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1. A Course Project on Topic-
Evaluation of Pedestrian Safety and Road
Crossing Behaviour at Midblock Crosswalk
Submitted by-
SHRIKRISHNA KESHARWANI
Roll no.-
22CEM3R23
Subject-
TRANSPORTATION DATA ANALYTICS
Master of Technology
In
TRANSPORTATION ENGINEERING
TRANSPORTATION DIVISION
DEPARTMENT OF CIVIL ENGINEERING
NATIONAL INSTITUTE OF TECHNOLOGY WARANGAL
DECEMBER, 2022

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SHRIKRISHNA KESHARWANI (22CEM3R23) 2
Table of Contents
Abbreviation ..............................................................................................................................3
ABSTRACT...............................................................................................................................4
1. Introduction- ......................................................................................................................5
2. Literature Review...............................................................................................................6
2.1 Factors affecting waiting time and other pedestrian crossing behaviour –.................6
2.2 Factors affecting Pedestrian Safety margins-..............................................................6
3. Methodology......................................................................................................................8
3.1 Methodology Followed-..............................................................................................8
3.2 Selected variables-.......................................................................................................9
3.4 Root mean square error (RMSE)...............................................................................10
4. Results and Analysis........................................................................................................11
4.1 MLR model analysis using waiting time as dependent variable- .............................11
4.1.1 Correlation matrix-.............................................................................................11
4.1.2 Regression analysis and MLR equation formulation- .......................................12
4.1.3 Validation- .........................................................................................................13
4.2 MLR model analysis using PSM as dependent variable...........................................14
4.2.1 Regression analysis and MLR equation formulation- .......................................14
4.2.2 Validation...........................................................................................................15
5. Conclusions......................................................................................................................16
References................................................................................................................................16

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List of figures-
Figure 1 Methodology Followed ...............................................................................................8
Figure 2 Validation graph for waiting time .............................................................................13
Figure 3 Validation graph for PSM .........................................................................................15
List of Tables-
Table 1 Description of selected variables-.................................................................................9
Table 2 Correlation matrix for waiting time............................................................................11
Table 3 Regression analysis.....................................................................................................12
Table 4 Regression analysis.....................................................................................................14
Abbreviation
MLR Multiple Linear Regression
W_Time Waiting time
FSB Frequency step backwards
Gen Gender (Male- 1, Female- 0)
PSM Pedestrian Safety Margins
RMSE Root mean square error

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SHRIKRISHNA KESHARWANI (22CEM3R23) 4
ABSTRACT
In developing countries like India, pedestrians follow non- complaint behaviour while crossing
the road due to negligence of government towards the rule and regulations for the pedestrians.
As a result pedestrian road crossing behaviour is becoming one of the major threat to the
pedestrian safety at midblock crossing.
There can be various factors that can directly and indirectly affect the pedestrian safety and
their road crossing behaviour, Therefore to improve the pedestrian safety and to reduce the
number of accidents it is important to know and study about these factors.
In this study a model is created to evaluate pedestrian safety and pedestrian road crossing
behaviour at mid-block crosswalk by using multilinear regression analysis technique by taking
PSM and Waiting time as dependent variable.

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SHRIKRISHNA KESHARWANI (22CEM3R23) 5
1. Introduction-
Today traffic accidents which are involving pedestrians have become a major safety problem
all over the world, especially in the developing countries because of the high population
density, rapid urbanization, and lack of commitment to traffic regulations by both pedestrians
and drivers.
Absence of foot over bridges in the intersections especially at the mid-block force the
pedestrians to cross at grade. Also lack of obedience towards the traffic rules and regulations
at pedestrian crossings particularly by drivers create a situation in which pedestrians may force
to take risk to cross the intersection so that approaching vehicles in the traffic stream should
apply brakes. Unprotected crossing of road and increase in motorised vehicle traffic is
increasing the pedestrians’ vulnerability.
Today more focus is only given to the rules and regulations for motor vehicles but at the same
time regulations for pedestrians are being completely neglected due to which pedestrians
follow non- complaint behaviour while crossing the road. As a result pedestrian road crossing
behaviour is becoming one of the major threat to the pedestrian safety at midblock crossing.
There can be various factors that can directly and indirectly affect the pedestrian safety and
their road crossing behaviour, Therefore to improve the pedestrian safety and to reduce the
number of accidents it is important to know and study about these factors.
In this study a model is created to evaluate pedestrian safety and pedestrian road crossing
behaviour at mid-block crosswalk by using multilinear regression analysis technique by using
PSM and Waiting time as dependent variable.
Objectives -
 To evaluate the pedestrian safety at mid-block crosswalks by modeling pedestrian
safety margin (PSM) using multiple linear regression (MLR) technique.
 To understand pedestrian road crossing behavior by modeling waiting time using MLR
technique.

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2. Literature Review
2.1 Factors affecting waiting time and other pedestrian crossing behaviour –
(Jain, Gupta, & Rastogi, 2014) Studied pedestrian crossing behaviour and found out that
pedestrian crossing behaviour generally gets affected by various kinds of factors related to
pedestrian movements, pedestrian characteristics, climatic conditions, environmental
surrounding, and traffic and road conditions. Also waiting time is also related to the age of
pedestrians for example children are found to have very less waiting time as compared to the
older people.
Hamid (2001) observed that approaching traffic volume and vehicle speeds are highly related
in determining the pedestrian’s waiting time (delay). Pedestrians, who are taking higher risk,
are having less waiting time, whereas pedestrians, who are less likely to take higher risk, have
higher waiting time at pedestrian crossings. In other words waiting time is directly proportional
to the risk taken by pedestrian to cross.
2.2 Factors affecting Pedestrian Safety margins-
Avinasha et al. (2018) developed a multiple linear regression model to find out the significant
factors related to pedestrian safety margins, the author found out that the developed regression
model shows that the pedestrian safety margins clearly depends on the availability of gap in
vehicular flow, speed of the approaching vehicle and pedestrian crossing behaviour. Further, it
is found that safety margin is directly proportional to the pedestrian speed and vehicular gap,
but inversely proportional to the rolling behaviour, while crossing the street. Author further
concluded that the vehicular gap size, vehicle speed, pedestrian speed and platoon size has the
maximum effect on pedestrian safety margin, also the pedestrian rolling behaviour, waiting
time, vehicle type and driver behaviour has also shows significant effect on PSM.
Many other studies results have shown that pedestrian behavioural characteristics significantly
affect the PSM value. The accepted vehicular gap size is also a very important variable, which
can increase the PSM value. (Kadali & Vedagiri, 2016)

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Kadali and Vedagiri (2013) developed a MLR model to understand the pedestrian road crossing
behaviour at uncontrolled midblock by the size of vehicular gaps accepted by pedestrian. And
they studied a four lane divided urban arterial in Hyderabad, India, for data collection. They
concluded that the pedestrian behavioural characteristics like the rolling gap, driver yielding
behaviour and frequency of attempt plays an important role in pedestrian uncontrolled road
crossing and these kind of inferences are helpful for pedestrian facility design and controlling
pedestrian safety issues at uncontrolled crossings.

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3. Methodology
3.1 Methodology Followed-
Figure 1 Methodology Followed

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3.2 Selected variables-
Table 1 Description of selected variables-

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3.3 Model adopted for study – (Multiple linear regression model)
The Multiple linear regression model is the commonest modelling technique to predict the
response of the linear continuous dependent variable for developing a relationship between
independent and dependent variable. The MLR model framework adopted in the study is as
follows-:
𝑌 = 𝛽0 + 𝛽1𝑋1 + 𝛽2𝑋2 + 𝛽3𝑋3 + … … + 𝛽𝑛𝑋𝑛
Where,
Y = Predicted value of dependent variable;
𝑋1−𝑛 =Explanatory variables;
𝛽1−𝑛= Estimated parameters from the model;
β0 = y-intercept of regression line
3.4 Root mean square error (RMSE)
The Root mean square error (RMSE) of an estimator of a population parameter is basically
calculated by doing the square root of the mean square error (MSE), and the mean square error
is defined as the expected value of the square of the difference between the estimated value
and the observed value of parameter. It is the total sum of variance and its squared Bias. The
value has to be less than 19 for a good fit of model.
RMSE value can be calculated by using the formula-
RMSE = √Σ(PREDICTED − OBSERVED)2/N

11. 4. Results and Analysis
4.1 MLR model analysis using waiting time as dependent variable-
4.1.1 Correlation matrix-
Table 2 Correlation matrix for waiting time
The above figure shows the selection of dependent variable with the help of correlation matrix has been done for the study. The dependent variables
whose values are nearby +-0.5 has been selected as the dependent variable for the MLR model for waiting time.

12. 4.1.2 Regression analysis and MLR equation formulation-
Regression Statistics
Multiple R 0.659166
R Square 0.4345
Adjusted R Square 0.426264
Standard Error 6.319745
Observations 210
Table 3 Regression analysis
Coeffici
ents
Stand
ard
Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept
-
5.21284
2.056
478
-
2.534
84
0.011
993
-
9.267
28
-
1.158
4
-
9.267
28
-
1.158
4
Frequency step
backwards (FSB) 2.70295
0.586
52
4.608
452
7.11E-
06
1.546
598
3.859
302
1.546
598
3.859
302
FREQ Attempted
2.43356
1
0.550
406
4.421
39
1.59E-
05
1.348
409
3.518
713
1.348
409
3.518
713
Accepted GAP or LAG
3.47251
9
1.219
214
2.848
162
0.004
843
1.068
781
5.876
256
1.068
781
5.876
256
After selecting independent variables for the model with the help of Correlation matrix
analysis, regression analysis is done with 70 percent of the randomly selected data, to check
the R square and P values also after that coefficient values for dependent variables have been
obtained from the above table.
The P values are checked to be less than 0.05.
After that the coefficients are multiplied with their independent variable and added to form the
following MLR analysis model-
Waiting Time = -5.21284 + 2.70295*FSB + 2.433561* Frequency Attempted+
3.472519*Accepted gap

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4.1.3 Validation-
Figure 2 Validation graph for waiting time
After making the MLR model from 70% of the randomly selected data, 30 percent of the
randomly selected data is used for the model validation checking, from validation graph we
can see that R square value is coming around 0.3799 which is not having much difference with
the R square value obtained from regression analysis of 70% data.
RMSE value can be calculated by using the formula-
RMSE = √Σ(PREDICTED − OBSERVED)2/N
RMSE= 7.0629 <19
The obtained RMSE value is less than 19 therefore it shows that the model is fitting
successfully.
R² = 0.3799
0
5
10
15
20
25
30
35
40
45
50
0 5 10 15 20 25 30 35 40 45 50
observed
Waiting
time
Predicted waiting time
VALIDATION GRAPH

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4.2 MLR model analysis using PSM as dependent variable.
4.2.1 Regression analysis and MLR equation formulation-
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.663324
R Square 0.439998
Adjusted R Square 0.437306
Standard Error 1.261797
Observations 210
Table 4 Regression analysis
Coefficien
ts
Standar
d Error
t Stat P-value Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercep
t
-0.8483 0.21436
6
-
3.95723
0.00010
4
-1.2709 -
0.42569
-1.2709 -
0.42569
Vehtim
e Gap
size
0.552266 0.0432 12.7838
8
5.37E-
28
0.46709
9
0.63743
2
0.46709
9
0.63743
2
Similarly for this model also, after selecting independent variables for the model with the help
of Correlation matrix analysis, regression analysis is done with 70 percent of the randomly
selected data, to check the R square and P values also after that coefficient values for dependent
variables have been obtained from the above table.
The P values are checked to be less than 0.05.
After that the coefficients are multiplied with their independent variable and added to form
the following MLR analysis model
PSM = -0.8483 + 0.552266* vehicle time gap size

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4.2.2 Validation
Figure 3 Validation graph for PSM
After making the MLR model from 70% of the randomly selected data, 30 percent of the
randomly selected data is used for the model validation checking, , from validation graph we
can see that R square value is coming around 0.3017 which is not having much difference with
the R square value obtained from regression analysis of 70% data.
RMSE value can be calculated by using the formula-
RMSE = √Σ(PREDICTED − OBSERVED)2/N
RMSE= 1.315 <19
The obtained RMSE value is less than 19 therefore it shows that the model is fitting
successfully.
R² = 0.3017
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7
Observed
PSM
value
Predicted PSM value
VALIDATION GRAPH

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5. Conclusions
 The MLR model for waiting time shows that the waiting time is directly related to FSB,
frequency Accepted and Gap or lag accepted. Which means with increase in these
values of independent variable the value of waiting time will also going to be increased
or vice versa.
 The MLR model for PSM shows that the waiting time is directly related to vehicle time
gap size. Which means with increase in these values of vehicle time gap size will
increase the value of waiting time or vice versa.
References
Avinasha, C., Shah , J., Shriniwas , A., Joshi , G., & Parida , M. (2018). Evaluation of
pedestrian safety margin at mid-block crosswalks in India. Safety Science.
Kadali, B., & Vedagiri, P. (2013). Modelling pedestrian road crossing behaviour under mixed
traffic condition. European Transport Trasporti Europei.
Hamid, M. M. (2001). Analysis of pedestrians behaviour at pedestrian crossings. safety science.
Jain, A., Gupta, A., & Rastogi, R. (2014). PEDESTRIAN CROSSING BEHAVIOUR
ANALYSIS AT INTERSECTIONS. International Journal for Traffic and Transport
Engineering, 1-14.
Kadali, B., & Vedagiri, P. (2016). Proactive pedestrian safety evaluation at unprotected mid-
block. Safety Science.