Korrelyatsiya koeffitsienti. Pearsonning korrelyatsion mezoni


Suvning qattiqligi (darajalarda)


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Korrelyatsiya koeffitsienti

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%).

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