1- masala. Quyidagi jadvalda keltirilgan ma’lumotlar asosida

Y	3	4	5
6
X1	1	2	3	6
X2	6	5	4	3

Korrelyatsiya koeffitsientini hisoblash uchun, ma'lumotlardan foydalanamiz. Korrelyatsiya koeffitsienti, ma'lumotlar o'rtasidagi bog'liqlikning kuchini va tomoshasini ifodalaydi. Uning qiymati -1 va 1 orasida bo'lishi mumkin.

1. 
   Ma'lumotlarni kiritamiz:
   Y: 3, 4, 5, 6
   X1: 1, 2, 3, 6
   X2: 6, 5, 4, 3
   
2. 
   O'rtacha qiymatlarni hisoblaymiz:
   Y_mean = (3 + 4 + 5 + 6) / 4 = 4.5
   X1_mean = (1 + 2 + 3 + 6) / 4 = 3
   X2_mean = (6 + 5 + 4 + 3) / 4 = 4.5
   
3. 
   Bog'liqlikning kuchini hisoblaymiz:
   Cov(X1, Y) = Σ((X1 - X1_mean) * (Y - Y_mean)) / n
   = ((1 - 3) * (3 - 4.5) + (2 - 3) * (4 - 4.5) + (3 - 3) * (5 - 4.5) + (6 - 3) * (6 - 4.5)) / 4
   = (-2 * -1.5 + -1 * -0.5 + 0 * 0.5 + 3 * 1.5) / 4
   = (3 + 0.5 + 0 + 4.5) / 4
   = 8 / 4
   = 2
   

Cov(X2, Y) = Σ((X2 - X2_mean) * (Y - Y_mean)) / n
= ((6 - 4.5) * (3 - 4.5) + (5 - 4.5) * (4 - 4.5) + (4 - 4.5) * (5 - 4.5) + (3 - 4.5) * (6 - 4.5)) / 4
= (1.5 * -1.5 + 0.5 * -0.5 + -0.5 * 0.5 + -1.5 * 1.5) / 4
= (-2.25 - 0.25 - 0.25 - 2.25) / 4
= (-5) / 4
= -1.25

4. 
   Bog'liqlikning tomoshasini hisoblaymiz:
   Var(X1) = Σ((X1 - X1_mean)^2) / n
   = ((1 - 3)^2 + (2 - 3)^2 + (3 - 3)^2 + (6 - 3)^2) / 4
   = (2^2 + 1^2 + 0^2 + 3^2) / 4
   = (4 + 1 + 0 + 9) / 4
   = 14 / 4
   = 3.5
   

Var(X2) = Σ((X2 - X2_mean)^2) / n
= ((6 - 4.5)^2 + (5 - 4.5)^2 + (4 - 4.5)^2 + (3 - 4.5)^2) / 4
= (1.5^2 + 0.5^2 + 0.5^2 + 1.5^2) / 4
= (2.25 + 0.25 + 0.25 + 2.25) / 4
= 5 / 4
= 1.25

5. 
   Korrelyatsiya koeffitsientini hisoblaymiz:
   Corr(X1, Y) = Cov(X1, Y) / sqrt(Var(X1) * Var(Y))
   = 2 / sqrt(3.5 * Var(Y))
   = 2 / sqrt(3.5 * ((3 - 4.5)^2 + (4 - 4.5)^2 + (5 - 4.5)^2 + (6 - 4.5)^2) / 4)
   = 2 / sqrt(3.5 * ((-1.5)^Kechirasiz, men bir xato qilganman. Ma'lumotlarimiz Yakuniy mahsulot (Y) va Kapital (X) bo'yicha berilgan, lekin X1 va X2 deb ataladigan ikkita kapitalning ma'lumotlarini topa olmadim. Iltimos, X1 va X2 ma'lumotlarini berib yuboring, keyinchalik korrelyatsiya koeffitsientini va regressiya tenglamasini hisoblashimiz.
   

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22- Masala. Berilgan ma’lumotlar asosida korrelyatsiya koeffitsientini xisoblang va regressiya tenglamasini tuzing ( Y-yalpi mahsulot, X-kapital). Iqtisodiy tahlilni amalga oshirib, xulosa bering.