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181
MAHSULOTLARGA SOF SOLIQLAR HAJMINI TREND MODELLARI
YORDAMIDA PROGNOZLASH
R.A. Xurramov
Termiz davlat universiteti o’qituvchisi
Annotatsiya:
Ushbu maqolada Surxondaryo viloyati mahsulotlarga sof soliqlari
hajmi eksponensial, chiziqli, polinomli, darajali, logarifmli trend modellari yordamida
2028 yilga qadar prognoz qilingan hamda iqtisodiy jarayonga eng mos model turi
aniqlangan.
Kalit so’zlar:
eksponensial, chiziqli, polinomli, darajali, logarifmli trend
modellari, regressiya.
Ko’rsatkichlarni yillar oralig’idagi o'zgarishini o'rganish ahamiyati katta. Sababi
ular vaqt davomida o'zgarib turadi. Bunday holatlarda trend modellari bilan
prognozlashtirish ko’rsatkichlarning nazariy qiymatlarini aniqlash orqali kelgusi
holatni tadqiq etish imkonini beradi. Trend modellari tajribalarda keng qo'llaniladigan
eng sodda prognozlash modellaridan biri hisoblanadi.
Trend – tasodifiy ta’sirlardan holi holda vaqt bo'yicha harakat qonuniyatidir.
Trend vaqt bo'yicha regressiya bo'lib, doimiy omillar ta’sirida yuzaga keladigan
rivojlanishning determinik tarkibiy qismidir. Trendlardagi chetlanishlar tasodifiy
omillar sababli yuzaga keladi. Unda natijaviy belgi sifatrida o'rganayotgan ko'rsatkich,
omil belgi sifatida esa kuzatuv davri soni olinadi. Odatda trend modellari umumiy
ko’rinishi quyidagicha bo’ladi
1
:
𝑦
𝑡
= 𝑓(𝑡) + 𝜀
𝑡
(1)
1
Фукина С.П. Трендовые модели в экономических исследованиях // Экономический анализ: теория и практика.
2011.
№11.
URL:
https://cyberleninka.ru/article/n/trendovye-modeli-v-ekonomicheskih-issledovaniyah
(дата
обращения: 28.11.2023).
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182
bu yerda,
𝑓(𝑡)
- jarayonlaming vaqt bo'yicha yo'nalishining doimiy tarkibiy qismi;
𝜀
𝑡
- tasodifiy tarkibiy qism;
Trend modellarining keng qo’llaniladigan quyidagi turlari mavjud
2
3
4
5
:
-
𝑦 = 𝑎 + 𝑏𝑡
- chiziqli trend modeli
-
𝑦 = 𝑎𝑒
𝑏𝑡
- eksponentsial trend modeli
-
𝑦 = 𝑎 + 𝑏
1
𝑥 + 𝑏
2
𝑥
2
- 2-darajali polinom
-
𝑦 = 𝑎𝑡
𝑏
- darajali
-
𝑦 = 𝑎 + 𝑏ln𝑡
- logarifmik trend tenglamalari
Odatda, trend parametrlari eng kichik kvadratlar usuli yordamida baholanadi.
Egri chiziqli trend modellari logarifmlash yo‘li bilan chiziqli trend ko‘rinishiga
keltiriladi va tegishli hisob-kitoblar amalga oshiriladi.
Eng maqbul modelni tanlash uchun ularning determinatsiya koeffitsienti va
xatoliklariga ko’zdan kechiriladi.
Surxondaryov viloyati mahsulotlarga sof soliqlari hajmini eksponentsial,
chiziqli, darajali va 2-tartibi polinom trend modellari bilan modellashtirish uchun
Microsoft Excel dasturiy ta’minotining «
Анализ данных
» paketidan foydalangan holda
amalga oshirildi. Dastlab tahlil uchun 1-jadvaldagi ma’lumotlardan foydalanildi.
1-jadval
Surxondaryo viloyati mahsulotlarga sof soliqlar hajmi (mlrd so’m)
6
Yillar
𝒚
Yillar
𝒚
2010
113,6
2017
372,5
2011
109,2
2018
528,7
2012
149
2019
880,6
2013
168,6
2020
701,6
2
Tuychiyeva, M. K., & Turayev, B. E. (2024). Trend modellari yordamida elektron tijorat aylanmasi hajmini
modellashtirish va prognozlashtirish. Technical science research in Uzbekistan, 2(2), 193-199.
3
Mirzohidovna, P. M., & Turayev, B. E. (2024). Surxondaryo viloyati asosiy kapitalga kiritilgan investitsiyalar hajmini
trend modellari orqali modellashtirish. Journal of Universal Science Research, 2(2), 296-302.
4
Xursanova, S. A., & Turayev, B. E. (2024). Hudud dehqonchilik mahsulotlari ishlab chiqarish hajmini trend modellari
yordamida prognozlashtirish. Technical science research in Uzbekistan, 2(2), 200-208.
5
Tulaganova, M. H., & Turayev, B. E. (2024). Asosiy kapitalga kiritilgan investitsiyalarni trend modellari yordamida
prognozlash (Surxondaryo viloyati misolida). Technical science research in Uzbekistan, 2(2), 223-230.
6
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183
2014
188,5
2021
696,5
2015
11114,4
2022
34385,3
2016
12179,6
2023
40909,8
Tajriba uchun ma’lumotlarni MS Excelga yuklab oldik. Ma’lumotlar oraligini
belgilab olib, “
Вставка – Диаграмма – Точечная – Точечная
” diagrammasini, keyin
esa, istalgan nuqtani belgilab, sichqonchaning o’ng tugmasini bosish orqali hosil
qilinadigan menyudan “
Добавить линию тренда...
” ni tanladik. Natijada quyidagiga
ega bo’ldik (1-rasm).
1-rasm. Eksponentsial trend modeli
7
Boshqa model turlarini tanlab 2-5-rasmlardagi natijalarga ega bo’lamiz.
2-rasm. Chiziqli trend modeli
7
Muallif ishlanmasi
y = 83,957e
0,1872x
R² = 0,9562
0,0
200,0
400,0
600,0
800,0
1 000,0
1 200,0
1 400,0
0
2
4
6
8
10
12
14
16
y = 72,13x - 91,019
R² = 0,8928
-200,0
0,0
200,0
400,0
600,0
800,0
1 000,0
1 200,0
0
2
4
6
8
10
12
14
16
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184
3-rasm. Logarifmik trend modeli
4-rasm. 2-darajali polinom trend modeli
5-rasm. 2-darajali trend modeli.
Shunday qilib, barcha turdagi modellarni tuzib oldik. Endi ularning sifatini va
ahamiyatliligini tekshirib ko’ramiz (2-jadval).
y = 341,24ln(x) - 164,07
R² = 0,6842
-400,0
-200,0
0,0
200,0
400,0
600,0
800,0
1 000,0
1 200,0
0
2
4
6
8
10
12
14
16
y = 3,4578x
2
+ 20,264x + 47,292
R² = 0,919
0,0
200,0
400,0
600,0
800,0
1 000,0
1 200,0
0
2
4
6
8
10
12
14
16
y = 61,712x
0,9514
R² = 0,8456
0,0
200,0
400,0
600,0
800,0
1 000,0
1 200,0
0
2
4
6
8
10
12
14
16
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185
2-jadval
Regression tahlil natijalari
8
T/r
Model turi
Model tenglam,asi
Determinatsiya
koeffitsienti
1
Eksponentsial
𝑦 = 83,957𝑒
0,1872𝑡
0,9562
2
Chiziqli
𝑦 = 72,13𝑡 − 91,019
0,8928
3
Logarifmik
𝑦 = 341,24 ln(𝑡) − 164,07
0,6842
4
Polinomli
𝑦 = 3,4578𝑡
2
− 20,264𝑡
+ 47,292
0,919
5
Darajali
𝑦 = 61.712𝑡
0.9514
0,8456
2-jadvaldan eksponentsial trend modeli bo’yicha determinatsiya koeffitsienti eng
katta. Demak, model sifati boshqalarga qaraganda yuqori. Modelning ahamiyatini
Fisher mezoni bilan va parametrlari statistik ishonchliligini Styudent t mezoni bilan
tekshirildi (3-jadval).
3-jadval
Regression tahlil natijalari
9
ВЫВОД
ИТОГОВ
Регрессионная
статистика
Множественны
й R
0,978
R-квадрат
0,956
8
Muallif ishlanmasi
9
MS Excelda shakllantirildi.
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186
Нормированный
R-квадрат
0,953
Стандартная
ошибка
0,175
Наблюдения
14
Дисперсионный
анализ
df
SS
MS
F
Значимост
ь F
Регрессия
1
7,974
7,974
261,749
0,000
Остаток
12
0,366
0,030
Итого
13
8,339
Коэффи
-циенты
Стандартна
я ошибка
t-ста-
тистик
а
P-
Значени
е
Нижние
95%
Y-пересечение
4,430
0,099
44,964
0,000
4,216
Переменная X 1
0,187
0,012
16,179
0,000
0,162
3-jadvalga ko’ra, Fisher F mezoni qiymati 261,749. Bu qiymat jadval qiymatidan
katta. Sababi, p-qiymat
0,000
ga teng. Shuningdek, parametrlarining Styudent t mezoni
bo’yicha qiymati esa 44,964 va 16,179 ga teng. Bunda p-qiymat 0,05 ahamiyatlilik
darajasidan kichik. Demak, model iqtisodiy jarayonga mos.
Shunday qilib, Surxondaryo viloyati mahsulotlarga sof soliqlar hajmi bo’yicha
modeli umumiy ko’rinishi quyidagicha bo’ldi:
𝑦 = 83,957𝑒
0,1872𝑡
(2)
Bu modeldan foydalanib keyingi bo’limlarda hudud mahsulotlarga sof soliqlar
hajmini prognoz qilindi. (6-rasm)
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187
6-rasm. Surxondaryo viloyati mahsulotlarga sof soliqlar hajmi prognozi (mlrd so’m).
6-rasmga ko’ra 2028 yilga kelib, hudud mahsulotlarga sof soliqlar hajmi 2943,7
mlrd so’mni, o’sish esa 3 barobarni tashkil etishi kutilmoqda.
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