CC BY
6UDC 338.27:656.1 DOI: https://doi.org/10.46783/smart-scm/2021-6-1
JEL Classification: C51, C52, R12, R41. Received: 22 February 2021
Savchenko L.V. PhD of Technical Sciences, Associate Professor, Associate Professor of Logistics Department of National Aviation University (Ukraine)
ORCID - 0000-0003-3581-6942 Researcher ID - Q-5323-2018 Scopus author id: -57208225385
Semeriahina M.M. Senior Lecturer of Logistics Department, National Aviation University (Ukraine)
ORCID - 0000-0001-7490-6874 Researcher ID - S-7158-2018 Scopus author id: -
Shevchenko I.V. PhD of Economic Sciences, Associate Professor of higher mathematics department of the National Aviation University (Ukraine)
ORCID - 0000-0001-7910-0490 Researcher ID -Scopus author id: -
MODELING OF REGIONAL FREIGHT FLOWS OF ROAD TRANSPORT IN UKRAINE
Lidiia Savchenko, Myroslava Semeryagina, Iryna Shevchenko "Modeling of regional freight flows of road transport in Ukraine". A transport system can be defined as a complex system characterized by a random value of transport demand, variable weather and climatic factors, a set of characteristics of transport infrastructure, and a complex system of interconnections. One of the key modes of transport providing freight transport both in domestic and international traffic is road. Its mobility and the ability to deliver cargo from door to door is a unique competitive advantage over other modes of transport.
To create an effective logistics infrastructure that meets the demand for domestic freight transport, first of all, information is needed on the needs for transport between regions of the country. Thus, it is necessary to look for mathematical approaches to modeling freight flows, combining their practical implementation using widely used software products (for example, MS Excel).
The purpose of the paper is to build effective multifactor regression models of demand for input and output transportation of goods by road for each region of Ukraine according to publicly available statistical data of the State Statistics Service of Ukraine.
The modern approach to modeling cargo flows requires fast processing of a large amount of statistical data. In addition, the method should be as universal as possible and capable of quick and simple changes under conditions of a change in statistical data. From this point of view, the most acceptable option can be considered to be the modeling of freight traffic using regression models based on correlation and regression analysis. In
general, the task is to find the dependence of the demand for transportation on the factors that influence it. Such factors in the existing models are connected with various macroeconomic indicators, as well as the distance of delivery.
The data of regional statistics of the State Statistics Service of Ukraine and data of the "Lardi-Trans" website as the most widely used by freight carriers and shippers were taken as the initial data for modeling.
A list of factors has been found that significantly influence the demand for freight transport by road between regions of Ukraine. A rating of influencing factors has been compiled, among which are the gross regional product, regional volumes of foreign trade in goods (imports) and gross regional product per one inhabitant of the region. The absolute values of the correlation coefficients are in the range 0.351-0.974. The lowest correlation coefficient is between the transportation distance and the demand for delivery, which proves a negligible relationship between the volume of regional transportation and the distance of delivery.
Multivariate regression models with thirteen, five and two factors of influence on demand are built. Accuracy parameter values are acceptable for all model variants. The normalized R-squared of the obtained models does not fall below 84%, and the average approximation error does not rise above 1.6%, which is an excellent performance of the models.
Keywords: demand for freight transportation, regional transportation of goods by road, domestic transportation, modeling the demand for transportation, correlation-regression analysis, linear multivariate regression.
Лiдiя Савченко, Мирослава Семеряг'ша, 1рина Шевченко "Моделювання регональних вантажопоток'в автомоб'тьного транспорту в УкраШ". Транспортну систему можна визначити як складну систему, яка характеризуеться випадковою величиною транспортного попиту, змiнними погодно-кл'!матичними факторами, набором характеристик транспортноУ iнфраструктури та складною системою взаемозв'язк'!в. Одним з ключових вид'т транспорту, що забезпечуе вантажн перевезення як у внутршньому, так i м'жнародному сполученш, е автомобльний. Його мобльнсть та можлuвiсть доставки вантажу «в'!д дверей до дверей» е ун'1кальною конкурентною перевагою перед '¡ншими видами транспорту.
Для створення ефективноУлог'!стичноУ iнфраструктури, що забезпечуе попит на внутршш вантажн перевезення, перш за все необхiдна iнформацiя про потреби в перевезеннях м'жрегонами краУни. Таким чином, необхiдно шукати математичн пдходи до моделювання вантажопоток'т, комбнуючи Ух практичну реалiзацiю з використанням широко використовуваних програмних продукт 'т (наприклад, MS Excel).
Метою статтi е побудова ефективних багатофакторних регреайних моделей попиту на вх'1дн'1 та вих'дш перевезення вантажiв автомобльним транспортом для кожноУ област'1 УкраУни за загальнодоступними статистичними даними ДержавноУ служби статистики УкраУни.
Сучасний пiдхiд до моделювання вантажопотокв вимагае швидкоУ обробки значноУ к'лькост'1 статистичних даних. Кр'!м того, метод мае бути максимально унiверсальнuм та здатним до швидких та простих змн у раз '1 змiнu наявних статистичних даних.
Найбльш прийнятним вар'юнтом з це точки зору може вважатися моделювання вантажопотокв з використанням регреайних моделей на основi проведення кореля^йно-регреайного анал'ву. У загальному виглядi задача полягае в знаходженнi залежностi попиту на перевезення вiд факторiв, що на нього визначальний вплив. Такими факторами е макроеконом'чш показники, а також в!дстань перевезення.
У якостi вих'!дних даних взятi данi рег'юнально'У статистики та данi сайта «Лард'-Транс» як найбльш широко використовуваногоу вантажоперев '1зник'1в, вiдправнuкiв тазамовник'в перевезень.
Знайдено фактори, що становлять значний вплив на попит на вантажн перевезення автотранспортом з та до областей УкраУни. Складено рейтинг фактор'т впливу, серед яких на перших пози^ях Валовий рег'юнальний продукт; Рег'юнальн обсяги зовншньоУ торг'1вл'1 товарами ('¡мпорт) та Валовий рег'юнальний продукт у розрахунку на одну особу. Абсолютн значення коефiцiентiв кореляцУ перебувають у д'юпазонi 0,351-0,974. Найнижчий коефiцiент кореляцИ' - м'ж
в 'дстанню перевезень та попитом на них, що доводить незначнийзв'язок м'жобсягами рег'юнальних перевезень та вiдстанню доставки.
Побудовано моделi багатофакторноУ регресп з тринадцятьма, п'ятьма i двома факторами впливу на попит. Значення параметр'¡в точностi е прийнятними для вах варiантiв моделей. Нормований R-квадрат отриманих моделей не опускаеться нижче 84%, а середня помилка апроксимацн не пiднiмаеться вище 1,6%, що е в1'дм1'нними показниками моделей.
Кпючов'1 слова: попит на вантажн перевезення, репональы перевезення вантажiв автомобтьним транспортом, внутршы перевезення, моделювання попиту на перевезення, кореляцшно-регресшний аналiз, лЫшна багатофакторна регреая.
Лидия Савченко, Мирослава Семерягина, Ирина Шевченко "Моделирование региональных грузопотоков автомобильного транспорта в Украине". Транспортную систему можно определить как сложную систему, которая характеризуется случайной величиной транспортного спроса, переменными погодно-климатическими факторами, набором характеристик транспортной инфраструктуры и сложной системой взаимосвязей. Одним из ключевых видов транспорта, обеспечивающим грузовые перевозки как во внутреннем, так и в международном сообщении, является автомобильный. Его мобильность и возможность доставки груза «от двери до двери» является уникальным конкурентным преимуществом перед другими видами транспорта.
Для создания эффективной логистической инфраструктуры, обеспечивающей спрос на внутренние грузовые перевозки, прежде всего необходима информация о потребностях в перевозках между регионами страны. Таким образом, необходимо искать математические подходы к моделированию грузопотоков, комбинируя их практическую реализацию с использованием широко используемых программных продуктов (например, MS Excel).
Целью статьи является построение эффективных многофакторных регрессионных моделей спроса на входные и выходные перевозки грузов автомобильным транспортом для каждой области Украины по общедоступными статистическим данным Государственной службы статистики Украины.
Современный подход к моделированию грузопотоков требует быстрой обработки большого количества статистических данных. Кроме того, метод должен быть максимально универсальным и способным к быстрым и простым изменениям в случае перемены статистических данных. Наиболее приемлемым вариантом с этой точки зрения может считаться моделирование грузопотоков с использованием регрессионных моделей на основе проведения корреляционно-регрессионного анализа. В общем виде задача состоит в нахождении зависимости спроса на перевозки от факторов, оказывающих на него влияние. Такими факторами в существующих моделях указываются различные макроэкономические показатели, а также расстояние перевозки.
В качестве исходных данных для моделирования взяты данные региональной статистики Государственной службы статистики Украины и данные сайта «Ларди-Транс» как наиболее широко используемого у грузоперевозчиков и грузоотправителей.
Определен перечень факторов, составляющих значительное влияние на спрос на грузовые перевозки автотранспортом между областями Украины. Составлен рейтинг факторов влияния, среди которых на первых позициях валовый региональный продукт, региональные объемы внешней торговли товарами (импорт) и валовый региональный продукт в расчете на одного жителя области. Абсолютные значения коэффициентов корреляции находятся в диапазоне 0,351-0,974. Самый низкий коэффициент корреляции - между расстоянием перевозок и спросом на них, что доказывает незначительную взаимосвязь между объемами региональных перевозок и расстоянием доставки.
Построены модели многофакторной регрессии с тринадцатью, пятью и двумя факторами влияния на спрос. Значения параметров точности являются приемлемыми для всех вариантов моделей. Нормированный R-квадрат полученных моделей не опускается ниже 84%, а средняя ошибка аппроксимации не поднимается выше 1,6%, что является отличными показателями моделей.
Ключевые слова: спрос на грузовые перевозки, региональные перевозки грузов автомобильным транспортом, внутренние перевозки, моделирование спроса на перевозки, корреляционно-регрессионный анализ, линейная многофакторная регрессия.
Introduction. The transport system can be defined as a complex system characterized by a random variable of transport demand, variable weather and climatic factors, a set of characteristics of transport infrastructure and a complex system of relationships. The main purpose of the transport system is to meet the demand of the population, business and government agencies for transport services. The correspondence between the capabilities of the transport system and the demand for its services is determined by the balance of demand and capacity of the transport system. In this regard, it is very important to accurately determine the demand for transport services.
In the text of the National Transport Strategy of Ukraine for the period up to 2030 [1] the priority of the industry as one of the most important in the national economy is identified. The volume of freight traffic directly reflects the financial and economic condition of the country and its regions, as well as a marker of trends in the business environment.
One of the key modes of transport that provides freight in both domestic and international traffic is road. Its mobility and ability for door-to-door delivery is a unique competitive advantage over other modes of transport. Transportation by other modes of transport mostly needs the involvement of road in the first and last stages of the delivery process. Thus, modeling the demand for transportation of goods by road is an urgent task, the correctness of the results of which depends on the quality of the whole process of transportation.
To create an effective logistics infrastructure that meets the demand for domestic freight transport, first of all, information is needed on the demand for transport between regions of the country.
Determination of real freight traffic is associated with a number of difficulties. The most accurate is the method of direct accounting, which consists of a direct full survey of cargo-generating and cargo-absorbing points of the region. This method
provides the most complete data for the characterization of traffic flows in a certain period of time. However, its disadvantage is the high labor intensity of data collection and processing. Unfortunately, the collection of such data involves direct interviewing, questioning each actual and potential point of departure and destination of cargo, which in reality is possible only in a small area (no more than a city microdistrict). The accounting of transported goods according to the nomenclature in organizations producing and consuming products, and in road transport enterprises, would certainly make it possible to easily collect the necessary information on freight traffic. However, at the moment in Ukraine there are no such reports for all enterprises, or access to them is limited. In addition, there is the problem of biased applications of consignors, lack of accounting for the frequency of transport and the weight of packages. The inaccuracy of accounting in the performed volumes of transportations in road transport enterprises also creates additional difficulties in determining the real traffic flows.
Thus, it is necessary to look for mathematical approaches to modeling freight traffic, combining their practical implementation using widely used software products (for example, MS Excel).
Analysis of the latest research. Basic principles and approaches to forecasting freight and passenger transportation are presented by the authors in [3]. Authors [7] considered the factors of influence on the evolution of transport systems, that is, they forecasted the trend regarding the volumes of transportation in dependence from factors of external environment. Analysis of trends in freight traffic in containers by the author [2] was carried out using econometric models built on the basis of time series analysis and correlation-regression analysis. Significant number of works (for example, [4]) dedicated to forecasting freight and passenger flows on the railway. It should be noted that despite identical objects (cargo), the principle of
forecasting demand for carriage by rail and road should be quite different due to the nature of functioning of these means of transport and the difference of the fields of their rational application.
Formulation of the purpose of the study. The purpose of the paper is to build effective multifactor regression models of demand for incoming and outgoing transportation of goods by road for each region of Ukraine according to publicly available statistical data of the State Statistics Service of Ukraine.
Presentation of the main research. The modern approach to modeling of cargo flows requires fast processing of a impressive amount of statistical data. In addition, the method should be as universal as possible and capable of quick and easy changes under the conditions of changes in current statistics.
From this point of view, the most acceptable option can be considered to be the modeling of freight traffic with regression models based on correlation and regression analysis.
Correlation-regression analysis is a set of statistical and mathematical methods used for quantitative analysis of the links between socio-economic phenomena and processes. A random variable is used as a dependent variable in regression analysis, and non-random variables are used as an independent variable.
Regression analysis is used when the relationships between variables can be quantified as some combination of these variables. The resulting combination is used to predict the value that can take the target (dependent) variable, which is calculated on a given set of values of input (independent) variables. In the simplest case, standard statistical methods, such as linear regression, are used.
The regression model includes the following parameters and variables:
- Unknown parameters denoted as (P);
- Independent variables, (X);
- Dependent variable, (Y).
The function y = f (x^ x2,..., xn),
which describes the dependence of the conditional mean value of the result characteristic (dependent variable) on the given values of arguments (independent variables) x1, x2,..., xn, is called the
regression equation.
Linear regression is described by a linear relationship between the studied variables:
y = A) + M +... + Pnxn, (1)
where y is the dependent variable;
x1, x2,..., xn - independent variables;
po P - regression coefficients.
The solution of the mathematical equations of the relationship between the dependent and independent factors involves the calculation of their unknown parameters from the initial data - the coefficients Po, Pi..., Pn. Determination of unknown regression coefficients [5], according to which the square of the deviation of the observed (statistical) values of the performance indicator yc is minimized from the model (obtained by the constructed regression equation) values yp = f(x The objective function, respectively, is the expression:
n
£(ya- ypr )2 ^ min
-1 (2)
The set of coefficients which will provide the minimum of the objective function (2), is taken to describe the dependence of the resulting parameter y on the factors {X}.
Consider the stages of regression analysis.
1. Task formulation. At this stage, preliminary hypotheses about the dependence of the studied phenomena are formed. A set of factors is selected that can affect the resulting indicator.
2. Collection of statistical data. Arrays of dependent variable and independent variables are obtained.
3. Formulation of a hypothesis about the form of relationships. Choosing the form of the regression function.
4. Calculation of numerical values of parameters ft of the regression equation.
5. Evaluation of the accuracy of regression analysis. Calculating the resulting error of the regression model.
6. Interpretation of the obtained results. The obtained results of regression analysis are compared with previous hypotheses. The correctness and plausibility of the obtained results are evaluated.
7. Prediction of unknown values of the dependent variable.
When conducting regression analysis, a well-grounded choice of not only the type (mathematical form) of the dependencies used, but also the factors themselves, is of great importance. That is why it is desirable to carry out correlation-regression analysis. In addition to the above steps of regression analysis it must be added the stage of estimating the correlation between the dependent and each independent variable. The degree of relationship (correlation) between the dependent and independent variables is determined using the correlation coefficient:
X (x -x )( - y)
rxy I , 2 2 , (3)
JX (x - x) (yi - y)
where rxy is the correlation coefficient between the dependent variable y and the independent variable x;
Xi, yi - the i-th value of the independent and dependent variables;
X, y - the average value of the
independent and dependent variables. Only those independent variables that have high values of the correlation coefficient (usually more than 0.5 in absolute value) are left in the regression model.
In general, the task is to find the dependence of the demand for transportation on the factors that have a decisive influence on it. These factors are macroeconomic indicators. For freight transportation, this is the gross domestic product, the volume of production by industry, the volume of imported and exported goods. When forecasting passenger traffic, the main factors are the size, mobility of the population, income and tariffs for transport services. The time factor is highlighted as significant, in which all the ongoing economic and social processes and factors influencing them are accumulated [3]. In the work [7] as a factor of the external environment was taken the GDP, which reflects the efficiency of the economy. The GDP factor is also used to predict freight traffic on the railroad by the author [4], indicating a clear mutual influence of these two factors on each other.
Since the purpose of the paper is to model the demand for road freight transport between the regions of Ukraine, the data of regional statistics [8] should be taken as initial data. As for the resulting factor - the demand for transportation, we use the data of the site "Lardi-Trans" as the most widely used by carriers, shippers and customers (Table 1).
Table 1. Demand for transportation to and from the regions of Ukraine (daily statistics "Lardi-
Trans" [6])
Region of Ukraine Number of orders for transportation from the region Number of orders for transportation to the region
Vinnytsia 128 114
Volyn 29 56
Dnepropetrovsk 318 162
Donetsk 34 41
Zhytomyr 96 71
Transcarpathian 17 57
Zaporozhye 163 153
Ivano-Frankivsk 8 44
Kyiv 1069 653
Kirovograd 39 170
Luhansk 33 35
Lviv 47 107
Mykolayivska 61 45
Odessa 117 101
Poltava 107 189
Rivne 70 58
Sumy 22 41
Ternopil 61 147
Kharkiv 166 149
Kherson 98 69
Khmelnytsky 43 62
Cherkasy 45 44
Chernivtsi 19 28
Chernihiv 24 21
Total, orders 2814 2617
Average value, orders 117.3 109.0
Source: Compiled by the authors
Since correlation-regression analysis is used in the article to model demand, we must find factors that have a significant impact on the resulting indicator (demand). The State Statistics Service of Ukraine systematically presents information on the regions of Ukraine, which could potentially have an impact on the demand for road freight:
1) Gross regional product (million UAH), latest data for 2018;
2) Gross regional product per capita (UAH), latest data for 2018;
3) Number of legal entities by region, latest data as of January 1, 2021;
4) Population as of December 1, 2020 (current population);
5) Population as of December 1, 2020 (permanent population);
6) Freight transportation by road in the region in 2020, thousand tkm;
7) Freight transportation by road in the region in 2020, thousand tons;
8) Regional volumes of foreign trade in goods in January-October 2020 (exports, thousand US dollars);
9) Regional volumes of foreign trade in goods in January-October 2020 (imports, thousand US dollars);
10) Regional volumes of foreign trade in services for 9 months of 2020 (exports, thousand US dollars);
11) Regional volumes of foreign trade in services for 9 months of 2020 (imports, thousand US dollars);
12) Volumes of manufactured construction products and indices of construction products in 2020, UAH million.
Another factor used in modeling the demand and volume of traffic for both cargo and passengers is always the distance of transportation. To model the demand for transportation to and from the regions, the average distances of transportation between all regions were calculated (Fig. 1).
900
E
800
lo aj
£ 700
o
aj
£ 600 o
£500
Region of Ukraine
Figure 1 - Rating of regions of Ukraine in relation to the average distance of delivery to
other regions Source: compiled by the authors
Analyzing Fig. 1, it can be assumed that in regions with large average distances of connections with other regions (Transcarpathian, Chernivtsi, Luhansk, etc.), domestic transportation or transportation between neighboring oblasts will be more developed. Whereas regions that have relatively small average distances of
connections with other regions (Kirovohrad, Kyiv, Cherkasy, etc.) will have a more extensive network of connections with all regions of Ukraine. However, this assumption must be verified by correlation analysis.
Here are all the statistics for each region of Ukraine, which are publicly available and updating with some regularity (Table 2).
Table 2. Regional statistics that may have an impact on the volume of road transport to and from the region of Ukraine
Region Gross regional product (UAH million), latest data for 2018. Gross regional product per capita (UAH), latest data for 2018. Number of legal entities by region, latest data as of January 1, 2021 Population per 1 December 2020 (current population) Population as of December 1, 2020 (permanent population) Freight transport by road in the region in 2020, thousand tkm Freight transport by road in the region in 2020, thousand tons Regional volumes of foreign trade in goods in January-October 2020 (exports, thousand US dollars) Regional volumes of foreign trade in goods in January-October 2020 (imports, thousand US dollars) Regional volumes of foreign trade in services for 9 months of 2020 (exports, thousand US dollars) Regional volumes of foreign trade in services for 9 months of 2020 (imports, thousand US dollars) Volumes of manufactured construction products and indices of construction products in 2020, UAH mln. The average distance from the region to other areas, km
1 2 3 4 5 6 7 8 9 10 11 12 13
Vinnytsia 111498 71104 33012 1530930 1523845 1004447.4 5428.9 1164104.9 452562.5 117159.4 28888.1 10731.3 455.2
Volyn 60448 58297 22897 1028062 1025334 2054934.2 4792.9 530265.9 1056962.4 62854.3 21724.3 2513.7 576.0
Dnepropetrovsk 369468 114784 103645 3146125 3142816 2846710.3 20889.4 6235536.8 3728578.2 121241.4 157767.0 17756.9 535.4
Donetsk 192256 45959 91822 4103490 4090605 477847.7 19150.4 3237089.0 1211423.0 59970.2 56381.5 10122.7 712.4
Zhytomyr 77110 62911 32046 1196996 1197765 462201.4 3044.5 539426.5 426725.7 56840.2 7775.6 2075.2 463.6
Transcarpathian 52445 41706 24137 1250767 1247934 4218056 5301.9 1095201.8 1012004.7 217563.2 18478.8 1905.8 840.4
Zaporozhye 147076 85784 48725 1669239 1668450 915655.6 3960.4 2392645.1 993194.3 127978.3 20489.13 2723 579.7
Ivano-Frankivsk 78443 57033 29459 1362132 1359406 1108184.9 9199.2 628021.8 508437.9 42472.9 17698.5 3743.3 650.1
Kyiv 1031229 395618 413128 4751881 4704795 8339948 40753.5 11589891.1 21351356.7 3150834.8 1938283.14 55490.6 425.1
Kirovograd 64436 67763 25348 921695 915280 651488.9 4643.6 730598.0 203125.9 17095.0 8467.56 1366.7 418.7
Luhansk 35206 16301 41344 2122914 2118317 400129 1225.3 107562.8 170199.2 15862.1 30637.28 669.6 831.1
Lviv 177243 70173 74475 2499711 2481341 4050253 12155.3 1882326.6 2792077.1 424529 56875.32 14142 644.6
Mykolayiv 79916 70336 49939 1109932 1109217 1085824.9 6835.8 1757653.7 646778.1 254409.14 14062.93 3139.7 537.9
Odessa 173241 72738 86456 2370134 2359074 2076435.8 8818.6 1078699.4 1642397.9 621113.15 209865.26 27925.5 578.0
Poltava 174147 123763 34608 1373517 1365679 1560473.2 7403.7 1807864.4 949267.0 28788.66 65018.35 8146.4 495.2
Rivne 56842 49044 23918 1149221 1148161 1883216.6 4061.2 387869.8 300628.3819 52473.21 19584.03 3265.4 543.3
Sumy 68489 62955 25128 1055053 1052861 681840 1624 725067.9 696884.7 17656.52 17122.73 1660.2 571.4
Ternopil 49133 46833 22771 1031521 1028270 918505.8 3796 366078.7 329292.3 76222.39 7539.4 2561 555.4
Kharkiv 233321 86904 83170 2637037 2621401 2491370.5 10655.2 1160753.8 1455952.1 284570.98 37023.87 14356.2 594.7
Kherson 55161 52922 29680 1018484 1017052 755484.4 3199.1 225241.8 292176.2 23716.08 12421.23 1241.5 574
Khmelnytsky 75646 59583 30474 1245167 1242004 1095859.6 6241.3 496033.6 400786.1 17999.82 11766.18 6472.1 489.4
Cherkasy 93315 76904 29848 1180189 1176560 1599965.3 5663.3 685448.9 349155.3 30404.99 15523.28 2519.8 442.6
Chernivtsi 33903 37441 16356 897295 894230 653127.3 1155.3 130633.4 137583.8 33409.22 2671.01 2056.6 840
Chernihiv 70624 69725 23062 978434 969892 964744.7 1338.6 652492.2 289754.0 22400.8 24164.24 2440.2 558.0
Source: Compiled by the authors
The correlation between the factors and Excel is implemented with the CORREL daily demand for transportation to and from function. the regions of Ukraine is evaluated in Table. 3. To do this, the formula (3) was used, which in
Table 3. Correlation coefficients between the volume of traffic to and from the regions of Ukraine and regional statistics
Region
to TD
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n o
o
CD to
to
e
CP "rö
n o
o
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ar
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s
te
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s
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n
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m CNJ
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io
TO 13
o
o o
e
Q
io
J2
13
o
CL
o
e n
TO
o o
e
o
e
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io
J2
13
o
CL
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io gi
e
T3
TO
o
o
in
ig ei
o
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o o
io gi
e
"O
TO
o
o
in
ig ei
e
-Q
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o
in TD
o
o g
■ë Ü to o ■fa TD
s= 00
£ -O O £=
TO
o %
CO O CD -C
H Ä
t s
JS o
Cá c^
8
e
-Q
o o
o
in TD
o
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s= 00
£ -O
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o 3 in o
CD -£=
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3
£4=
t s
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Oí C^
9
in
e
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to o ■fa TD
s= 00
£ -O O £=
TO
o %
CO O CD -C
H Ä
t s
Ä O Oí C^
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9
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s= 00
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ijg J3 £
S O
12
13
Transport ation from the region
0.974
0.967
0.961
0.696
0.694
0.801
0.862
0.928
0.969
0.939
0.963
0.887
Transport ation to the region
0.930
0.954
0.909
0.627
0.624
0.784
0.813
0.866
0.929
0.909
0.924
0.848
1
2
3
4
5
6
7
Source: Compiled by the authors
Let's make a rating of independent variables (factors of influence) on demand for transportation from and to regions of Ukraine (Fig. 2). For convenience of visual
i
c 0,8
£ 0,6 lieu
8 0,4
.1 0,2 (0
(U 0
<3 -0,2 1
-0,4 —
representation of material, the name of the factor is replaced by its number (Tab. 3).
0,95
§ 0,75 u
ffi 0,55 e
8 0,35 n
° 0,15
JO
<u -0,05 -
£ 2 1
-0,25 -
-0,45 -
9 2 11 3 10 8 12 7 6 4 5 3
Factor number
9 11 3 10 8 12 7 6 4 5
Factor number
13
Figure 2 - Correlation coefficients of demand for freight transport by road from thirteen factors: a) from the regions of Ukraine; b) to the regions of Ukraine Source: compiled by the authors
It can be seen that the difference between the rating of the most important factors influencing the demand for
transportation from and to the regions is insignificant and is observed only in the first three factors. For the demand for
transportation from the regions, the most influential factors are 1) Gross regional product; 2) Regional volumes of foreign trade in goods (imports); 3) Gross regional product per capita. Whereas for the demand for transportation to the regions the most influential factors are 1) Gross regional product per capita; 2) Gross regional product; 3) Regional volumes of foreign trade in goods (imports). Absolute values of correlation coefficients are in the range of 0.351-0.974 (demand for transportation from the regions) and 0.409-0.954 (demand for transportation to the regions). It can prove that all thirteen factors have a significant impact on the demand for transportation both from and to the Ukrainian regions. The lowest and rather insignificant correlation coefficient between the demand for transportation and the distance is surprising. After all, the distance of transportation has always been one of the determining factors in modeling the demand for transportation of both goods and passengers. The research conducted here proves that the formation of demand for
RESULTS
Regression statistics
Multiple R 0.996
R-square 0.993
Normalized R-
square 0.983
Standard error 6955.482
Observations 24
ANOVA
df 55 M5 F Significance of F
Regression 13 65869905471.2 5066915805.5 104.734 0.000
Residuals 10 483787245.3 48378724.5
Total 23 66353692716.5
Coefficients Standard error t-statistic P-Value Lower 95% Upper 95% Lower 99.0% Upper 99.0%
Y-intersection 61602.722 23999.435 2.567 0.028 8128.649 115076.795 -14458.031 137663.475
Variable X 1 0.66859 0.179 3.728 0.004 0.269 1.068 0.100 1.237
Variable X 2 -0.65344 0.272 -2.401 0.037 -1.260 -0.047 -1.516 0.209
Variable X 3 -0.36900 0.485 -0.761 0.464 -1.450 0.712 -1.906 1.168
Variable X 4 -0.97183 0.611 -1.591 0.143 -2.332 0.389 -2.907 0.964
Variable X 5 0.96527 0.616 1.567 0.148 -0.407 2.338 -0.987 2.918
Variable X 6 -0.00116 0.003 -0.343 0.738 -0.009 0.006 -0.012 0.010
Variable X 7 -1.75311 0.847 -2.070 0.065 -3.640 0.134 -4.437 0.931
Variable X 8 0.00001 0.004 0.003 0.998 -0.008 0.008 -0.012 0.012
Variable X 9 -0.00671 0.006 -1.033 0.326 -0.021 0.008 -0.027 0.014
Variable X 10 0.05463 0.043 1.272 0.232 -0.041 0.150 -0.082 0.191
Variable X 11 0.07424 0.051 1.466 0.173 -0.039 0.187 -0.086 0.235
Variable X 12 -1.25481 0.733 -1.712 0.118 -2.888 0.378 -3.578 1.068
Variable X 13 -41.664 21.869 -1.905 0.086 -90.390 7.063 -110.972 27.644
regional transportation in Ukraine is almost without the influence of the factor of the distance between the points of departure and receipt. In addition, the distance factor is the only one of others that has a negative correlation coefficient. This indicates the inverse relationship between the demand for transportation and its distance. This conclusion is quite logical, because with increasing distance, the demand for transportation should fall, and vice versa. Such interdependence is based on the desire to save money and time, because longdistance transportation is more expensive than short-distance one.
For the next stage - regression analysis -we will transfer the daily demand obtained from the one-time statistics of "Lardi-Trans" into the annual one, multiplying it by the number of working days in a year (251). A regression analysis was carried out using the "Regression" tool of the "Data Analysis" add-in for MS Excel spreadsheets. The analysis results are shown in Fig. 3 and Fig. 4.
Figure 3 - Regression analysis - data from the regions Source: compiled by the authors
RESULTS
Regression statistics
Multiple R 0.966
R-square 0.933
Normalized R-
square 0.846
Standard error 12459.303
Observations 24
ANOVA
df 55 M5 F Significance of F
Regression 13 2.17E+10 1.67E+09 10.7468 0.0003
Residuals 10 1.55E+09 1.55E+08
Total 23 2.32E+10
Coefficients Standard error t-statistic P-Value Lower 95% Upper 95% Lower 99.0% Upper 99.0%
Y-intersection 55527.9 42990.012 1.292 0.226 -40259.784 151315.650 80719.139 191775.004
Variable X 1 0.494 0.321 1.538 0.155 -0.222 1.210 -0.524 1.512
Variable X 2 -0.315 0.488 -0.646 0.533 -1.401 0,771 -1.860 1.230
Variable X 3 -1.120 0.869 -1.290 0.226 -3.056 0.815 -3.874 1.633
Variable X 4 0.569 1.094 0.520 0.614 -1.868 3.007 -2.897 4.036
Variable X 5 -0.564 1.104 -0.511 0.620 -3.023 1.895 -4.062 2.933
Variable X 6 -0.004 0.006 -0.683 0.510 -0.018 0.009 -0.023 0.015
Variable X 7 -0.183 1.517 -0.121 0.906 -3.563 3.198 -4.991 4.625
Variable X 8 0.000 0.007 0.066 0.949 -0.015 0.016 -0.021 0.022
Variable X 9 -0.005 0.012 -0.409 0.691 -0.031 0.021 -0.042 0.032
Variable X 10 0.103 0.077 1.334 0.212 -0.069 0.274 -0.141 0.347
Variable X 11 0.029 0.091 0.321 0.755 -0.173 0.231 -0.258 0.317
Variable X 12 -1.593 1.313 -1.213 0.253 -4.518 1.332 -5.754 2.568
Variable X 13 -40.10 39.173 -1.024 0.330 -127.382 47.185 -164.250 84.052
Figure 4 - Regression ana
ysis - data to the regions
Source: compiled by the authors
The results obtained allow us to make the following conclusions. Since the values of the multiple correlation coefficient are 0.996 and 0.966 (for the demand for transportation from and to the region, respectively), which is more than the accepted boundary value of 0.7, we can say about a strong relationship between the dependent value (demand for freight transportation by road between regions of Ukraine) and selected thirteen factors. The values of the adjusted coefficient of determination mean that, respectively, 98.3 and 84.6% of the variations in the demand for transportation from and to the region are explained by the variation of the selected thirteen factors, and the remaining 1.7 and 15.4% are explained by other factors unaccounted in this regression mod el. The
values obtained are high and acceptable for decision making. The next block is analysis of variance. The Fisher test is used to check the statistical significance of the regression equation as a whole. The actual values of the criterion are 104.7 and 10.8 with the corresponding significance levels of about 0. Thus, the actual values of the Fisher test significantly exceed the significance levels, which means that the regression equation can be recognized as statistically significant with a very high probability. The next section contains information about the values of the regression coefficients. The resulting models are follows:
- annual demand for transportation from the region:
y = 61602,7 + 0,67x - 0,65x2 - 0,37x3 - 0,97x4 + 0,97x5 - 0,001x6 --1,75x7 + 0,0001x8 - 0,01x9 + 0,06x10 + 0,07xu -1,26x12 - 41,66x13
- annual demand for transportation to the region:
y = 55527,9 + 0,49x1 - 0,32x2 -1,12x3 + 0,57x4 - 0,56x5 - 0,004x6 --0,18x7 + 0,0001x8 - 0,01x9 + 0,1x10 + 0,03x11 -1,59x12 - 40,1x13
The free coefficient of the equation can be considered as the value of the demand for regional transportation, which does not depend on the selected factors. Surprisingly, the coefficients in the equations do not always coincide in sign with the corresponding correlation coefficients. The obtained values are checked for statistical significance using the Student's t-test. The p-value column contains the significance levels at which the regression coefficients are considered statistically significant different from zero. The limiting value in practice is usually considered to be 0.05 (95% probability). If the actual p-value is less than the limiting, the regression coefficient is considered statistically significant. It can be seen that such a condition is satisfied for a small number of factors. According to p-values, only the coefficients at xi and X2 are statistically significant for modeling demand from the region (values 0.004 and 0.037).
None of the regression coefficients that model demand to regions are statistically significant. To increase the significance of the regression coefficients, the number of factors should be reduced by removing those of them that have the greatest pairwise correlation. It should be noted that the regression coefficients can also be obtained using the LINEST function in MS Excel. However, the function does not provide additional information about the resulting model; thus, information about the R-square estimates, Fisher's tests, t-statistics, etc. will have to be obtained using additional calculations, including using MS Excel functions. To reduce the number of independent regression variables, we will carry out a correlation analysis - calculate the matrix of pair correlation coefficients. For this purpose, we use the Correlation tool of the Data Analysis in MS Excel Spreadsheet Add-in. The correlation matrix is presented in Table 4 and Table 5.
Table 4. Pairwise correlations matrix (demand for transportation from the region)
Transportatio n from the region 1 2 3 4 5 6 7 8 9 10 11 12 13
Transportatio n from the region
1 0.974
2 0.967 0.963
3 0.961 0.983 0.937
4 0.696 0.804 0.631 0.817
5 0.694 0.801 0.628 0.814 1.000
6 0.801 0.833 0.808 0.826 0.612 0.609
7 0.862 0.940 0.847 0.927 0.891 0.890 0.788
8 0.928 0.962 0.905 0.932 0.811 0.810 0.782 0.946
9 0.969 0.972 0.962 0.980 0.714 0.711 0.866 0.886 0.919
10 0.939 0.933 0.934 0.966 0.673 0.669 0.860 0.832 0.850 0.978
11 0.963 0.950 0.957 0.970 0.673 0.670 0.822 0.846 0.881 0.990 0.984
12 0.887 0.929 0.870 0.933 0.804 0.801 0.810 0.887 0.854 0.895 0.910 0.889
13 -0.351 -0.306 -0.436 -0.238 0.013 0.015 -0.104 -0.225 -0.263 -0.257 -0.239 -0.270 -0.273
Source: compiled by the authors
Table 5. Pairwise correlations matrix (demanc
Transporta tion to the region 1 2 3 4 5 6 7 8 9 10 11 12 13
Transportat ion to the region
1 0.930
2 0.954 0.963
3 0.909 0.983 0.937
4 0.627 0.804 0.631 0.817
5 0.624 0.801 0.628 0.814 1.000
6 0.784 0.833 0.808 0.826 0.612 0.609
7 0.813 0.940 0.847 0.927 0.891 0.890 0.788
8 0.866 0.962 0.905 0.932 0.811 0.810 0.782 0.946
9 0.929 0.972 0.962 0.980 0.714 0.711 0.866 0.886 0.919
10 0.909 0.933 0.934 0.966 0.673 0.669 0.860 0.832 0.850 0.978
11 0.924 0.950 0.957 0.970 0.673 0.670 0.822 0.846 0.881 0.990 0.984
12 0.848 0.929 0.870 0.933 0.804 0.801 0.810 0.887 0.854 0.895 0.910 0.889
13 -0.409 -0.306 -0.436 -0.238 0.013 0.015 -0.104 -0.225 -0.263 -0.257 -0.239 -0.270 -0.273
for transportation to the region)
Source: compiled by the authors
It can be observed that from all factors, only the 13th is independent from the other factors (although there is some connection with factor 2).
We offer the following method of successive exclusion of factors from the model:
1. Find the largest number in the matrix of pairwise correlations.
2. Of the two factors, the pair of which has the maximum value of pair correlation, leave in the model the factor that has the greatest value of the correlation with the final (dependent) factor.
3. Repeat the procedure of steps 1-2 until the regression coefficients are significant according to the p-value or a sufficient level of accuracy is achieved (for example, an acceptable average approximation error is obtained):
*=1X
n.
y^i - y n
•100%
where- i-th value of the statistical series of the dependent quantity;
ymi - I- th value of the theoretical series of the dependent quantity, calculated using the obtained regression equation.
There are three variants of the regression model were considered:
- with the maximum number of factors (thirteen);
- with five factors;
- with two factors.
The reduction of the obtained basic model with thirteen factors was carried out using the described above algorithm. The linear regression equations obtained using the above technique, as well as the characteristics of the models, are grouped in Table 6 and Table 7.
Table 6. Regression analysis from the regions
13 factors 5 factors 2 factors
List of factors in the model 1-13 1, 4, 6, 12, 13 1, 13
Regression model y = 61602,7 + 0,67x - 0,65x -0,37x3 - 0,97x4 + 0,97x5 --0,001x6 -1,75 x7 + 0,0001x8 -0,01x9 + 0,06x10 + 0,07x11 --1,26x12 - 41,66x13 y = -956,3 + 0,35x - 0,02x -0,004x6 - 0,08x12 + 20,24. y = 6867,2 + 0,25xj - 25,7
Normalized R-square, % 98.3 96.6 94.8
Checking Fisher's criterion Regression equation as a whole is statistically significant Regression equation as a whole is statistically significant Regression equation as a whole is statistically significant
Significant factors according to p-value 1. 2 1. 4 1
Average approximati on error, % 1.18 1.54 1.14
Source: compiled by the authors
Table 7. Regression analysis to the regions
13 factors 5 factors 2 factors
List of factors in the model 1-13 2, 4, 6, 12, 13 2, 13
Regression model y = 55527,9 + 0,49x1 - 0,32 -1,12x3 + 0,57x4 - 0,56x5 --0,004x6 - 0,18x7 + 0,0001 -0,01x9 + 0,1x10 + 0,03 x11 --1,59x12 - 40,1x13 y = -4376 + 0,39x2 + 0,0008 +0,0005x6 + 0,11x12 - 3,79xl y = -7684,2 + 0,43x2 +2,2
Normalized R-square, % 84.6 88.7 90.1
Checking Fisher's Regression equation as a whole is statistically Regression equation as a whole is statistically significant Regression equation as a whole is statistically
criterion significant significant
Significant factors according to p-value 2 2
Average approximati on error, % 0.74 0.60 0.71
Source: compiled by the authors
The normalized R-square and the average approximation error were analyzed for the three scenarios (Fig. 5)
1,6
1,5 1,4 1,3 1,2 1,1 1
13 factors
5 factors
2 factors
Average approximation error, % Normalized R-square, %
99 98 97 96 95 94
0,75 0,7 0,65 0,6 0,55
a)
13 factors
5 factors
2 factors
Average approximation error, % Normalized R-square, %
91 90 89 88 87 86 85 84
b)
Figure 5 - Values of parameters of regression model accuracy for three scenarios of modeling of demand for freight transportations by road transport: a) from the regions; b) to the regions Source: compiled by the authors
It can be observed that the values of the accuracy parameters are acceptable for all six variants of the models. The normalized R-square does not fall below 84%, and the average approximation error does not rise above 1.6%. If the decision on the best variant of the regression equation is made on the basis of the average error of approximation, then for modeling of demand from the regions it is necessary to choose two-factor model, and for modeling of demand for the regions - five-factor. If the optimality criterion is a normalized R-square, the best choice for modeling the demand from the regions will be a 13-factor model, and for modeling the demand for the region - a two-factor.
The perspectives of the research should be the choice of the best regression equation that would describe the demand for regional transportation in Ukraine. After that, it will be possible to create a matrix of demand for transportation between all regions of Ukraine.
Conclusions. Regional freight transportation by road ensures the satisfaction of demand for goods within the
country and is necessary for the smooth operation of manufacturing and service enterprises. Forecasting the demand for transportation between regions and the subsequent planning and organization of freight flows are important economic tasks. In this regard, reliable mathematical models are needed to predict regional freight traffic by road transport based on annual (quarterly) statistical data for the regions of Ukraine.
The performed correlation-regression analysis made it possible to establish the functional dependences of the demand for road transportation of goods to and from the Ukrainian region, namely, the multiple regression equations. The main factors that have the greatest impact on interregional transportation are determined, and a comparative analysis of models with thirteen, five and two linear regression factors is carried out. Indicators of errors and reliability allow us to speak about the sufficient accuracy of the model in relation to real data obtained using the platform for the search for cargo and transport "Lardi-Trans".
References
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2. Avtomonova L.Yu. Prognozirovanie ob'Yomov konteynernyih perevozok s ispolzovaniem ekonometricheskih modeley. Sistemnyiy analiz i logistika. 2018. #1(16). p.60-69.
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