Korrelyatsiya koeffitsienti. Pearsonning korrelyatsion mezoni

Suvning qattiqligi (darajalarda)	Suvdagi kaltsiy miqdori (mg / l)	d x	d y		d x x d y		d x 2
d y 2
4 8 11 27 34 37	28 56 77 191 241 262	-16 -12 -9 +7 +14 +16	-114 -86 -66 +48 +98 +120		1824 1032 594 336 1372 1920		256 144 81 49 196 256		12996 7396 4356 2304 9604 14400
M x \u003d Σ x / n	M y \u003d Σ y / n			Σ d x x d y \u003d 7078		Σ d x 2 \u003d 982		Σ d y 2 \u003d 51056
M x \u003d 120/6 \u003d 20	M y \u003d 852/6 \u003d 142

1. 
   Formulalar bo'yicha "x" va "y" qatorlaridagi M x qator parametrlarining o'rtacha qiymatlarini aniqlang:
   M x \u003d Σx / n (1-ustun) va
   M y \u003d /y / n (2-ustun)
   
2. 
   "X" qatorida va "y" qatorida hisoblangan o'rtacha qiymatdan har bir variantning og'ishini (d x va d y) toping.
   d x \u003d x - M x (3-ustun) va d y \u003d y - M y (4-ustun).
   
3. 
   D x x d y burilishlar sonini toping va ularni yig'ing: Σ d x x d y (5-ustun)
   
4. 
   Har bir og'ish d x va d y kvadrat va "y" qatorlari uchun ularning qiymatlarini jamladi: Σ d x 2 \u003d 982 (6-ustun) va Σ d y 2 \u003d 51056 (7-ustun).
   
5. 
   X d x 2 x Σ d y 2 mahsulotini aniqlang va shu mahsulotdan kvadrat ildizni oling
   
6. 
   Olingan qiymatlar Σ (d x x d y) va (Xd x 2 x Σd y 2)  korrelyatsiya koeffitsientini hisoblash formulasida o'rnini bos:
   
7. 
   Korrelyatsiya koeffitsientining ishonchliligini aniqlang:
   1-usul. Formuladan foydalanib, korrelyatsiya koeffitsientining (mr xy) va t mezonining xatosini toping:
   

Mezon t \u003d 14.1, bu xatosiz bashorat qilish p-99,9% ga to'g'ri keladi.

2-usul. Korrelyatsiya koeffitsientining ishonchliligi "Standart korrelyatsiya koeffitsientlari" jadvaliga muvofiq baholanadi (1-ilovaga qarang). Erkinlik darajalari soni bilan (n - 2) \u003d 6 - 2 \u003d 4, bizning xisoblangan korrelyatsiya koeffitsienti r xy \u003d + 0.99, jadvaldagidan kattaroqdir (r \u003d 99% p \u003d 99%).