25- Masala. Berilgan ma’lumotlar asosida xususiy korrelyatsiya koeffitsientlarini shchisoblang va tahlil qiling. Iqtisodiy tahlilni amalga oshirib, xulosa bering.
Di
|
1,2
|
0,8
|
0,6
|
0,4
|
0,2
|
Si
|
2
|
5
|
6
|
7
|
10
|
P
|
5
|
6
|
8
|
10
|
12
|
Korrelyatsiya koeffitsientlarini hisoblash uchun, berilgan ma'lumotlardan foydalanamiz:
Di: 1.2, 0.8, 0.6, 0.4, 0.2
Si: 2, 5, 6, 7, 10
P: 5, 6, 8, 10, 12
O'rtacha qiymatlarni hisoblaymiz:
Di_mean = (1.2 + 0.8 + 0.6 + 0.4 + 0.2) / 5 = 0.64
Si_mean = (2 + 5 + 6 + 7 + 10) / 5 = 6
P_mean = (5 + 6 + 8 + 10 + 12) / 5 = 8.2
Bog'liqlikning kuchini hisoblaymiz:
Cov(Di, Si) = Σ((Di - Di_mean) * (Si - Si_mean)) / n
= ((1.2 - 0.64) * (2 - 6) + (0.8 - 0.64) * (5 - 6) + (0.6 - 0.64) * (6 - 6) + (0.4 - 0.64) * (7 - 6) + (0.2 - 0.64) * (10 - 6)) / 5
= (-0.56 * -4 + 0.16 * -1 + -0.04 * 0 + -0.24 * 1 + -0.44 * 4) / 5
= (2.24 + -0.16 + 0 + -0.24 + -1.76) / 5
= 0 / 5
= 0
Cov(Di, P) = Σ((Di - Di_mean) * (P - P_mean)) / n
= ((1.2 - 0.64) * (5 - 8.2) + (0.8 - 0.64) * (6 - 8.2) + (0.6 - 0.64) * (8 - 8.2) + (0.4 - 0.64) * (10 - 8.2) + (0.2 - 0.64) * (12 - 8.2)) / 5
= (-0.56 * -3.2 + 0.16 * -2.2 + -0.04 * -0.2 + -0.24 * 1.8 + -0.44 * 3.8) / 5
= (1.792 + -0.352 + 0.008 + -0.432 + -1.672) / 5
= -0.656 / 5
= -0.1312
Cov(Si, P) = Σ((Si - Si_mean) * (P - P_mean)) / n
= ((2 - 6) * (5 - 8.2) + (5 - 6) * (6 - 8.2) + (6 - 6) * (8 - 8.2) + (7 - 6) * (10 - 8.2) + (10 - 6) * (12 - 8.2)) / 5
= (-4 * -3.2 + -1 * -2.2 + 0 * -0.2 + 1 * 1.8 + 4 * 3.8) / 5
= (12.8 + 2.2 + 0 + 1.8 + 15.2) / 5
= 32 / 5
= 6.4
Bog'liqlikning tomoshasini hisoblaymiz:
Var(Di) = Σ((Di - Di_mean)^2) / n
= ((1.2 - 0.64)^2 + (0.8 - 0.64)^2 + (0.6 - 0.64)^2 + (0.4 - 0.64)^2 + (0.2 - 0.64)^2) / 5
= (0.3136 + 0.0256 + 0.0016 + 0.0256 + 0.3136) / 5
= 0.68 / 5
= 0.136
Var(Si)Korrelyatsiya koeffitsientlarini hisoblash uchun, berilgan ma'lumotlardan foydalanamiz:
Di: 1.2, 0.8, 0.6, 0.4, 0.2
Si: 2, 5, 6, 7, 10
P: 5, 6, 8, 10, 12
O'rtacha qiymatlarni hisoblaymiz:
Di_mean = (1.2 + 0.8 + 0.6 + 0.4 + 0.2) / 5 = 0.64
Si_mean = (2 + 5 + 6 + 7 + 10) / 5 = 6
P_mean = (5 + 6 + 8 + 10 + 12) / 5 = 8.2
Kovaryansi hisoblash uchun formuladan foydalanamiz:
Cov(X, Y) = Σ((Xi - X_mean) * (Yi - Y_mean)) / n
Cov(Di, Si) = ((1.2 - 0.64) * (2 - 6) + (0.8 - 0.64) * (5 - 6) + (0.6 - 0.64) * (6 - 6) + (0.4 - 0.64) * (7 - 6) + (0.2 - 0.64) * (10 - 6)) / 5
= (-0.56 * -4 + 0.16 * -1 + -0.04 * 0 + -0.24 * 1 + -0.44 * 4) / 5
= (2.24 + -0.16 + 0 + -0.24 + -1.76) / 5
= 0 / 5
= 0
Cov(Di, P) = ((1.2 - 0.64) * (5 - 8.2) + (0.8 - 0.64) * (6 - 8.2) + (0.6 - 0.64) * (8 - 8.2) + (0.4 - 0.64) * (10 - 8.2) + (0.2 - 0.64) * (12 - 8.2)) / 5
= (-0.56 * -3.2 + 0.16 * -2.2 + -0.04 * -0.2 + -0.24 * 1.8 + -0.44 * 3.8) / 5
= (1.792 + -0.352 + 0.008 + -0.432 + -1.672) / 5
= -0.656 / 5
= -0.1312
Cov(Si, P) = ((2 - 6) * (5 - 8.2) + (5 - 6) * (6 - 8.2) + (6 - 6) * (8 - 8.2) + (7 - 6) * (10 - 8.2) + (10 - 6) * (12 - 8.2)) / 5
= (-4 * -3.2 + -1 * -2.2 + 0 * -0.2 + 1 * 1.8 + 4 * 3.8) / 5
= (12.8 + 2.2 + 0 + 1.8 + 15.2) / 5
= 32 / 5
= 6.4
Korelyatsiya koeffitsientini hisoblash uchun formuladan foydalanamiz:
r(X, Y) = Cov(X, Y) / (σ(X) * σ(Y))
σ(X) - X ning standart deviasiya (o'zgaruvchining o'lchov markazi)
σ(Y) - Y ning standart deviasiya (o'zgaruvchining o'lchov markazi)
σ(Di) = sqrt(Var(Di))
Var(Di) = Σ((Di - Di_mean)^2) / n
σ(Si) = sqrt(Var(Si))
Var(Si) = Σ((Si - Si_mean)^2) / n
σ(P) = sqrt(Var(P))
Var(P) = Σ((P - P_mean)^2) / n
r(Di, Si) = Cov
26- Masala. Berilgan ma’lumotlar asosida korrelyatsion tahlil usulini qo‘llab, modelda qatnashadigan omillarni tanlang, natijalarni izohlang. Iqtisodiy tahlilni amalga oshirib, xulosa bering.
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