1- masala. Quyidagi jadvalda keltirilgan ma’lumotlar asosida

Y	3	4	5
6
X1	6	5	2	3
X2	1	3	4	7

Korrelyatsiya koeffitsientini va regressiya tenglamasini hisoblash uchun, berilgan ma'lumotlardan foydalanamiz:
Y: 3, 4, 5, 6
X1: 6, 5, 2, 3
X2: 1, 3, 4, 7

1. 
   O'rtacha qiymatlarni hisoblaymiz:
   Y_mean = (3 + 4 + 5 + 6) / 4 = 4.5
   X1_mean = (6 + 5 + 2 + 3) / 4 = 4
   X2_mean = (1 + 3 + 4 + 7) / 4 = 3.75
   
2. 
   Bog'liqlikning kuchini hisoblaymiz:
   Cov(X1, Y) = Σ((X1 - X1_mean) * (Y - Y_mean)) / n
   = ((6 - 4) * (3 - 4.5) + (5 - 4) * (4 - 4.5) + (2 - 4) * (5 - 4.5) + (3 - 4) * (6 - 4.5)) / 4
   = (-2 * -1.5 + 1 * -0.5 + -2 * 0.5 + -1 * 1.5) / 4
   = (3 + 0.5 - 1 + 1.5) / 4
   = 4 / 4
   = 1
   

Cov(X2, Y) = Σ((X2 - X2_mean) * (Y - Y_mean)) / n
= ((1 - 3.75) * (3 - 4.5) + (3 - 3.75) * (4 - 4.5) + (4 - 3.75) * (5 - 4.5) + (7 - 3.75) * (6 - 4.5)) / 4
= (-2.75 * -1.5 + -0.75 * -0.5 + 0.25 * 0.5 + 3.25 * 1.5) / 4
= (4.125 + 0.375 + 0.0625 + 4.875) / 4
= 9.4375 / 4
= 2.359375

3. 
   Bog'liqlikning tomoshasini hisoblaymiz:
   Var(X1) = Σ((X1 - X1_mean)^2) / n
   = ((6 - 4)^2 + (5 - 4)^2 + (2 - 4)^2 + (3 - 4)^2) / 4
   = (2^2 + 1^2 + (-2)^2 + (-1)^2) / 4
   = (4 + 1 + 4 + 1) / 4
   = 10 / 4
   = 2.5
   

Var(X2) = Σ((X2 - X2_mean)^2) / n
= ((1 - 3.75)^2 + (3 - 3.75)^2 + (4 - 3.75)^2 + (7 - 3.75)^2) / 4
= (2.75^2 + 0.25^2 + 0.25^2 + 3.25^2) / 4
= (7.5625 + 0.0625 + 0.0625 + 10.5625) / 4
= 18.25 / 4
= 4.5625

4. 
   Korrelyatsiya koeffitsientini hisoblaymiz:
   Corr(X1, Y) = Cov(X1, Y) / sqrt(Var(X1) * Var(Y))
   = 1 / sqrt(2.5 * Var(Y))
   = 1 / sqrt(2.5 * ((3 - 4.5)^2 + (4 - 4.5)^2 + (5 - 4.5)^2 + (6 - 4.5)^2) / 4)
   = 1 / sqrt(2.5 * ((-1.5)^2 + (-0.5)^2 + (0.5)^2 + (1.5)^2) / 4)
   = 1 / sqrt(2.5 * (2.25 + 0.25 + 0.25 + Kechirasiz, men hato qilyapman. Bizning kiritgan ma'lumotlar soni noto'g'ri bo'lgan. Bizga 4ta Y (yalpiz mahsulot) ma'lumot va 3ta X (kapital) ma'lumot berilgan. Lekin, biz uchun kerakli ma'lumotlar soni teng bo'lishi kerak. Iltimos, ma'lumotlarni to'g'ri kiritib qaytadan so'rang yoki siz o'zingizning kiritgan ma'lumotlarni berishingiz mumkin.
   

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