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y  ^{ }
86
⁸⁶ 
y  ^{ }
79

     

¹⁹

5. 
   x  ^
   

37
²⁸

14
 ⁶⁵
y  ^{ }
57
⁸⁵
y  ^{ }
60

     

2. 
   n=4 uchun (yahshi bahoga davogar uchun)
   

¹⁵
41 12
³⁸
 ⁶⁸
⁸⁰ 

     

^ 32
_{A) x  } 24 25
_ 16
16 35
47 14 _


36 19 ^
26 28
_{y  } 78_

 ₉₈
 
58
_{y  } 60_

 ₉₀
 
70

     

 ²⁵
21 28
³⁷ 
 ⁵⁵
 ⁶⁶

     


_{B) x  } 45 37


32 16
^ 41 26
47 17 _
36 19 ^
26 44^
_{y  } 65_

 ₈₅
 
97
_ 75_

y 
 ₉₀
_{ 70}_

     

 ²⁴
47 12
¹¹
 ⁶³
 ⁷⁰

     

^ 29
_{C) x  } 46 19
_ 16
38 35
42 49_


31 19 ^
22 28
_{y  } 73_

 ₉₃
 
53
_{y  } 85_

 ₆₆
 
78

     

 ²⁹
41 12
¹⁵ 
⁵⁴
 ⁷⁵

     

^ 34
D) x  ^{ 45}

16
25 34
47 18
35 26
19 _


46^
28
_{y  } 78_

₈₇ 
 
91
_{y  } 78_

₉₀
 
95

     

 ^{26 19
28 38}
 ⁵⁷ 
 ⁵⁵

     

^ 32
E) x  ^{ 44}

46
25 47
22 15
35 26
14 _


25^
33
_{y  } 77 _

 ₆₇ 
 
97
_{y  }86 _

 ₇₀
 
93

     

3. 
   n=5 uchun (a’lo bahoga davogar uchun)
   

^15 	35	49	47	^31 	 ^64  	 ^72  
 32	44	39	14	21	 75	 70
^A)x  ^41	24	29	28	45^	y  ^86 ^	y  ^80 ^  
 ^28 ^26	37 16	19 14	29 36	^18 35^	^97  54	 ^94  68  
^18 	35	41	19	^31 	 ^58  	 ^78  
 45	47	35	26	21	 69	86
^B)x  ^35	18	31	33	45^	y  ^75^	y  ^95^  
 ^23	26	16	29	^18	^86	^85

   

   
   

^19

45 24

41 35^
 ₉₁
 ₉₅

     

3. 
   

    ^25 	35	49	42	^32 	 ^58  	 ^63  
    35	44	26	45	31	 68	 74
   ^42	24	15	49	26^y  ^78^y		 ^85^

   
   
   
   x  _
   

    

 ^{28 37
} 26 16
27 16
14 36
¹⁸ 
35^
 ⁹⁸
 ₆₆
 ⁷⁰
 ₉₀

     

3. 
   

    ^45 	19	49	47	^39 	 ^59  	 ^63  
   19	44	22	48	21	87 	84 
   ^41	33	29	28	49^y  ^76^y		 ^80 ^

   
   
   
   x  _
   

    

 ^28
 24
37 11
44 14
^{25 18} 
36 35^
 ⁹²
 ₅₁
 ⁸⁸
 ₆₀

     

 ^41 	14	26	49	^31 	 ^77  	^84  
 39	44	39	14	29	87 	 85

^E) x  ^ 29 32 30 28 40^ y  ^ 59 ^ y  ^ 64^
     

 ^{28 37 19
} 26 16 14
^{29 25}
37 35^
 ⁹⁷ 
 ₆₆
 ⁹⁵
 ₇₀

     

12. - laboratoriya ishi

Statistika faoliyatida avtomatlashtirilgan axborot tizimlari va texnologiyalari

Statistik funksiyalardan foydalanish

Koreliatsion va regression taxlilda Excel funksiyalari foydalanish mumkin. Quyida regressia tenglamalarini tuzish va prognoz ma’lumot olish texnologiyasini ko’ramiz.

1. Chiziqli koreliatsiya.
Quyidagi kuzatuv natijalari berilgan bo’lsin:

y	x
^y1	^x1
^y2	^x2
…	…
^yn	^xn

y ni x ga chiziqli bog’liqlik funksiyasini tuzing.
Bunday masalani Microsort Excel dasturida СТАТИСТИЧЕСКАЯ funksiyalaridan foydalanib, chiziqli bog’lanishni aniqlash mumkin. Buning uchun berilgan ma’lumotlar Excel jadvaliga kiritiladi va shu jadval ostidan 2x5 o’lchamda yacheykani ajratamiz va unga ЛИНЕЙН funksiyasini kiritamiz.

1	Y	x
2	^Y1	^x1
3	^Y2	^x2
…	…	…
N	^yn	^xn
N+1	=ЛИНЕЙН(A1:A4;B1:B4;;1)
N+2
N+3
N+4
N+5

Funksiya argumentlari kiritilgandan so’ng CTRL+SHIT+ENTER tugmalari bosiladi, natijada n+1dan n+5 satrlarda quyidagi parametrlar qiymatlari hosil bo’ladi:

	A	B
1	m	b
2	^sen	^seb
3	^R2	^sey
4	F	^df
5	^ssper	^ssocт

Bu yerda:
m- chiziqli funksiya burchak koeffisiyenti b- chiziqli funksiya ozod hadi.
se- m koeffisient uchun standart xatolik ^sen^{- n ozod had uchun standart xatolik
r}2^{- determinatsiya koeffisiyenti. U 0 va 1 orasidagi son bo’lib x}i ^{va y}i ^qiymatlarni chiziqli bog’liqlik darajasini ko’rsatadi.

^r2	Bog’lanish darajasi
0-0,2 0,2-0,5 0,5-0,75 0,75-0,95 0,95-1	Bog’lanish deyarli yo’q Kuchsiz bog’lanish Sezilarli darajada bog’lanish Yaqin darajada bog’lanish Kuchli bog’lanish, funksional bog’lanishga yaqin.

^sey^{- y qiymat uchun standart xatolik}
F- F-statistika yoki F-kuzatuv qiymati. F-statistika bog’liq va bog’liq bo’lmagan tasodifiy miqdorlar o’rtasida o’zaro aloqa kuzatiladimi yo’qmi aniqlash uchun ishlatiladi.
df- erkinlik darajasi.
^ssper^{- regressiya kvadratlari yig’indisi ss}ocт^{- xatolik kvadratlari yig’indisi.}

Misol ko’raylik:

Kuzatuv natijalari berilgan bo’lsin:

	A	B
1	x	y
2	2	6
3	3	9
4	4	10
5	5	12
6	6	13

Bu ma’lumotlarni Microsoft Excel dasturiga kiritamiz. A7 – B11 yacheyka ^{ajratiladi va f}x ^{dan ЛИНЕЙН tanlanadi x ga A2dan A6gacha kiritiladi, y ga B2dan B6gacha} kiritiladi.

Natijada quyidagiga ega bo’lamiz: