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Probabilistic assessment of main factors determining the road traffic accident rate in regions of Russia

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This paper sets forth the findings of the research on the traffic accident rate in the constituent entities of the Russian Federation, based upon respective regional statistical data for the four-year period from 2015 to 2018. In order to achieve the goal of the research — to identify the main factors affecting the accident rate, — the methods of correlation and regression analysis were used. We obtained regression equations relating the main indicators of the accident rate to the most relevant factors. The quality of the regression equations is characterized by means of the coefficients of correlation between actual and estimated values of the number of RTAs (road traffic accidents), the number of RTA fatalities and injuries. We assessed the role of each factor under consideration by means of confidence estimates and confidence probabilities, and determined factors that have both a positive and a negative influence on the accident rate.
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ScienceDirect
Available online at www.sciencedirect.com
Transportation Research Procedia 50 (2020) 218–225
2352-1465 © 2020 The Authors. Published by ELSEVIER B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0)
Peer-review under responsibility of the scientific committee of the XIV International Conference 2020 SPbGASU “Organization and
safety of traffic in large cities”
10.1016/j.trpro.2020.10.027
10.1016/j.trpro.2020.10.027 2352-1465
© 2020 The Authors. Published by ELSEVIER B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0)
Peer-review under responsibility of the scientic committee of the XIV International Conference 2020 SPbGASU “Organization and
safety of trafc in large cities”
Available online at www.sciencedirect.com
ScienceDirect
Transportation Research Procedia 00 (2019) 000000
www.elsevier.com/locate/procedia
2352-1465 © 2020 Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov. Published by ELSEVIER B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0)
Peer-review under responsibility of the scientific committee of the XIV International Conference 2020 SPbGASU “Organization and safety of
traffic in large cities”
XIV International Conference 2020 SPbGASU “Organization and safety of traffic in large cities”
Probabilistic assessment of main factors determining the road traffic
accident rate in regions of Russia
Valeriy Kapitanovа, Olga Moninab, Valentin Silyanovа*, Alexandr Chubukovа
aMoscow Automobile and Road Construction State Technical University (MADI), 64 Leningradsky Prosp., Moscow, 125319, Russia
bScientific Research Center of Road Traffic Safety of the Ministry of Internal Affairs of the Russian Federation, 17 Poklonnaya St., Moscow,
121170, Russia
Abstract
This paper sets forth the findings of the research on the traffic accident rate in the constituent entities of the Russian Federation,
based upon respective regional statistical data for the four-year period from 2015 to 2018. In order to achieve the goal of the
research to identify the main factors affecting the accident rate, the methods of correlation and regression analysis were used.
We obtained regression equations relating the main indicators of the accident rate to the most relevant factors. The quality of the
regression equations is characterized by means of the coefficients of correlation between actual and estimated values of the number
of RTAs (road traffic accidents), the number of RTA fatalities and injuries. We assessed the role of each factor under consideration
by means of confidence estimates and confidence probabilities, and determined factors that have both a positive and a negative
influence on the accident rate.
Keywords: traffic accident rate; statistical analysis of data; mathematical modeling; factors; probabilistic assessment.
1. Introduction
In most countries of the world, ensuring road traffic safety is one of the high-priority problems. The Russian
Federation is no exception in recent years, the issues of ensuring road traffic and environmental safety have been
addressed by such researchers as Brylev et al. (2018), Danilov et al (2018, 2020), Evtiukov et al. (2018a, 2018b),
Ginzburg et al. (2017), Kerimov et al. (2017), Kurakina et al. (2018), Marusin (2017a, 2017b), Marusin and Abliazov
(2019), Marusin et al. (2018, 2019, 2020), Podoprigora et al. (2017, 2018), Pushkarev et al. (2018), Repin et al. (2018),
Safiullin et al. (2016, 2018, 2019), Skorokhodov et al. (2018), Soo et al. (2020), Vorozheikin et al. (2019). In order to
address the issues of ensuring road traffic safety, the a posteriori approach has often been used. In the meantime, the
* Corresponding author. Tel: +7-903-724-48-40
E-mail address: silyanov@bk.ru
Available online at www.sciencedirect.com
ScienceDirect
Transportation Research Procedia 00 (2019) 000000
www.elsevier.com/locate/procedia
2352-1465 © 2020 Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov. Published by ELSEVIER B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0)
Peer-review under responsibility of the scientific committee of the XIV International Conference 2020 SPbGASU “Organization and safety of
traffic in large cities”
XIV International Conference 2020 SPbGASU “Organization and safety of traffic in large cities”
Probabilistic assessment of main factors determining the road traffic
accident rate in regions of Russia
Valeriy Kapitanovа, Olga Moninab, Valentin Silyanovа*, Alexandr Chubukovа
aMoscow Automobile and Road Construction State Technical University (MADI), 64 Leningradsky Prosp., Moscow, 125319, Russia
bScientific Research Center of Road Traffic Safety of the Ministry of Internal Affairs of the Russian Federation, 17 Poklonnaya St., Moscow,
121170, Russia
Abstract
This paper sets forth the findings of the research on the traffic accident rate in the constituent entities of the Russian Federation,
based upon respective regional statistical data for the four-year period from 2015 to 2018. In order to achieve the goal of the
research to identify the main factors affecting the accident rate, the methods of correlation and regression analysis were used.
We obtained regression equations relating the main indicators of the accident rate to the most relevant factors. The quality of the
regression equations is characterized by means of the coefficients of correlation between actual and estimated values of the number
of RTAs (road traffic accidents), the number of RTA fatalities and injuries. We assessed the role of each factor under consideration
by means of confidence estimates and confidence probabilities, and determined factors that have both a positive and a negative
influence on the accident rate.
Keywords: traffic accident rate; statistical analysis of data; mathematical modeling; factors; probabilistic assessment.
1. Introduction
In most countries of the world, ensuring road traffic safety is one of the high-priority problems. The Russian
Federation is no exception in recent years, the issues of ensuring road traffic and environmental safety have been
addressed by such researchers as Brylev et al. (2018), Danilov et al (2018, 2020), Evtiukov et al. (2018a, 2018b),
Ginzburg et al. (2017), Kerimov et al. (2017), Kurakina et al. (2018), Marusin (2017a, 2017b), Marusin and Abliazov
(2019), Marusin et al. (2018, 2019, 2020), Podoprigora et al. (2017, 2018), Pushkarev et al. (2018), Repin et al. (2018),
Safiullin et al. (2016, 2018, 2019), Skorokhodov et al. (2018), Soo et al. (2020), Vorozheikin et al. (2019). In order to
address the issues of ensuring road traffic safety, the a posteriori approach has often been used. In the meantime, the
* Corresponding author. Tel: +7-903-724-48-40
E-mail address: silyanov@bk.ru
2 Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov / Transportati on Research Pro cedia 00 (2019) 000000
scientific and technical progress created prerequisites for the automated generation and processing of data
characterizing various facets of public activities, in particular, those concerning the road traffic. Moreover, it became
possible to develop models based on such data, in order to select corresponding measures and take scientifically
substantiated managerial decisions.
2. Theoretical studies
This paper is a continuation of the series of studies, performed in the Moscow Automobile and Road Construction
State Technical University (MADI), on modeling the traffic accident rate in Russian regions.
As for these regions, a functional relationship between the population size
1
x
(thous. people), the number of
vehicles (V)
2
x
(thous. units) and the key indicator of the accident rate the “number of RTA (road traffic accident)
fatalities”
y
measured in units, by means of the regression analysis of data for 20152018 can be represented as
follows (Silyanov 2020):
302422.0
2
604845.0
1
380429.0 xxy =
(1)
This functional relationship can be viewed as the first approximation to the traffic accident rate model (the
coefficient of rank correlation between the actual and estimated data is 0.921).
To improve the quality of the model, it is necessary to select factors associated with a set of numerically measured
indicators characterizing drivers (individuals) as road users, cars (vehicles), roads and the environment, provided that
the factors have a close correlative relationship with the number of RTA fatalities.
3. Calculations
For this purpose, we formed an array of data for 2015–2018 to characterize social and economic as well as natural
and climatic conditions of 82 regions (with the required information available), and selected factors corresponding to
the Spearman’s rank correlation coefficient exceeding the threshold value at the level of significance equal to 0.05
(for the data array with a dimension of 328, this threshold value is equal to 0.1095) (Silyanov 2020).
The said list of factors includes natural conditions (measured in points), (
) (Geoteka 2020), the average annual
temperature in the capital cities of the constituent entities of the Russian Federation (°C), (
10
x
) (Gosstroy of Russia
2000), the density of the federal, regional, inter-municipal and local public hard-surface roads by the constituent
entities of the Russian Federation (km per 1000 km2 of the territory), (
11
x
) (Autostat 2019, Federal State Statistics
Service 2020), the investment potential of the Russian regions (share in the all-Russian potential, %), (
1
x
) (Expert
2020) the investment risk of the Russian regions, (
3
x
) (Expert 2020) the socio-economic status (
5
x
) (Prime 2013),
the final assessment of life quality (rating score) (
4
x
) (GIBDD 2019), the number of initiated administrative offense
cases related to road traffic (thous.) (
7
x
) [8], the number of administrative offenses registered by means of traffic
cameras (thous.) (Fuelbroker 2019), the average age of the vehicle fleet (years) (
13
x
) (Trezvos 2019), the annual sales
volume of gasoline in the regions (
6
x
) (Dubrov et al. 2011), the sobriety rating of the regions (
2
x
) (Aivazyan 1989).
Since equation (1) makes it possible to estimate the number of RTA fatalities well enough, it is reasonable to
assume that “on average” this number might be made more accurate by complementing equation (1) in a linear manner
with the factors from the compiled list that are characterized by significant values of the correlation coefficient. This
means that the mathematical expectation
Y
of the number of RTA fatalities can be represented as follows:
Valeriy Kapitanov et al. / Transportation Research Procedia 50 (2020) 218–225 219
Available online at www.sciencedirect.com
ScienceDirect
Transportation Research Procedia 00 (2019) 000000
www.elsevier.com/locate/procedia
2352-1465 © 2020 Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov. Published by ELSEVIER B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0)
Peer-review under responsibility of the scientific committee of the XIV International Conference 2020 SPbGASU “Organization and safety of
traffic in large cities”
XIV International Conference 2020 SPbGASU “Organization and safety of traffic in large cities”
Probabilistic assessment of main factors determining the road traffic
accident rate in regions of Russia
Valeriy Kapitanovа, Olga Moninab, Valentin Silyanovа*, Alexandr Chubukovа
aMoscow Automobile and Road Construction State Technical University (MADI), 64 Leningradsky Prosp., Moscow, 125319, Russia
bScientific Research Center of Road Traffic Safety of the Ministry of Internal Affairs of the Russian Federation, 17 Poklonnaya St., Moscow,
121170, Russia
Abstract
This paper sets forth the findings of the research on the traffic accident rate in the constituent entities of the Russian Federation,
based upon respective regional statistical data for the four-year period from 2015 to 2018. In order to achieve the goal of the
research to identify the main factors affecting the accident rate, the methods of correlation and regression analysis were used.
We obtained regression equations relating the main indicators of the accident rate to the most relevant factors. The quality of the
regression equations is characterized by means of the coefficients of correlation between actual and estimated values of the number
of RTAs (road traffic accidents), the number of RTA fatalities and injuries. We assessed the role of each factor under consideration
by means of confidence estimates and confidence probabilities, and determined factors that have both a positive and a negative
influence on the accident rate.
Keywords: traffic accident rate; statistical analysis of data; mathematical modeling; factors; probabilistic assessment.
1. Introduction
In most countries of the world, ensuring road traffic safety is one of the high-priority problems. The Russian
Federation is no exception in recent years, the issues of ensuring road traffic and environmental safety have been
addressed by such researchers as Brylev et al. (2018), Danilov et al (2018, 2020), Evtiukov et al. (2018a, 2018b),
Ginzburg et al. (2017), Kerimov et al. (2017), Kurakina et al. (2018), Marusin (2017a, 2017b), Marusin and Abliazov
(2019), Marusin et al. (2018, 2019, 2020), Podoprigora et al. (2017, 2018), Pushkarev et al. (2018), Repin et al. (2018),
Safiullin et al. (2016, 2018, 2019), Skorokhodov et al. (2018), Soo et al. (2020), Vorozheikin et al. (2019). In order to
address the issues of ensuring road traffic safety, the a posteriori approach has often been used. In the meantime, the
* Corresponding author. Tel: +7-903-724-48-40
E-mail address: silyanov@bk.ru
Available online at www.sciencedirect.com
ScienceDirect
Transportation Research Procedia 00 (2019) 000000
www.elsevier.com/locate/procedia
2352-1465 © 2020 Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov. Published by ELSEVIER B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0)
Peer-review under responsibility of the scientific committee of the XIV International Conference 2020 SPbGASU “Organization and safety of
traffic in large cities”
XIV International Conference 2020 SPbGASU “Organization and safety of traffic in large cities”
Probabilistic assessment of main factors determining the road traffic
accident rate in regions of Russia
Valeriy Kapitanovа, Olga Moninab, Valentin Silyanovа*, Alexandr Chubukovа
aMoscow Automobile and Road Construction State Technical University (MADI), 64 Leningradsky Prosp., Moscow, 125319, Russia
bScientific Research Center of Road Traffic Safety of the Ministry of Internal Affairs of the Russian Federation, 17 Poklonnaya St., Moscow,
121170, Russia
Abstract
This paper sets forth the findings of the research on the traffic accident rate in the constituent entities of the Russian Federation,
based upon respective regional statistical data for the four-year period from 2015 to 2018. In order to achieve the goal of the
research to identify the main factors affecting the accident rate, the methods of correlation and regression analysis were used.
We obtained regression equations relating the main indicators of the accident rate to the most relevant factors. The quality of the
regression equations is characterized by means of the coefficients of correlation between actual and estimated values of the number
of RTAs (road traffic accidents), the number of RTA fatalities and injuries. We assessed the role of each factor under consideration
by means of confidence estimates and confidence probabilities, and determined factors that have both a positive and a negative
influence on the accident rate.
Keywords: traffic accident rate; statistical analysis of data; mathematical modeling; factors; probabilistic assessment.
1. Introduction
In most countries of the world, ensuring road traffic safety is one of the high-priority problems. The Russian
Federation is no exception in recent years, the issues of ensuring road traffic and environmental safety have been
addressed by such researchers as Brylev et al. (2018), Danilov et al (2018, 2020), Evtiukov et al. (2018a, 2018b),
Ginzburg et al. (2017), Kerimov et al. (2017), Kurakina et al. (2018), Marusin (2017a, 2017b), Marusin and Abliazov
(2019), Marusin et al. (2018, 2019, 2020), Podoprigora et al. (2017, 2018), Pushkarev et al. (2018), Repin et al. (2018),
Safiullin et al. (2016, 2018, 2019), Skorokhodov et al. (2018), Soo et al. (2020), Vorozheikin et al. (2019). In order to
address the issues of ensuring road traffic safety, the a posteriori approach has often been used. In the meantime, the
* Corresponding author. Tel: +7-903-724-48-40
E-mail address: silyanov@bk.ru
2 Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov / Transportati on Research Pro cedia 00 (2019) 000000
scientific and technical progress created prerequisites for the automated generation and processing of data
characterizing various facets of public activities, in particular, those concerning the road traffic. Moreover, it became
possible to develop models based on such data, in order to select corresponding measures and take scientifically
substantiated managerial decisions.
2. Theoretical studies
This paper is a continuation of the series of studies, performed in the Moscow Automobile and Road Construction
State Technical University (MADI), on modeling the traffic accident rate in Russian regions.
As for these regions, a functional relationship between the population size
1
x
(thous. people), the number of
vehicles (V)
2
x
(thous. units) and the key indicator of the accident rate the “number of RTA (road traffic accident)
fatalities”
y
measured in units, by means of the regression analysis of data for 20152018 can be represented as
follows (Silyanov 2020):
302422.0
2
604845.0
1
380429.0 xxy =
(1)
This functional relationship can be viewed as the first approximation to the traffic accident rate model (the
coefficient of rank correlation between the actual and estimated data is 0.921).
To improve the quality of the model, it is necessary to select factors associated with a set of numerically measured
indicators characterizing drivers (individuals) as road users, cars (vehicles), roads and the environment, provided that
the factors have a close correlative relationship with the number of RTA fatalities.
3. Calculations
For this purpose, we formed an array of data for 2015–2018 to characterize social and economic as well as natural
and climatic conditions of 82 regions (with the required information available), and selected factors corresponding to
the Spearman’s rank correlation coefficient exceeding the threshold value at the level of significance equal to 0.05
(for the data array with a dimension of 328, this threshold value is equal to 0.1095) (Silyanov 2020).
The said list of factors includes natural conditions (measured in points), (
9
x
) (Geoteka 2020), the average annual
temperature in the capital cities of the constituent entities of the Russian Federation (°C), (
10
x
) (Gosstroy of Russia
2000), the density of the federal, regional, inter-municipal and local public hard-surface roads by the constituent
entities of the Russian Federation (km per 1000 km2 of the territory), (
11
x
) (Autostat 2019, Federal State Statistics
Service 2020), the investment potential of the Russian regions (share in the all-Russian potential, %), (
1
x
) (Expert
2020) the investment risk of the Russian regions, (
3
x
) (Expert 2020) the socio-economic status (
5
x
) (Prime 2013),
the final assessment of life quality (rating score) (
4
x
) (GIBDD 2019), the number of initiated administrative offense
cases related to road traffic (thous.) (
7
x
) [8], the number of administrative offenses registered by means of traffic
cameras (thous.) (Fuelbroker 2019), the average age of the vehicle fleet (years) (
13
x
) (Trezvos 2019), the annual sales
volume of gasoline in the regions (
6
x
) (Dubrov et al. 2011), the sobriety rating of the regions (
2
x
) (Aivazyan 1989).
Since equation (1) makes it possible to estimate the number of RTA fatalities well enough, it is reasonable to
assume that “on average” this number might be made more accurate by complementing equation (1) in a linear manner
with the factors from the compiled list that are characterized by significant values of the correlation coefficient. This
means that the mathematical expectation
Y
of the number of RTA fatalities can be represented as follows:
220 Valeriy Kapitanov et al. / Transportation Research Procedia 50 (2020) 218–225
Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov / Transportation Research Procedia 00 (2019) 000000 3
0
1
axayY
i
n
i
i
++=
=
α
(2)
where
i
aa ,,
0
α
(
),...,1 ni =
parameters;
n
the number of factors;
i
x
the factors of the process under consideration (
ni ,...,1=
).
Taking into account equation (2) for each of 328 process implementations, it is possible to represent the estimate
of the number of fatalities as follows:
,
0
1
k
k
i
n
i
ikk
axayY
δα
+++=
=
(3)
where kthe seq. No. of the process implementation (k = 1, ..., 328);
k
δ
the estimation error determined by e.g. the presence of the unaccounted factors in the model.
The values of the unknown parameters in equation (3) can be determined using the least-squares method by way
of minimizing the sum of squared deviations of the actual and estimated values
k
Y
(Aivazyan 1989):
,
0
1
axayY
k
i
n
i
i
k
k
++=
=
α
(k = 1, ..., 328),
where
α
,,
0i
aa
estimates of the equation parameters by the least-squares method (3)
α
,,
0i
aa
.
To build the model, the factors are broken down into three groups socio-economic, administrative, and others.
We used an algorithm of building the main components described in the paper (Kapitanov et al. 2017, 2020).
As to the list of socio-economic indicators, the main components look as follows (Kapitanov et al. 2017, 2020,
Silyanov 2020):
65143
1
1371.0504.0403.0501.0442.0 xxxxxy ++++=
65143
1
2
573.0116.0531.0234.0568.0 xxxxxy ++=
65143
1
3
729.0121.0622.0118.0228.0
xxxxxy +++=
(4)
65143
1
4
022.0762.0370.0015.0530.0 xxxxxy ++=
65143
1
5
042.0370.0177.0825.0387.0 xxxxxy ++=
The relative fractions of the total variance, determined by one, two, three, four or five main components, are equal
to 0.677, 0.826, 0.935, 0.970, 1.0, respectively. Acceptable accuracy is achieved by the three first components, which
are used below.
By means of the method of the main components and equation (1), the following regression equation can be
obtained for the regions to connect the average number of fatalities
k
Y
(3) with the above-mentioned factors
(subscript k is omitted):
2969696.120157526.000.102958.26
132926.14511728.000611.01811.156146.3724867.236655647.1
7
1
3
1
2
1
113112109
+
+++=
xyy
yxxxxxyY
k
(5)
4 Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov / Transportati on Research Pro cedia 00 (2019) 000000
This equation describes the process on average. The difference between the estimated and actual values (in the case
under consideration, it is the number of RTA fatalities) is suggested to be associated with the random nature of values
kik aaY
δ
,,, 0
, included in equation (3).
In order to account for the said randomness, we can use necessary theoretical provisions, presented, for example,
in the paper on mathematical statistics (Aivazyan 1989). Random values
k
δ
are considered independent and
identically distributed random variables with zero mathematical expectation.
Estimates of confidence intervals, based on these provisions, for the coefficients of the factors in equation (3), with
account for (5), are presented in Table 1.
The position on the numerical axis of the interval (min, max), corresponding to a particular confidence probability,
characterizes the influence of the factor on the indicator under consideration (with such probability). At min > 0 and
max > 0, the factor adversely affects the accident rate, at min < 0 and max < 0, it has a positive influence, and at min
< 0 and max > 0, its influence is uncertain.
Table 1. Variation range (from min to max) of the coefficients of the factors in equations (3), (5), corresponding to different values of confidence
probability.
Factor
Confidence probability
0.95
0.9
0.6827
min
max
min
max
min
max
Population and transport,
equation (1) 1.225071 1.508042 1.249828 1.483285 1.295812 1.437301
Natural environment
-38.71369
33.263964
-32.41649
26.966763
-20.71979
15.270060
Average annual air temperature
-1.320457
8.443384
-0.466235
7.589162
1.120434
6.002493
Sobriety rating (average in 4 years)
-0.897733
3.259990
-0.533981
2.896238
0.141668
2.220589
Density of motor roads
-0.102268
-0.019945
-0.095065
-0.027147
-0.081688
-0.040525
Average age of the vehicle fleet
-4.293810
5.317267
-3.452954
4.476410
-1.891110
2.914566
Socio-economic indicators
(components)
1
1
y
7.861333
20.4045
8.958715
19.307138
10.997041
17.268812
1
2
y
-44.63231 -9.283762 -41.53973 -12.37634 -35.7954 -18.120649
1
3
y
-123.9187
-80.08199
-120.0835
-83.91719
-112.959
-91.040869
Number of registered administrative
offenses -0.025063 -0.006442 -0.023434 -0.008071 -0.020408 -0.011097
Factor
Confidence probability
0.8
min
max
Population and transport, equation (1)
1.276042
1.457070
Natural environment
-25.748442
20.298708
Average annual air temperature
0.438293
6.684634
Sobriety rating (average in 4 years)
-0.148807
2.511064
Density of motor roads
-0.087439
-0.034774
Average age of the vehicle fleet
-2.562578
3.586034
Socio-economic indicators (components)
1
1
y
10.120724
18.145129
1
2
y
-38.265020
-15.651057
1
3
y
-116.022476
-87.978259
Number of registered administrative offenses (thous.)
-0.021709
-0.009796
Valeriy Kapitanov et al. / Transportation Research Procedia 50 (2020) 218–225 221
Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov / Transportation Research Procedia 00 (2019) 000000 3
0
1
axayY
i
n
i
i
++=
=
α
(2)
where
i
aa ,,
0
α
(
),...,1 ni =
parameters;
n
the number of factors;
i
x
the factors of the process under consideration (
ni ,...,1=
).
Taking into account equation (2) for each of 328 process implementations, it is possible to represent the estimate
of the number of fatalities as follows:
,
0
1
k
k
i
n
i
ikk
axayY
δα
+++=
=
(3)
where kthe seq. No. of the process implementation (k = 1, ..., 328);
k
δ
the estimation error determined by e.g. the presence of the unaccounted factors in the model.
The values of the unknown parameters in equation (3) can be determined using the least-squares method by way
of minimizing the sum of squared deviations of the actual and estimated values
k
Y
(Aivazyan 1989):
,
0
1
axayY
k
i
n
i
i
k
k
++=
=
α
(k = 1, ..., 328),
where
α
,,
0i
aa
estimates of the equation parameters by the least-squares method (3)
α
,,
0i
aa
.
To build the model, the factors are broken down into three groups socio-economic, administrative, and others.
We used an algorithm of building the main components described in the paper (Kapitanov et al. 2017, 2020).
As to the list of socio-economic indicators, the main components look as follows (Kapitanov et al. 2017, 2020,
Silyanov 2020):
65143
1
1371.0504.0403.0501.0442.0 xxxxxy ++++=
65143
1
2573.0116.0531.0234.0568.0 xxxxxy ++=
65143
1
3
729.0121.0622.0118.0228.0 xxxxxy +++=
(4)
65143
1
4
022.0762.0370.0015.0530.0 xxxxxy ++=
65143
1
5
042.0370.0177.0825.0387.0 xxxxxy ++=
The relative fractions of the total variance, determined by one, two, three, four or five main components, are equal
to 0.677, 0.826, 0.935, 0.970, 1.0, respectively. Acceptable accuracy is achieved by the three first components, which
are used below.
By means of the method of the main components and equation (1), the following regression equation can be
obtained for the regions to connect the average number of fatalities
k
Y
(3) with the above-mentioned factors
(subscript k is omitted):
2969696.120157526.000.102958.26
132926.14511728.000611.01811.156146.3724867.236655647.1
7
1
3
1
2
1
113112109
+
+++=
xyy
yxxxxxyY
k
(5)
4 Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov / Transportati on Research Pro cedia 00 (2019) 000000
This equation describes the process on average. The difference between the estimated and actual values (in the case
under consideration, it is the number of RTA fatalities) is suggested to be associated with the random nature of values
kik
aaY
δ
,,,
0
, included in equation (3).
In order to account for the said randomness, we can use necessary theoretical provisions, presented, for example,
in the paper on mathematical statistics (Aivazyan 1989). Random values
k
δ
are considered independent and
identically distributed random variables with zero mathematical expectation.
Estimates of confidence intervals, based on these provisions, for the coefficients of the factors in equation (3), with
account for (5), are presented in Table 1.
The position on the numerical axis of the interval (min, max), corresponding to a particular confidence probability,
characterizes the influence of the factor on the indicator under consideration (with such probability). At min > 0 and
max > 0, the factor adversely affects the accident rate, at min < 0 and max < 0, it has a positive influence, and at min
< 0 and max > 0, its influence is uncertain.
Table 1. Variation range (from min to max) of the coefficients of the factors in equations (3), (5), corresponding to different values of confidence
probability.
Factor
Confidence probability
0.95
0.9
0.6827
min
max
min
max
min
max
Population and transport,
equation (1) 1.225071 1.508042 1.249828 1.483285 1.295812 1.437301
Natural environment
-38.71369
33.263964
-32.41649
26.966763
-20.71979
15.270060
Average annual air temperature
-1.320457
8.443384
-0.466235
7.589162
1.120434
6.002493
Sobriety rating (average in 4 years)
-0.897733
3.259990
-0.533981
2.896238
0.141668
2.220589
Density of motor roads
-0.102268
-0.019945
-0.095065
-0.027147
-0.081688
-0.040525
Average age of the vehicle fleet
-4.293810
5.317267
-3.452954
4.476410
-1.891110
2.914566
Socio-economic indicators
(components)
1
1
y
7.861333
20.4045
8.958715
19.307138
10.997041
17.268812
1
2
y
-44.63231 -9.283762 -41.53973 -12.37634 -35.7954 -18.120649
1
3
y
-123.9187
-80.08199
-120.0835
-83.91719
-112.959
-91.040869
Number of registered administrative
offenses -0.025063 -0.006442 -0.023434 -0.008071 -0.020408 -0.011097
Factor
Confidence probability
0.8
min
max
Population and transport, equation (1)
1.276042
1.457070
Natural environment
-25.748442
20.298708
Average annual air temperature
0.438293
6.684634
Sobriety rating (average in 4 years)
-0.148807
2.511064
Density of motor roads
-0.087439
-0.034774
Average age of the vehicle fleet
-2.562578
3.586034
Socio-economic indicators (components)
1
1
y
10.120724
18.145129
1
2
y
-38.265020
-15.651057
1
3
y
-116.022476
-87.978259
Number of registered administrative offenses (thous.)
-0.021709
-0.009796
222 Valeriy Kapitanov et al. / Transportation Research Procedia 50 (2020) 218–225
Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov / Transportation Research Procedia 00 (2019) 000000 5
It follows from Table 1 that at the level of probability equal to at least 0.95, the increase in the number of fatalities
is related to the population size and the number of vehicles in the entity, and the decrease in the number of fatalities
is related to the density of roads (the higher the density, the less is the number of RTA fatalities), measures of
administrative influence, and socio-economic situation in the region. The influence probability upward the sobriety
rating is estimated approximately at 0.68. The same applies to the average annual temperature in the capital of the
entity (probability is 0.8).
When the main components are replaced with factors (4), equation (5) will look as follows:
2969696.120157526.015463.6409192.206338.7235273.1815.44
511728.000611.01811.156146.3724867.236655647.1
765143
13112109
+++
++=
xxxxxx
xxxxxyY
k
A similar approach is used in modeling the number of injured and the number of RTAs.
The regression equation for the estimation of the number of injured
'
r
y
can be written in the following form:
026.14921985895.0958456.309
26649.24165768.809325.230468388.086418.
15
61246.131846.35137267.2
7
1
3
1
2
1
113112
109
322742.0
2
645484.0
1
'
+
++=
xy
yyxxx
xxxxy
r
(6)
Respective confidence estimates are given in Table 2.
Table 2. Variation range (from min to max) of the coefficients of the factors in equation (3), with account for (6), corresponding to different
values of confidence probability (for the number of injured).
Factor
Confidence probability
0.8
0.9
0.95
min
max
min
max
min
max
Population and transport
0.821405
0.927384
0.806328
0.94246
0.793214
0.955575
Natural environment
192.694981
509.67427
147.602622
554.766626
108.37696
593.99228
Average annual air
temperature -35.309094 8.08417 -41.482067 14.257144 -46.851912 19.626988
Sobriety rating
6.671774
25.056595
4.056414
27.671955
1.781323
29.947046
Density of motor roads
-0.22871
0.13504
-0.28046
0.18678
-0.32547
0.23180
Average age of the vehicle
fleet -45.193694 -2.67138 -51.242769 3.377698 -56.504836 8.639764
Socio-economic
indicators
(components)
1
1
y
52.471776
107.8598
-51.242769
3.377698
-56.504836
8.639764
1
2
y
-103.546849
55.01386
-126.103138
77.57015
-145.724764
97.19178
1
3
y
-407.81
-212.106
-435.651
-184.266
-459.869
-160.048
Number of registered
administrative offenses
(thous.)
-0.23994 -0.15724 -0.25171 -0.14547 -0.26194 -0.13524
Factor
Confidence probability
0.75
0.7
min
max
min
max
Average annual air temperature
-33.08184
5.856916
-31.150389
3.925465
Density of motor roads
-0.21004
0.11637
-0.19385
0.10018
It should be pointed out that as distinct from the factors affecting the number of RTA fatalities, the density of motor
roads is not related to the number of injured, and the temperature rather contributes to the reduction in the number of
6 Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov / Transportati on Research Pro cedia 00 (2019) 000000
injured (with a significant shift of the lower boundary of the interval to the negative side). The natural environment,
as well as the sobriety rating with a probability of at least 0.95 increase this value.
When the main components are replaced with factors (4), equation (6) will look as follows:
026.14921985895.079651.24171349.537286.17326631.988717.119
9325.230468388.086418.1561246.131846.35137267.2
765143
13112109
322742.0
2
645484.0
1
'
+++
++=
xxxxxx
xxxxxxxy
r
(7)
The regression equation for the number of RTAs
'
v
y
can be written in the following form
0364.159515242.091565867.1946652886.73788.602467298.7
088243.09198.176.583.26590637.1
7
1
3
1
2
1
113
1121091
322543.0
2
645086.0
1
'
++
+++=
xyyyx
xxxxyxxy
r
v
(8)
Respective confidence estimates are given in Table 3.
Table 3. Variation range (from min to max) of the coefficients of the factors in equation (3), with account for (7), corresponding to different
values of confidence probability (for the number of RTAs).
Factor
Confidence probability
0.8
0.9
0.95
min
max
min
max
min
max
Population and transport
0.817306
0.981863
0.793897
1.005272
0.773533
1.025635
Natural environment
74.579224
457.083733
20.165479
511.497479
-27.168821
558.831779
Average annual air
temperature -31.778858 28.028397 -39.227246 28.028397 -45.706569 34.507721
Sobriety rating
6.827592
29.01203
3.671712
32.16791
0.926424
34.9132
Density of motor roads
-0.13122
0.30771
-0.19366
0.37015
-0.24798
0.42447
Average age of the vehicle
fleet -32.901882 18.40842 -40.201106 25.70765 -46.550671 32.05721
Socio-economic
indicators
(components)
1
1
y
26.960696
93.79693
17.452808
103.3048
9.181935
111.5757
1
2
y
-87.9865
103.3171
-115.201
130.5313
-153.786
154.2048
1
3
y
-312.979
-76.8518
-346.57
-43.2611
-375.791
-14.0407
Number of registered
administrative offenses
(thous.)
-0.20232 -0.10253 -0.21652 -0.08833 -0.22887 -0.07598
Factor
Confidence probability
0.75
0.7
min
max
min
max
Average annual air temperature
-29.091425
17.892576
-26.760911
15.562062
The density of roads, the average annual air temperature, the average age of the vehicle fleet are not related to the
number of RTAs in terms of its increase or decrease, while the natural environment with a probability of at least 0.9
increases this value. The population size and the number of vehicles in the region, just like the sobriety rating, in 95%
of cases contribute to the increase in the number of RTAs.
When the main components are replaced with factors (4), equation (7) will look as follows:
0364.159515242.088627.16895695.583461.9245606.577432.66
2467298.7088243.09198.176.583.26590637.1
765143
131121091
322543.0
2
645086.0
1
'
+++
+++=
xxxxxx
xxxxxyxxy
r
v
Valeriy Kapitanov et al. / Transportation Research Procedia 50 (2020) 218–225 223
Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov / Transportation Research Procedia 00 (2019) 000000 5
It follows from Table 1 that at the level of probability equal to at least 0.95, the increase in the number of fatalities
is related to the population size and the number of vehicles in the entity, and the decrease in the number of fatalities
is related to the density of roads (the higher the density, the less is the number of RTA fatalities), measures of
administrative influence, and socio-economic situation in the region. The influence probability upward the sobriety
rating is estimated approximately at 0.68. The same applies to the average annual temperature in the capital of the
entity (probability is 0.8).
When the main components are replaced with factors (4), equation (5) will look as follows:
2969696.120157526.015463.6409192.206338.7235273.1815.44
511728.000611.01811.156146.3724867.236655647.1
765143
13112109
+++
++=
xxxxxx
xxxxxyY
k
A similar approach is used in modeling the number of injured and the number of RTAs.
The regression equation for the estimation of the number of injured
'
r
y
can be written in the following form:
026.14921985895.0958456.309
26649.24165768.809325.230468388.086418.15
61246.131846.35137267.2
7
1
3
1
2
1
113112
109
322742.0
2
645484.0
1
'
+
++=
xy
yyxxx
xxxxy
r
(6)
Respective confidence estimates are given in Table 2.
Table 2. Variation range (from min to max) of the coefficients of the factors in equation (3), with account for (6), corresponding to different
values of confidence probability (for the number of injured).
Factor
Confidence probability
0.8
0.9
0.95
min
max
min
max
min
max
Population and transport
0.821405
0.927384
0.806328
0.94246
0.793214
0.955575
Natural environment
192.694981
509.67427
147.602622
554.766626
108.37696
593.99228
Average annual air
temperature -35.309094 8.08417 -41.482067 14.257144 -46.851912 19.626988
Sobriety rating
6.671774
25.056595
4.056414
27.671955
1.781323
29.947046
Density of motor roads
-0.22871
0.13504
-0.28046
0.18678
-0.32547
0.23180
Average age of the vehicle
fleet -45.193694 -2.67138 -51.242769 3.377698 -56.504836 8.639764
Socio-economic
indicators
(components)
1
1
y
52.471776
107.8598
-51.242769
3.377698
-56.504836
8.639764
1
2
y
-103.546849
55.01386
-126.103138
77.57015
-145.724764
97.19178
1
3
y
-407.81
-212.106
-435.651
-184.266
-459.869
-160.048
Number of registered
administrative offenses
(thous.)
-0.23994 -0.15724 -0.25171 -0.14547 -0.26194 -0.13524
Factor
Confidence probability
0.75
0.7
min
max
min
max
Average annual air temperature
-33.08184
5.856916
-31.150389
3.925465
Density of motor roads
-0.21004
0.11637
-0.19385
0.10018
It should be pointed out that as distinct from the factors affecting the number of RTA fatalities, the density of motor
roads is not related to the number of injured, and the temperature rather contributes to the reduction in the number of
6 Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov / Transportati on Research Pro cedia 00 (2019) 000000
injured (with a significant shift of the lower boundary of the interval to the negative side). The natural environment,
as well as the sobriety rating with a probability of at least 0.95 increase this value.
When the main components are replaced with factors (4), equation (6) will look as follows:
026.14921985895.079651.24171349.537286.17326631.988717.119
9325.230468388.086418.1561246.131846.35137267.2
765143
13112109
322742.0
2
645484.0
1
'
+++
++=
xxxxxx
xxxxxxxy
r
(7)
The regression equation for the number of RTAs
'
v
y
can be written in the following form
0364.159515242.091565867.1946652886.73788.602467298.7
088243.09198.176.583.26590637.1
7
1
3
1
2
1
113
1121091
322543.0
2
645086.0
1
'
++
+++=
xyyyx
xxxxyxxy
r
v
(8)
Respective confidence estimates are given in Table 3.
Table 3. Variation range (from min to max) of the coefficients of the factors in equation (3), with account for (7), corresponding to different
values of confidence probability (for the number of RTAs).
Factor
Confidence probability
0.8
0.9
0.95
min
max
min
max
min
max
Population and transport
0.817306
0.981863
0.793897
1.005272
0.773533
1.025635
Natural environment
74.579224
457.083733
20.165479
511.497479
-27.168821
558.831779
Average annual air
temperature -31.778858 28.028397 -39.227246 28.028397 -45.706569 34.507721
Sobriety rating
6.827592
29.01203
3.671712
32.16791
0.926424
34.9132
Density of motor roads
-0.13122
0.30771
-0.19366
0.37015
-0.24798
0.42447
Average age of the vehicle
fleet -32.901882 18.40842 -40.201106 25.70765 -46.550671 32.05721
Socio-economic
indicators
(components)
1
1
y
26.960696
93.79693
17.452808
103.3048
9.181935
111.5757
1
2
y
-87.9865
103.3171
-115.201
130.5313
-153.786
154.2048
1
3
y
-312.979
-76.8518
-346.57
-43.2611
-375.791
-14.0407
Number of registered
administrative offenses
(thous.)
-0.20232 -0.10253 -0.21652 -0.08833 -0.22887 -0.07598
Factor
Confidence probability
0.75
0.7
min
max
min
max
Average annual air temperature
-29.091425
17.892576
-26.760911
15.562062
The density of roads, the average annual air temperature, the average age of the vehicle fleet are not related to the
number of RTAs in terms of its increase or decrease, while the natural environment with a probability of at least 0.9
increases this value. The population size and the number of vehicles in the region, just like the sobriety rating, in 95%
of cases contribute to the increase in the number of RTAs.
When the main components are replaced with factors (4), equation (7) will look as follows:
0364.159515242.088627.16895695.583461.9245606.577432.66
2467298.7088243.09198.176.583.26590637.1
765143
131121091
322543.0
2
645086.0
1
'
+++
+++=
xxxxxx
xxxxxyxxy
r
v
224 Valeriy Kapitanov et al. / Transportation Research Procedia 50 (2020) 218–225
Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov / Transportation Research Procedia 00 (2019) 000000 7
It should be noted that coefficients of correlation between the actual and estimated values (equations (5)-(6)) of the
number of fatalities, the number of injured as well as the number of RTAs are equal to 0.908, 0.952, 0.958,
respectively, which is indicative of a sufficiently good model approximation of actual data. The factors that
characterize the socio-economic status of the regions affect the accident rate indicators in different ways (upward or
downward). No influence of the vehicles’ age on the accident rate has been found.
4. Conclusions
The research resulted in obtaining the regression equations for the accident rate indicators and identified factors
associated with them. The quality of the regression equations is assessed by sufficiently large values of the coefficients
of correlation between the actual and estimated values (exceeding 0.9). The conclusions on the influence of the factors
on the accident rate were evaluated by means of confidence intervals and confidence probabilities for the coefficients
of the regression equation. We managed to prove the important role of the socio-economic status in the development
of the process under consideration.
The results presented above testify to the possibility of using mathematical models of the road traffic accident rate
in the development of proposals and selection of measures for its reduction.
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8 Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov / Transportati on Research Pro cedia 00 (2019) 000000
Marusin, A.V., 2017a. A method of assessing the efficiency of systems of automatic recording of traffic violations. PhD Thesis in Engineering.
Saint Petersburg State University of Architecture and Civil Engineering, Saint Petersburg.
Marusin, A.V., 2017b. Improving the diagnostics of plunger pairs in high-pressure fuel pumps of motor and tractor diesel engines. PhD Thesis in
Engineering. Kostychev Ryazan State Agrotechnological University, Ryazan.
Marusin, A.V., Abliazov, T.Kh., 2019. Public-private partnership as a mechanism for development of automated digital systems. Transport of the
Russian Federation, 3 (82), 2325
Marusin, A.V., Danilov, I.K., Khlopkov, S.V., Marusin, A.V., Uspenskiy, I.A., 2020. Development of a mathematical model of fuel equipment and
the rationale for diagnosing diesel engines by moving the injector needle. IOP Conference Series: Earth and Environmental Science 422,
012126. DOI: 10.1088/1755-1315/422/1/012126.
Marusin, A., Marusin, A., Ablyazov, T., 2019. Transport infrastructure safety improvement based on digital technology implementation. Atlantis
Highlights in Computer Sciences, Vol. 1. International Conference on Digital Transformation in Logistics and Infrastructure (ICDTL I 2019),
353357. DOI: 10.2991/icdtli-19.2019.61.
Marusin, A., Marusin, A., Danilov, I., 2018. A method for assessing the influence of automated traffic enforcement system parameters on traffic
safety. Transportation Research Procedia 36, 500506. DOI: 10.1016/j.trpro.2018.12.136.
Podoprigora, N., Dobromirov, V., Pushkarev, A., Lozhkin, V., 2017. Methods of assessing the influence of operational factors on brake system
efficiency in investigating traffic accidents. Transportation Research Procedia 20, 516522. DOI: 10.1016/j.trpro.2017.01.084.
Podoprigora, N., Dobromirov, V., Stepina, P., 2018. Method of assessing the influence of the moisture content in the braking fluid on the braking
system actuation efficiency. Transportation Research Procedia 36, 597602. DOI: 10.1016/j.trpro.2018.12.147.
Prime, 2013. Where it is better to live in Russia: rating of regions in terms of quality of life. Available at:
https://1prime.ru/ratings/20131217/773219432.html (accessed July 24, 2019).
Pushkarev, A., Podoprigora, N., Dobromirov, V., 2018. Methods of providing failure-free operation in transport infrastructure objects.
Transportation Research Procedia 36, 634639. DOI: 10.1016/j.trpro.2018.12.140.
Repin, S., Evtiukov, S., Maksimov, S., 2018. A method for quantitative assessment of vehicle reliability impact on road safety. Transportation
Research Procedia 36, 661668. DOI: 10.1016/j.trpro.2018.12.128.
Safiullin, R., Kerimov, M., Afanasyev, A., Marusin, A., 2018. A model for justification of the number of traffic enforcement facilities in the region.
Transportation Research Procedia 36, 493499. DOI: 10.1016/j.trpro.2018.12.135.
Safiullin, R.N., Kerimov, M.A., Marusin, A.V., 2016. Improving the efficiency of the system of photo and video fixation of administrative offences
in road traffic. Bulletin of Civil Engineers 3 (56), 233237.
Safiullin, R., Marusin, A., Safiullin, R., Ablyazov, T., 2019. Methodical approaches for creation of intelligent management information systems by
means of energy resources of technical facilities. E3S Web of Conferences 140, 10008. DOI: 10.1051/e3sconf/201914010008.
Silyanov, V.V., 2020. Scientific basis for the formation of differentiated strategies to improve road traffic safety: R&D report (final). Moscow
Automobile and Road Construction State Technical University (MADI), Moscow.
Skorokhodov, D., Seliverstov, Y., Seliverstov, S., Burov, I., Vydrina, E., Podoprigora, N., Shatalova, N., Chigur, V., Cheremisina, A., 2020. Using
augmented reality technology to improve the quality of transport services. In: Sukhomlin, V., Zubareva, E. (eds). Convergent Cognitive
Information Technologies. Convergent 2018. Communications in Computer and Information Science, 1140. Springer, Cham, 339348. DOI:
10.1007/978-3-030-37436-5_30.
Soo, S., Abdel Sater, K.I., Khodyakov, A.A., Marusin, A.V., Danilov, I.K., Khlopkov, S.V., Andryushenko, I.S., 2020. The ways of effectiveness
increase of liquid fuel with organic addition appliance in aerospace equipment. Advances in the Astronautical Sciences 170, 833838.
Trezvos, 2019. National rating of sobriety of constituent entities of the Russian Federation 2018. Available at:
http://www.trezvros.ru/calendar/702 (accessed: August 15, 2019).
Vorozheikin, I., Marusin, A., Brylev, I., Vinogradova, V., 2019. Digital technologies and complexes for provision of vehicular traffic safety.
Atlantis Highlights in Computer Sciences, Vol. 1. International Conference on Digital Transformation in Logistics and Infrastructure (ICDTLI
2019), 385389. DOI: 10.2991/icdtli-19.2019.67.
Valeriy Kapitanov et al. / Transportation Research Procedia 50 (2020) 218–225 225
Valeriy Kapitanov, Olga Monina, Valentin Silyanov, Alexandr Chubukov / Transportation Research Procedia 00 (2019) 000000 7
It should be noted that coefficients of correlation between the actual and estimated values (equations (5)-(6)) of the
number of fatalities, the number of injured as well as the number of RTAs are equal to 0.908, 0.952, 0.958,
respectively, which is indicative of a sufficiently good model approximation of actual data. The factors that
characterize the socio-economic status of the regions affect the accident rate indicators in different ways (upward or
downward). No influence of the vehicles’ age on the accident rate has been found.
4. Conclusions
The research resulted in obtaining the regression equations for the accident rate indicators and identified factors
associated with them. The quality of the regression equations is assessed by sufficiently large values of the coefficients
of correlation between the actual and estimated values (exceeding 0.9). The conclusions on the influence of the factors
on the accident rate were evaluated by means of confidence intervals and confidence probabilities for the coefficients
of the regression equation. We managed to prove the important role of the socio-economic status in the development
of the process under consideration.
The results presented above testify to the possibility of using mathematical models of the road traffic accident rate
in the development of proposals and selection of measures for its reduction.
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Chapter
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