Forecasting Road Accident Fatalities in India

1. FORECASTING ROAD ACCIDENT
FATALITIES IN INDIA
Operations Management II
ABSTRACT
The project aims to analyze the historical data and
understand the factors that affect the no. of fatalities
caused by road accidents across five states in India and
to create a forecast model for the same.
Group 6
Aayush Jain (B15063) | Aishwary Gupta (B15066)
Akshay Ratan (B16068) | Ankit Anand (B15071)
Avinash Bhandaru (B15079) | Rohit Chalasani (B15103)

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Contents
1. Introduction ..........................................................................................................................................2
1.1 Need for forecast ................................................................................................................................2
2. Objective...............................................................................................................................................3
3. Factors Affecting Road Accident Deaths...............................................................................................3
3.1 Registered Vehicles in a state.............................................................................................................3
3.2 Rainfall ................................................................................................................................................4
3.3 Roads Network....................................................................................................................................4
3.4 Government spending on Infrastructure............................................................................................5
3.5 State Population..................................................................................................................................5
3.6 Other Factors ......................................................................................................................................5
4. Methodology of Forecasting.................................................................................................................6
4.1 TIME SERIES BASED MODELS..............................................................................................................7
4.1.1 SIMPLE MOVING AVERAGE..........................................................................................................7
4.1.2 Exponential Smoothening............................................................................................................7
4.1.3 Holt-Winter’s Multiplicative method...........................................................................................7
4.2 CAUSALITY BASED MODELS ................................................................................................................8
4.2.1 MULTIPLE LINEAR REGRESSION ...................................................................................................8
5. Results & Analysis .................................................................................................................................9
ANDHRA PRADESH....................................................................................................................................9
MAHARASHTRA.......................................................................................................................................10
WEST BENGAL.........................................................................................................................................11
DELHI.......................................................................................................................................................12
6. References ..........................................................................................................................................15
7. Annexure.............................................................................................................................................15

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1. Introduction
India possesses the world’s second largest road network of more than 4 crores kilometers. Road transport
in India is popular to numerous reasons of inaccessibility of other means of transport, paved/unpaved
road, emerging markets etc. Before, India did not allocate much resources to build and maintain the
quality of the roads. In the past decade however, major efforts have been made to improve the quality of
roads.
However, the frequency of traffic collisions in India is one of the highest in India. According to national
reports, more than 135,000 traffic-collision related deaths occur in India. The rate of road accidents and
fatality in India is very high. Number of vehicles have been increasing dramatically which tends to
contribute more towards deaths on roads. The neglect of Indian roads is evident from the fact that in the
first Plan the outlay was around 7% of the total expenditure which has gradually declined to 3% by the
eighth plan. The fatality rate is almost 20-25 times of that of USA.
The daily newspapers are testimonial to the ever increasing road deaths. Various factors are contributing
to the rise of the cases such as weather conditions, road-population density, increasing road network,
behavioral factors such as carelessness of drivers about traffic signals, insufficient training etc, mechanical
factors such as failure of machinery parts of the vehicles.
1.1 Need for forecast
As per WHO report, India ranks 2nd in number of deaths due to road accidents. Moreover India has 20.74
deaths per 1,00,000 vehicles. This number is huge when compared to other developing and developed
countries. Thus it is imperative to forecast number of fatal road accidents
Every year, millions of people in India are killed in fatal road accidents. As per WHO report, India is 2nd in
ranking in number of fatal road accidents. Moreover India registers 20.74 deaths per 1,00,000 vehicles.
This number is huge when compared to other developing and developed countries. Thus it is imperative
for government to forecast the number of fatal road accidents. Controlling Road accidents is very critical
because they result in waste of resources such as those hospital services that could be used for other
purposes, and loss of savings and working days of the accident victims which may improve the future life
style of their families, but also they in worst case may result death of people.
Such state-wise forecast helps government to decide their budget allocation on public infrastructure.
Moreover such forecast helps government to decide policies. These forecasts help government in:
 Understanding and analysing effect of policies on road accidents
 Budget allocation on road quality improvement
 Budget allocation on development of new roads
 Budget allocation on public transports
 Policy on design standards and operational practices of automobile
 Public policy related to drunk driving

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2. Objective
The average cost of Road Traffic Accidents in India cost the exchequer approximately $12.5 Billion
annually. This does not include the economic burden of permanent disability of more than 10 lakh people
who survive major accidents every year. Accident fatalities and serious injuries place a huge strain on the
economic and social fabric of the family and the society at large. The family loses the source of income in
addition to their loved one. Searching for a new source of income is a challenging task and is fraught with
uncertainties and exploitations. The larger ramifications of this include children dropping out from the
school for employment and elderly being forced to work.
We hope that with this project, we might be able to devise an accurate forecasting model for road
accidents in different states in India. For that we will demonstrate various forecasting methodologies and
compare them to check the mean error and select the one with lowest error. These forecasting models
may help in identifying the worst affected states and prepare contingency plans for the same.
3. Factors Affecting Road Accident Deaths
3.1 Registered Vehicles in a state
One of the factors that might influence accidental deaths is the number of registered vehicles. As seen
from the data, the accidental deaths in Delhi were showing the same trend as the number of registered
vehicles. However, the accidents started reducing after 2006 which is attributed to two factors
1. Stricter enforcement of traffic laws.
2. Increasing vehicular density in Delhi.
Both factors combined have led to a reduction in cases of drunk driving as well as over speeding – two
leading causes of accidents in Urban Delhi. Hence it is visible that if external environment remains same,
the accidental deaths are directly related to no of vehicles registered.
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Year 2003 2004 2005 2006 2007 2008 2009 2010
Accidents & Registered Vehicles, New Delhi
Accidental Deaths Total Vehicles registered

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3.2 Rainfall
The average rainfall in the state in a given month is measured in mm by the meteorological department.
Since rainfall in a given state is seasonal and increases significantly in the months of Jul-Sep. Rainfall affects
a lot of factors, most importantly for us being the road conditions which are known to deteriorate
significantly during the period. The graph below indicates Rainfall in Delhi & Number of road accidents
monthly over a two year period.
From the above graph, it is evident that the average monthly rainfall has almost no effect on the number
of road accidents.
3.3 Roads Network
The percentage of roads surfaced vary across different states owing to different factors. The different
types of roads are highways, urban roads and project roads. The following graph demonstrates the
percentage of different kinds of roads surfaced and compares it to the total number of accidents in the
state of Andhra Pradesh.
The above graph demonstrates that the percentage of different kinds of roads surfaced in the state and
the total number of accidents are not correlated.
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Delhi - Rainfall Vs. Road Accidents
Rainfall (mm) Road Accidents
40000
45000
40%
2008 2009 2010 2011
Andhra Pradesh - Total Accidents Vs.
Surfaced Roads
Highways - Surfaced % Urban Roads - Surfaced %
Project Roads - Surfaced % Total Surfaced Road Length %
Total Accidents

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3.4 Government spending on Infrastructure
Though construction of roads and increasing road connectivity is important for social and economic
development of the society, it comes at a cost. As can be seen from the graph below, we can see that
there is direct correlation between the amounts of expenditure incurred by a state on construction of
new roads to fatalities in road accidents. This can be understood from the fact that, increase in road
network increases the usage of cars. Improvement of road quality results in speeding of cars especially in
highways which are one of the major cause of deaths due to road accidents
3.5 State Population
Population and number of deaths in road accident are directly co-related. Increase in population causes
increased usage of public transport and at times overloading of the same. Moreover with increase in
population, the number of vehicles newly registered also increases. Taking Andhra Pradesh’s data we can
see the relation between population and deaths due to road accidents.
3.6 Other Factors
Other Qualitative factors which may affect deaths due to road accidents:
 Government policies on drunk driving, truck loading capacity operational standards etc.
 Advertising campaigns
 Increasing/decreasing responsible behavior
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2004 2005 2006 2007 2008 2009
Expenditure (in
lakhs)
Deaths
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2004 2005 2006 2007 2008 2009 2010
Deaths
Population lakhs

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4. Methodology of Forecasting
In this project, we have constructed various forecasting models to forecast the number of deaths that
occur due to road accidents in four states of our country, Andhra Pradesh from the South, Delhi from the
North, West Bengal from the East and Maharashtra from the West.
To achieve the above task, we considered all Quantitative Forecasting techniques available to us under
the following two heads:
• TIME SERIES BASED
• CAUSALITY BASED
The methodology decided for all the states was that we will first run the Time series based models, if the
forecasting accuracy metric MAPE achieved was less than 10%, we would conclude that our dependent
variable is sufficiently explained by time. However, if the MAPE obtained is more than 10%, we would use
the factors cited above and run causality based models, I.e. Multiple Linear Regression (MLR) to determine
other factors that are affecting our dependent variable.
We have used the data of road accident deaths from 2001 to 2008 and forecasted the data for 2009 and
2010. We further compared this forecasted data with the actuals and calculated forecasting accuracy
metrics.
STEP 1: VISUALIZE THE DATA
STEP 2: TIME SERIES BASED MODELS
1. SIMPLE MOVING AVERAGE
2. SIMPLE EXPONENTIAL SMOOTHING
3. HOLT-WINTER EXPONENTIAL SMOOTHING
STEP 3:
IF MAPE
> 10%
YES
STEP 4: MLR
END
NO

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4.1 TIME SERIES BASED MODELS
4.1.1 SIMPLE MOVING AVERAGE
The classical method of time series decomposition originated in the 1920s and was widely used until the
1950s. It still forms the basis of later time series methods, and so it is important to understand how it
works. The first step in a classical decomposition is to use a moving average method to estimate the trend-
cycle, so we begin by discussing moving averages.
A moving average of order mm can be written as
T^t=1m∑j=−kkyt+j, T^t=1m∑j=−kkyt+j,
Where m=2k+1. That is, the estimate of the trend-cycle at time tt is obtained by averaging values of the
time series within kk periods of tt. Observations that are nearby in time are also likely to be close in value,
and the average eliminates some of the randomness in the data, leaving a smooth trend-cycle component.
We call this an mm-MA meaning a moving average of order mm.
For the purpose of the forecast, a 12 month moving average has been used. After deseasonalizing the
data, a Simple Linear Regression (SLR) is run to see how much of the change in the forecast is explained
by time.
4.1.2 Exponential Smoothening
Exponential Smoothening is suitable for forecasting data with no trend or seasonal pattern.
Ft = Ft-1 + α (At-1 – Ft-1)
Ft = Forecast for period t
Ft-1 = Forecast for previous period, t-1
α is a smoothening constant
At-1 = Actual demand for the previous period
So, the Exponential Smoothening Model essentially forecasts based on the below methodology:
Next Forecast = Previous Forecast – α (Previous Actual – Previous Forecast)
The smoothening constant α represents the percentage of forecast error. Each new forecast is
equal to the previous forecast plus a percentage of the previous error. However, Exponential
Smoothening does not factor trend and seasonality. It does not de-seasonalise the data and may
lead to high values of errors in data where trend and seasonality are present.
4.1.3 Holt-Winter’s Multiplicative method
The Holt-Winters method factors trend and seasonality. This method is more applicable for data
where seasonality is predominant. In the case of road accident deaths, the data is seasonal with
accidents shooting up in the monsoons for some states like Maharashtra and when there is low
visibility in the winters in the northern states like that of Delhi.

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There are two variations to this method that differ in the nature of the seasonal component. The
additive method is preferred when the seasonal variations are roughly constant through the
series, while the multiplicative method is preferred when the seasonal variations are changing
proportional to the level of the series.
We have applied Holt-Winters seasonal method with Multiplicative Seasonality as the seasonal
variations were found to be changing proportional to the level of the series.
The Holt-Winters seasonal method with Multiplicative Seasonality comprises the forecast
equation and three smoothing equations — one for the level Et, one for trend Tt, and one for the
seasonal component denoted by St, with smoothing parameters α, β and γ.
The level, Et of period t is given by:
Et = α* (Yt/St-p) + (1- α) * (Et-1 + Tt-1)
The trend, Tt of period t is given by:
Tt = β * (Et - Et-1) + (1- β) Tt-1
The seasonality factor, St of period t is given by:
St = γ*(
𝑌𝑡
(𝐸𝑡−1+𝑇𝑡−1)
) + (1- γ) *St-p
The seasonality equation is weighted average between current seasonal index and the last
seasonal index of last year for the same season.
4.2 CAUSALITY BASED MODELS
4.2.1 MULTIPLE LINEAR REGRESSION
In multiple regression there is one variable to be forecast and several predictor variables. The model
assists us in understanding which of the predictor variables explains the movement in the forecasted
variable.
The general notation for MLR is:
Y = b0 + b1X1 + b2X2 + b3X3...ßnXn + ei
Where:
Y = independent variable
ß0 = Y-intercept or constant
ßi = coefficient or weights
Xi = independent variables
ei = remaining error or forecast error
The assumptions of an MLR model are as follows:
 The X’s are non-stochastic.
 No exact linear relationship exists between two or more of the explanatory variables.
 Errors corresponding to different observations are independent and therefore uncorrelated.
 The error variable is distributed normally or has a Poisson distribution.
 The error variable has an expected value of 0.

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5. Results & Analysis
ANDHRA PRADESH
The moving average method gave us a MAPE of 13.05%. This was slightly above the 10% limit that we had
set for ourselves. Hence, the forecast obtained by this method was not acceptable. Calculations and
details about the forecast can be found in the excel sheet.
The exponential smoothing model was then run which reduced the MAPE to 5.89%. We then ran the Holt
Winter’s Exponential smoothing to further reduce the MAPE to 2.76%. The forecast value were hence
deemed acceptable.
At this stage, we decided not to use carry out the MLR since the MAPE obtained was very low.
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JANUARY
FEBRUARY
MARCH
APRIL
MAY
JUNE
JULY
AUGUST
SEPTEMBER
OCTOBER
NOVEMBER
DECEMBER
JANUARY
FEBRUARY
MARCH
APRIL
MAY
JUNE
JULY
AUGUST
SEPTEMBER
OCTOBER
NOVEMBER
DECEMBER
2009 2010
ANDHRA PRADESH: FORECASTED USING MOVING AVERAGES
ACTUAL FORECAST

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MAHARASHTRA
The moving average method gave us a MAPE of 10.82%. This was slightly above the 10% limit that we had
set for ourselves. Hence, the forecast obtained by this method was not acceptable. Calculations and
details about the forecast can be found in the excel sheet.
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3500
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4500
5000
JANUARY
FEBRUARY
MARCH
APRIL
MAY
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JULY
AUGUST
SEPTEMBER
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NOVEMBER
DECEMBER
JANUARY
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AUGUST
SEPTEMBER
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NOVEMBER
DECEMBER
200920092009200920092009200920092009200920092009201020102010201020102010201020102010201020102010
ANDHRA PRADESH: FORECASTED USING HOLT WINTER'S Method
Actual Forecast
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6000
JANUARY
FEBRUARY
MARCH
APRIL
MAY
JUNE
JULY
AUGUST
SEPTEMBER
OCTOBER
NOVEMBER
DECEMBER
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MAY
JUNE
JULY
AUGUST
SEPTEMBER
OCTOBER
NOVEMBER
DECEMBER
2009 2010
MAHARASHTRA: FORECASTED USING MOVING AVERAGES
actual
FORECAST

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The exponential smoothing model was then run which reduced the MAPE to 6.61%. We then ran the Holt
Winter’s Exponential smoothing to further reduce the MAPE to 2.16%. The forecast value were hence
deemed acceptable.
At this stage, we decided not to use carry out the MLR since the MAPE obtained was very low.
WEST BENGAL
The moving average method gave us a MAPE of 7079%. Although this was lesser than the 10% limit that
we had set for ourselves, to improve it further we decided to run other methods. Calculations and details
about the forecast can be found in the excel sheet.
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5500
JANUARY
FEBRUARY
MARCH
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MAY
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JULY
AUGUST
SEPTEMBER
OCTOBER
NOVEMBER
DECEMBER
JANUARY
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MARCH
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JULY
AUGUST
SEPTEMBER
OCTOBER
NOVEMBER
DECEMBER
200920092009200920092009200920092009200920092009201020102010201020102010201020102010201020102010
Maharashtra: Forecasted using Holt - Winters method
Actual Forecast
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1400
JANUARY
FEBRUARY
MARCH
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MAY
JUNE
JULY
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OCTOBER
NOVEMBER
DECEMBER
JANUARY
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MARCH
APRIL
MAY
JUNE
JULY
AUGUST
SEPTEMBER
OCTOBER
NOVEMBER
DECEMBER
2009 2010
WEST BENGAL FORECASTED USING MOVING AVERAGES
ACTUAL FORECAST

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The exponential smoothing model was then run which reduced the MAPE to 6.21%. We then ran the Holt
Winter’s Exponential smoothing to further reduce the MAPE to 5.03%. The forecast value were hence
deemed acceptable.
At this stage, we decided not to use carry out the MLR since the MAPE obtained was very low.
DELHI
The moving average method gave us a MAPE of 30.93%. This was way above the 10% limit that we had
set for ourselves. Hence, the forecast obtained by this method was not acceptable. Calculations and
details about the forecast can be found in the excel sheet.
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SEPTEMBER
OCTOBER
NOVEMBER
DECEMBER
200920092009200920092009200920092009200920092009201020102010201020102010201020102010201020102010
West Bengal Forecasted using Holt - Winters method
Actual Forecast
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950
JANUARY
FEBRUARY
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NOVEMBER
DECEMBER
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APRIL
MAY
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JULY
AUGUST
SEPTEMBER
OCTOBER
NOVEMBER
DECEMBER
2009 2010
DELHI FORECASTED USING MOVING AVERAGES
ACTUAL
FORECAST

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The exponential smoothing model was then run which reduced the MAPE to 6.53%. We then ran the Holt
Winter’s Exponential smoothing to further reduce the MAPE to 4.38%. The forecast value were hence
deemed acceptable.
At this stage, we decided not to use carry out the MLR since the MAPE obtained was very low.
Hence, using the methodology decided upon, the forecast of number of road accidents for each of the
four states were obtained for the year 2009 and 2010. They were then compared to the actual values and
the forecast accuracy metrics were deemed to be in acceptable range. The final results table is as below:
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750
800
JANUARY
FEBRUARY
MARCH
APRIL
MAY
JUNE
JULY
AUGUST
SEPTEMBER
OCTOBER
NOVEMBER
DECEMBER
JANUARY
FEBRUARY
MARCH
APRIL
MAY
JUNE
JULY
AUGUST
SEPTEMBER
OCTOBER
NOVEMBER
DECEMBER
200920092009200920092009200920092009200920092009201020102010201020102010201020102010201020102010
Delhi Forecasted using Holt - Winters method
Actual Forecast

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From the above table, we see a clear improvement in the values of forecasting performance accuracy
metrics in terms of MAPE, SMAPE, MSE and MAD as the forecasting methods were improved from Simple
Moving Average to Exponential Smoothening and further to Holt-Winter’s method. We found the best
results through Holt-Winter’s Exponential Smoothing method as it takes care of trend and seasonality
effects on the data.
Forecasting
Method Location Alpha Beta Gamma MSE Bias MAD MAPE SMAPE
Simple
Moving
Average
Andhra
Pradesh - - - 230252.53 -451.04 451.04 13.05 12.14
Maharashtra - - - 213634.45 -447.37 447.37 10.82 10.23
West Bengal - - - 11492.93 89.89 94.24 7.79 8.20
Delhi - - - 37735.88 -189.42 189.42 30.93 26.59
Exponential
Smoothening
Andhra
Pradesh 0.4508 - - 55850.23 2670.09 187.18 5.89 5.92
Maharashtra 1.0000 - - 99481.63 1308.25 255.82 6.61 6.57
West Bengal 0.3503 - - 6933.37 793.87 64.69 6.21 6.23
Delhi 0.4335 - - 5748.26 -332.01 49.50 6.53 6.44
Holt-Winter's
Exponential
Smoothening
Andhra
Pradesh 0.5559 0.152475 0.223769 14717.34 -93.30 95.22 2.76 2.75
Maharashtra 0.5071 0.425169 0.0374 12136.54 612.31 87.80 2.16 2.18
West Bengal 0.0020 1 0.130334 5633.98 492.96 60.58 5.03 5.10
Delhi 0.3263 0.038164 0.089521 1213.81 110.59 27.17 4.38 4.41

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6. References
1. Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts,
2014.
2. TNN. "Fatal Road Accidents in Delhi at 26-yr-low. Jams behind Drop? - Times of India." The Times
of India. 13 Jan. 2016. Web.
3. Stevenson, William J., and Chee Chuong Sum. Operations management. Vol. 8. Boston, MA:
McGraw-Hill/Irwin, 2009.
4. Data extracted from www.data.gov.in
7. Annexure
1. Data for forecasting using Moving Averages method.
BM-B_Group6_Movi
ngAverage.xlsx
2. Data for forecasting using the Holt Winter Exponential Smoothing method.
BM-B_Group6_Holt
WinterExponentialSmothing.xlsx