1- masala. Quyidagi jadvalda keltirilgan ma’lumotlar asosida

28- Masala. Talab D_i, taklif S_i va narx P bo‘yicha ma’lumotlar asosida korrelyatsion tahlil usulini qo‘llab, modelda qatnashadigan omillarni tanlang. Iqtisodiy tahlilni amalga oshirib, xulosa bering.

Di	2,2	1,8	1,6	1,4	1,2
Si	2	4	6	8	10
P	5	6	8	10	12

Korrelyatsion tahlil usulini qo'llab, Di (talab), Si (taklif) va P (narx) o'rtasidagi munosabatlarni tahlil qilish uchun quyidagi ma'lumotlar berilgan:

Di: 2, 2, 1.8, 1.6, 1.4, 1.2

Si: 2, 4, 6, 8, 10
P: 5, 6, 8, 10, 12

Di, Si va P o'rtasidagi munosabatlarni o'rganish uchun korrelyatsion ko'effitsiyentlarini hisoblaymiz. Korrelyatsion ko'effitsiyenti (-1 va 1 orasida bo'lgan qiymat) bilan Di va Si o'rtasidagi tasviriy munosabatni, shuningdek, Di va P o'rtasidagi narxning tasvirlashini topamiz.

Korrelyatsion ko'effitsiyenti (r) hisoblanishi:

Di va Si o'rtasidagi korrelyatsion ko'effitsiyenti:
r(Di, Si) = (Σ(Di - Di_mean) * (Si - Si_mean)) / (sqrt(Σ(Di - Di_mean)^2) * sqrt(Σ(Si - Si_mean)^2))

Di va P o'rtasidagi korrelyatsion ko'effitsiyenti:

r(Di, P) = (Σ(Di - Di_mean) * (P - P_mean)) / (sqrt(Σ(Di - Di_mean)^2) * sqrt(Σ(P - P_mean)^2))

Di, Si va P larni qiymatlarini hisoblash:

Di_mean = (2 + 2 + 1.8 + 1.6 + 1.4 + 1.2) / 6 = 1.8
Si_mean = (2 + 4 + 6 + 8 + 10) / 5 = 6
P_mean = (5 + 6 + 8 + 10 + 12) / 5 = 8.2

Korrelyatsion ko'effitsiyentlarni hisoblash:

r(Di, Si) = ((2 - 1.8) * (2 - 6) + (2 - 1.8) * (4 - 6) + (1.8 - 1.8) * (6 - 6) + (1.6 - 1.8) * (8 - 6) + (1.4 - 1.8) * (10 - 6)) / (sqrt((2 - 1.8)^2 + (2 - 1.8)^2 + (1.8 - 1.8)^2 + (1.6 - 1.8)^2 + (1.4 - 1.8)^2) * sqrt((2 - 6)^2 + (4 - 6)^2 + (6 - 6)^2 + (8 - 6)^2 + (10 - 6)^2))
= (-0.4 * -4 + -0.4 * -2 + 0 * 0 + -0.2 * 2 + -0.4 * 4) / (sqrt(0.04 + 0.04 + 0 + 0.04 + 0.04) * sqrt(16 + 4 + 0 + 4 + 16))
= (-1.6 + 0.8 + 0 + -0.4 + -1.6) / (sqrt(0.16 + 0.16 + 0.04 + 0.16 + 0.16) * sqrt(40))
= -2 / (0.8 * 6.324)
= -2 / 5.059
= -0.395

r(Di, P) = ((2 - 1.8) * (5 - 8.2) + (2 - 1.8) * (6 - 8.2) + (1.8 - 1.8) * (8 - 8.2) + (1.6 - 1.8) * (10 - 8.2) + (1.4 - 1.8) * (12 - 8.2)) / (sqrt((2 - 1.8)^2 + (2 - 1.8Korrelyatsion tahlil usulini qo'llab, Di (talab), Si (taklif) va P (narx) o'rtasidagi munosabatlarni tahlil qilish uchun quyidagi ma'lumotlar berilgan:

Di: 2, 2, 1.8, 1.6, 1.4, 1.2

Si: 2, 4, 6, 8, 10
P: 5, 6, 8, 10, 12

Di, Si va P o'rtasidagi munosabatlarni o'rganish uchun korrelyatsion ko'effitsiyentlarini hisoblaymiz. Korrelyatsion ko'effitsiyenti (-1 va 1 orasida bo'lgan qiymat) bilan Di va Si o'rtasidagi tasviriy munosabatni, shuningdek, Di va P o'rtasidagi narxning tasvirlashini topamiz.

Korrelyatsion ko'effitsiyenti (r) hisoblanishi:

Di va Si o'rtasidagi korrelyatsion ko'effitsiyenti:
r(Di, Si) = (Σ(Di - Di_mean) * (Si - Si_mean)) / (sqrt(Σ(Di - Di_mean)^2) * sqrt(Σ(Si - Si_mean)^2))

Di va P o'rtasidagi korrelyatsion ko'effitsiyenti:

r(Di, P) = (Σ(Di - Di_mean) * (P - P_mean)) / (sqrt(Σ(Di - Di_mean)^2) * sqrt(Σ(P - P_mean)^2))

Di, Si va P larni qiymatlarini hisoblash:

Di_mean = (2 + 2 + 1.8 + 1.6 + 1.4 + 1.2) / 6 = 1.8
Si_mean = (2 + 4 + 6 + 8 + 10) / 5 = 6
P_mean = (5 + 6 + 8 + 10 + 12) / 5 = 8.2

Korrelyatsion ko'effitsiyentlarni hisoblash:

r(Di, Si) = ((2 - 1.8) * (2 - 6) + (2 - 1.8) * (4 - 6) + (1.8 - 1.8) * (6 - 6) + (1.6 - 1.8) * (8 - 6) + (1.4 - 1.8) * (10 - 6)) / (sqrt((2 - 1.8)^2 + (2 - 1.8)^2 + (1.8 - 1.8)^2 + (1.6 - 1.8)^2 + (1.4 - 1.8)^2) * sqrt((2 - 6)^2 + (4 - 6)^2 + (6 - 6)^2 + (8 - 6)^2 + (10 - 6)^2))
= (-0.4 * -4 + -0.4 * -2 + 0 * 0 + -0.2 * 2 + -0.4 * 4) / (sqrt(0.04 + 0.04 + 0 + 0.04 + 0.04) * sqrt(16 + 4 + 0 + 4 + 16))
= (-1.6 + 0.8 + 0 + -0.4 + -1.6) / (sqrt(0.16 + 0.16 + 0.04 + 0.16 + 0.16) * sqrt(40))
= -2 / (0.8 * 6.324)
= -2 / 5.059
= -0.395

r(Di, P) = ((2 - 1.8) * (5 - 8.2) + (2 - 1.8) * (6 - 8.2) + (1.8 - 1.8) * (8 - 8.2) + (1.6 - 1.8) * (10 - 8.2) + (1.4 - 1.8) * (12 - 8.2)) / (sqrt((2 - 1.8)^2 + (2 - 1.8

29- Masala. Berilgan ma’lumotlar asosida korrelyatsion tahlil usulini qo‘llab, modelda qatnashadigan omillarni tanlang, natijalarni izohlang. Iqtisodiy tahlilni amalga oshirib, xulosa bering.

Y	9	15	16	20	25
X1	11	12	13	13	15
X2	6	9	11	13	16

Korrelyatsion tahlil usulini qo'llab, Y, X1 va X2 o'rtasidagi munosabatlarni tahlil qilish uchun berilgan ma'lumotlar asosida korrelyatsion ko'effitsiyentlarni hisoblaymiz.

Y: 9, 15, 16, 20, 25

X1: 11, 12, 13, 13, 15
X2: 6, 9, 11, 13, 16

Korrelyatsion ko'effitsiyentlarini hisoblash uchun quyidagi formulalardan foydalanamiz:

r(Y, X1) = (Σ(Y - Y_mean) * (X1 - X1_mean)) / (sqrt(Σ(Y - Y_mean)^2) * sqrt(Σ(X1 - X1_mean)^2))

r(Y, X2) = (Σ(Y - Y_mean) * (X2 - X2_mean)) / (sqrt(Σ(Y - Y_mean)^2) * sqrt(Σ(X2 - X2_mean)^2))

Y, X1 va X2 larni qiymatlarini hisoblash:

Y_mean = (9 + 15 + 16 + 20 + 25) / 5 = 17
X1_mean = (11 + 12 + 13 + 13 + 15) / 5 = 12.8
X2_mean = (6 + 9 + 11 + 13 + 16) / 5 = 11

Korrelyatsion ko'effitsiyentlarni hisoblash:

r(Y, X1) = ((9 - 17) * (11 - 12.8) + (15 - 17) * (12 - 12.8) + (16 - 17) * (13 - 12.8) + (20 - 17) * (13 - 12.8) + (25 - 17) * (15 - 12.8)) / (sqrt((9 - 17)^2 + (15 - 17)^2 + (16 - 17)^2 + (20 - 17)^2 + (25 - 17)^2) * sqrt((11 - 12.8)^2 + (12 - 12.8)^2 + (13 - 12.8)^2 + (13 - 12.8)^2 + (15 - 12.8)^2))
= (-8 * -1.8 + -2 * -0.8 + -1 * 0.2 + 3 * 0.2 + 8 * 2.2) / (sqrt(64 + 4 + 1 + 9 + 64) * sqrt(3.24 + 0.04 + 0.04 + 0.04 + 4.84))
= (14.4 + 1.6 + 0.2 + 0.6 + 17.6) / (sqrt(142) * sqrt(12.2))
= 34 / (11.92 * 3.49)
= 34 / 41.68
= 0.815

r(Y, X2) = ((9 - 17) * (6 - 11) + (15 - 17) * (9 - 11) + (16 - 17) * (11 - 11) + (20 - 17) * (13 - 11) + (25 - 17) * (16 - 11)) / (sqrt((9 - 17)^2 + (15 - 17)^2 + (16 - 17)^2 + (20 - 17)^2 + (25 - 17)^2) * sqrt((6 - 11)^2 + (9 - 11)^2 + (11 - 11)^2 + (13 - 11)^2 + (16 - 11)^2))

= (-8 * -5 + -2 * -2 + -1 * 0 + 3 * 2 + 8 * 5) / (sqrt(64 + 4 + 1 + 9 + 64) * sqrt(25 + 4 + 0 + 4 + 25))
= (40 + 4 + 0 + 6 + 40) / (sqrt(142) * sqrt(58))
= 90 / (11.92 * 7.62)
= 90 / 90.82
= 0.991

Natijalar:

r(Y, X1Korrelyatsion tahlil usulini qo'llab, Y, X1 va X2 o'rtasidagi munosabatlarni tahlil qilish uchun berilgan ma'lumotlar asosida korrelyatsion ko'effitsiyentlarni hisoblaymiz.

Y: 9, 15, 16, 20, 25

X1: 11, 12, 13, 13, 15
X2: 6, 9, 11, 13, 16

Korrelyatsion ko'effitsiyentlarini hisoblash uchun quyidagi formulalardan foydalanamiz:

r(Y, X1) = (Σ(Y - Y_mean) * (X1 - X1_mean)) / (sqrt(Σ(Y - Y_mean)^2) * sqrt(Σ(X1 - X1_mean)^2))

r(Y, X2) = (Σ(Y - Y_mean) * (X2 - X2_mean)) / (sqrt(Σ(Y - Y_mean)^2) * sqrt(Σ(X2 - X2_mean)^2))

Y, X1 va X2 larni qiymatlarini hisoblash:

Y_mean = (9 + 15 + 16 + 20 + 25) / 5 = 17
X1_mean = (11 + 12 + 13 + 13 + 15) / 5 = 12.8
X2_mean = (6 + 9 + 11 + 13 + 16) / 5 = 11

Korrelyatsion ko'effitsiyentlarni hisoblash:

r(Y, X1) = ((9 - 17) * (11 - 12.8) + (15 - 17) * (12 - 12.8) + (16 - 17) * (13 - 12.8) + (20 - 17) * (13 - 12.8) + (25 - 17) * (15 - 12.8)) / (sqrt((9 - 17)^2 + (15 - 17)^2 + (16 - 17)^2 + (20 - 17)^2 + (25 - 17)^2) * sqrt((11 - 12.8)^2 + (12 - 12.8)^2 + (13 - 12.8)^2 + (13 - 12.8)^2 + (15 - 12.8)^2))
= (-8 * -1.8 + -2 * -0.8 + -1 * 0.2 + 3 * 0.2 + 8 * 2.2) / (sqrt(64 + 4 + 1 + 9 + 64) * sqrt(3.24 + 0.04 + 0.04 + 0.04 + 4.84))
= (14.4 + 1.6 + 0.2 + 0.6 + 17.6) / (sqrt(142) * sqrt(12.2))
= 34 / (11.92 * 3.49)
= 34 / 41.68
= 0.815

r(Y, X2) = ((9 - 17) * (6 - 11) + (15 - 17) * (9 - 11) + (16 - 17) * (11 - 11) + (20 - 17) * (13 - 11) + (25 - 17) * (16 - 11)) / (sqrt((9 - 17)^2 + (15 - 17)^2 + (16 - 17)^2 + (20 - 17)^2 + (25 - 17)^2) * sqrt((6 - 11)^2 + (9 - 11)^2 + (11 - 11)^2 + (13 - 11)^2 + (16 - 11)^2))

= (-8 * -5 + -2 * -2 + -1 * 0 + 3 * 2 + 8 * 5) / (sqrt(64 + 4 + 1 + 9 + 64) * sqrt(25 + 4 + 0 + 4 + 25))
= (40 + 4 + 0 + 6 + 40) / (sqrt(142) * sqrt(58))
= 90 / (11.92 * 7.62)
= 90 / 90.82
= 0.991
30- Masala. Berilgan ma’lumotlar asosida bir omilli ekonometrik modelini tuzing va Fisher mezoni qiymatini hisoblang va tahlil qiling. Iqtisodiy tahlilni amalga oshirib, xulosa bering.