894333	22,18059	62,32049	33,7425	94,805825
13	2,784294	15,49092	7,752292	21,58466	60,09803	43,13127	120,09013
summa	36,13794	150,7558	100,5106	279,6949	778,7112	419,1459	1165,9531
urtacha	2,779841	11,5966	7,731586	21,51499	59,90086	32,24199	89,6887

2.5-jadval.
Olingan natijalar asosida sistema quyidagi ko’rinishda bo’ladi:

Bu sistemani yechib quyidagi ildizlarga ega bo’lamiz:

Demak, X2 va Y2 o’rtasidagi chiziqli regression bo’gliqlik funksiyasi quyidagi ko’rinishda bo’ladi:

Y^ = 1,2984x + 7,9872