A system for finding trip rate for both motorised and all modes (transport)

The primary purpose of the transportation planning process is to generate information useful for decision makers on the subject of the consequences of alternative transportation-related actions Transportation decisions impact many aspects of urban life. Young and old similar are pretentious by the viability and relative ease of travelling to destinations on foot, by bike, transit, or dependence on private vehicles. Transportation investments are arguably the single largest shaper of urban places and of progress patterns. The safety, speed, and comfort for a particular mode of travel are a function of the money that have been made in definite types of travel options. Regions, and parts of regions, differ considerably in terms of their supportiveness of travelling in ways that are health promoting (active) and environmentally4sustainable.

Transportation planning is experience a new beginning. The connections between transportation, land use, air pollution, greenhouse gas emission, physical activity, and obesity are becoming better understood. Considerable media attention in modern years has been devoted to the impacts of the built environment on climate change and the environment. Attention has also been determined on the economic impacts of transportation investments and more recently on how transportation influence physical activity and health. Several are concerned about the impacts of urban sprawl on overall sustainability and on how transportation investments can create or help to reduce sprawl. These and other issues provide some context and backdrop for this class.

Transportation investment decisions affect our travel choices which in turn have dramatic impacts on our environment and our physical condition. Transportation is about providing access to locations and impacts social equity, and the benefits or burden felt by dissimilar segment of the population. Transportation networks are commonly the single most significant determinant of a community, and the most distinct physical feature that characterizes a place.

Currently, the principle methodology for influential through trip rates cited in the literature involves the application of a sequences of regression models, that were developed from data collected in the early on 1980s. The models use functional classification, the usual daily traffic ADT at the external station, the percentage of trucks not including forefronts and pickups, the percentage of vans and pickups, and the population of the study area in a two-step equation to forecast the external trip exchange Martin and McGuckin 1998. As an another, Anderson presented a spatial economic model to manufacture a through trip table that incorporates nearby communities and their impact, and although this model has not4seen widespread use, it was shown to be more correct than the common regression-based model for limited applications Anderson91999; Anderson and Souleyrette 2000.

Human and vehicle population increases drastically in last decade. For the daily work, people have to rely on transportation infrastructure. Thus, Transportation infrastructure has become the backbone of a city growth. Trips generated by a city are the proxy of its development. Thus, Estimation of trips of a city determines the infrastructure requirements of that particular city. The existing facilities not only cater to needs of traffic, but also lead to accidents, congestion and delays.

Transportation plays vital role in the development of country. So, selection, construction and planning of these transportation facilities are to be balanced and properly organized. It is also plays a vital role in improvement of socio-economic conditions of the population inside the city. And, provide harmony within the city in terms of culture, prosperity.

The insufficient transportation facilities retard the growth of the city. Plenty of transportation facilities of a region lead to social and economic development. So, the transportation facilities are the important indicators of a particular region’s development. The new government has taken decision in developing new cities in the country. As a result transportation parameters are needed to be estimated to provide proper transportation of these new cities

For the best transportation system to develop we have studied about transportation parameter’s like trip rate, trip length, population, population density, area, per capita income, walk, public transport, city buses (govt.+pvt.), congestion index, pt. accessibility index, city bus supply index, road safety index, road length.

AIM AND OBJECTIVES

Aim – To find a convenient & simple way to get trip rate by forming equations with the help of considered travel parameters using single variant analysis & multi regression analysis.

Objectives

 To provide an easy and simple way to find trip rate for both motorised and all modes, which helps in planning transportation facility.

 To learn about regression5analysis as our thesis is based on regression analysis.

 To collect the required travel parameters details of the considered cities.

 To study the relation and variations of trip rate with different travel parameters so that to know how trip rates varies with that parameters to provide alternate method to know trip rate according to that parameters.

 With the help of software like mat lab drawing graphs for the analysis.

 With the simplify of simple6linear regression analyses and multiple linear regression analyses to find an alternate equation to find trip rate with those parameters.

 To know what suggestions we can provide to help transportation department through this study.

IMPORTANCE AND SCOPE OF TRIP RATE

Approximate vehicular trips and person trips are important input for many analysis and decision-making procedure. Because subtle changes in estimates can have significant impacts, trip rate is a pivotal concern in planning for a enlargement and to urban planning in general. The trip types studied in a specific area depend on the types of transport planning issue to be resolved. The results of trip generation are commonly used in many assessment capacities, including those to:

i. Inform choice makers on the impacts or benefits of a development through mandate environmental impact statements or reports.

ii. Determine or evaluate short- or long-range capital improvement investments

iii. Identify the travel impacts and required mitigation measures as part of the development entitlement process

iv. Predict the special effects of congestion management policies such as congestion pricing and travel demand management (TDM) programs.

v. Determine site vehicular right to use needs as well as associated roadway and site-plan modifications and improvements, and

vi. Assess impact fees on latest development to fund infrastructure improvements.

The decisions that result from these actions can result in a variety of impacts, including those that can affect local government, private investment, and the community. These effects can be far reaching and affect a variety of interests, including those associated to fiscal, environmental, quality of life, local circulation and access, and related economic development concerns. Impacts can also affect one-time transportation modes either directly or indirectly. Increasingly, there is concern that necessary mitigations can result in accidental consequences such as adversely affecting the ability of people to walk, bicycle, or use community transportation as increasingly larger vehicular facilities reduce or negatively affect opportunities for non-motorized mode.

LITERATURE REVIEW

Daniel A. Badoe, and Judith L. Mwakalonge- The paper “Estimating Household Trip Rates for Cross-Classification5Cells with No Data: Alternative Methods and Their Performance in Prediction of Travel” written by those investigates a number of alternative methods for addressing the empty-cell problem of conventional cross-classification analysis. Data used in the learning were collected in the Toronto region in 1986, 1996, 2001, and 2006. Alternative models, urban on each year’s data, were assessed for how well they predicted travel at the disaggregate household stage and at the aggregate travel analysis zone level in the respective years. In addition, the alternative model estimated on the41986 data set were assessed for their ability to replicate travel in 1996 and 2006. The results show that a process proposed by Mandel and a model developed in this research, which estimates the household trip rate for an blank cell through a linear combination of the predictions yielded by row and column models, overall give the most excellent forecast performance of travel. They perform better than multiple classification analysis, which is the present industry standard for addressing this inadequacy of traditional cross-classification analysis. The mutual categories model also performed actual fine, particularly in predicting travel at the aggregate level of planning concern.

JohnoS. Miller, P.E.1; Lester A. Hoel, P.E.2; Arkopal K. Goswami3; and Jared M. Ulmer4

In paper “Borrowing Residential Trip Generation Rates” Residentialotrip generation rates are a fundamental component of transportation planning. To investigate discrepancy in these rates, residentialhtrip generation rates for nine suburban neighbourhoods were computed by means of four different methods: _1_ ground counts conducted at the neighbourhoods, _2_ household surveys distributed to the neighbourhoods, _3_ application of nationwide trip generation rates published by the Institute of Transportation Engineers _ITE_, and _4_ rates derived from the trip generation constituent of regional urban travel demand models for the neighbourhoods. Agencies commonly use one of these rates, and by determining all four for the same set of neighbourhoods in a controlled study, one can determine the extent to which these rates are likely transferable. Rates based on the first three methods were not considerably different. For developments composed solely of single-family detached homes, the average housing trip generation rate was 10.8 based on the site-specific ground counts, 9.2 based on site-specific household surveys, and 9.6 base on ITE’s trip generation rates. However, rates based on the fourth method were significantly different, with a mean rate of 6.4. The greatest difference occurred when the long-range regional model used person trips that were transformed to vehicle trips rather than predicting vehicle trips directly. Although the summary statistics presented in this paper will not disclosure transportation planners, they illustrate two caveats for balancing data collection costs and necessitate for site-specific information. First, a subtle change in how some rates are calculated limits their utility elsewhere. Second, even when matching methods for determining rates are used for similar neighbour hoods, differences will occur because of the huge and random variation inherent in trip generation. Borrowing rates may indeed be tolerable, but only if one gives the packed range of rates possible from this probabilistic process rather than just the normal mean rate. Both caveats are treatable provided they are explicitly addressed through uncertainty analysis or adjustments for expected bias.

D. A. Badoe1 and C. Chen2

In paper “Modeling Trip Generation with Data from Single and Two Independent5Cross-Sectional Travel Surveys” They investigates the opportunity of developing trip generation models by means of data collected at two or more points in time in self-determining cross-sectional travel surveys conducted in the similar urban area. Alternative methods for formulating a forecasting model based on the availability of cross-sectional data from two time periods are obtainable. Models are then estimated on the study data and the models assessed in terms of their ability to replicate the amount of trips made at the disaggregate household level, and at the aggregate transportation zone level in the two model-estimation datasets, respectively. The presentation of these jointly estimated models is compared to the extrapolative performance of a conventional solitary cross-section trip generation model approximate on each period’s data only. The formulated models are then useful to forecast trips at the disaggregate household level, and at the aggregate transportation zone level on a third self-governing cross-sectional dataset gathered in the same urban area but at a dissimilar point in time. Again, forecast presentation of the formulated jointly estimated models is compared to forecast presentation of the conventional model estimated on this third independent dataset. The results show that very well specified joint models estimated on data from two time periods yield superior disaggregate and aggregate forecasts to those acquire from conventional forecasting models, which are estimated with data from a single cross-sectional survey.

Michael D. Anderson1 and Justin P. Olander2

In their paper “Evaluation of Two Trip Generation Techniques for Small Area4Travel Models” They5studies the essentially of using a single internal trip purpose to generate the production and fascination values for traffic analysis zones in small urban community travel models. In previous research efforts, Quick-Response techniques, initially developed for cities with populations between 50,000 and 199,999, have been successfully applied to perform trip generation in small urban municipal travel models. Focusing on the reduction of data requirements and complication of the trip generation analysis, a single trip purpose technique, based solely on aggregate numbers of families and businesses in a traffic analysis zone, has been proposed as a method to simplify the trip generation calculation and reduce data requirements. This paper presents the fundamentals of the Quick-Response and single trip purpose techniques, tests the benefit of multiple trip purposes in a small sample network, and applies the two methodologies in a small urban community within Alabama to regulate if significant differences exist when performing trip generation. The paper concludes that, for minor urban community travel models, where different trip purposes are assumed to have similar trip lengths, both the Quick-Response and the solo trip purpose technique produce similar results for the total productions and attractions in a traffic analysis region. This similarity, and the results of the test showing that different trip determinations are not vital for trip distribution in small networks, substantiates the use of the simplified solitary trip purpose technique for trip generation.

Michael D. Anderson1; Yasir M. Abdullah2; Sampson E. Gholston3; and Steven L. Jones4

This paper “Development of a Methodology to Predict Through-Trip Rates for Small Communities” examines a new methodology to forecast external trip exchanges in small urban communities. The paper documents a study performed on numerous small communities in Alabama and includes a video surveillance data collection methodology, data analysis, model development, and test against existing models. The new model presented in this paper is shown to provide more accurate results when compared to present models and demonstrated transferability to a similar city.

By Edward S. Neumann,1 M. ASCE, John Halkias,2 and Mervat Elrazaz3

In the paper “Estimating Trip rates from Traffic Counts”The research objective was to apply routinely collected traffic ground counts to estimate directly area-wide, all-purpose trip production rates. The methodology allocates and assigns zonal socio-economic variables (autos, dwelling units and population) straight to the study area network. Ground counts must be reduced by internal-external and external-internal trips. The residual, condensed ground counts are entered into a linear regression model as the dependent variable and the assigned socio-economic variables are arrived as the independent variable. The resulting regression coefficients are guesstimates of the area-wide, all-purpose production rates. The method is sensitive to the friction factor curves used in the distribution step. The methodology was verified in Lynchburg, Virginia and Lexington, Kentucky. Estimated production rates obtained were within 96% of accurate rates. The method appears to produce accurate results and can be used to verify plagiarised production rates in synthetic procedures. It may be useful for cities which cannot undertake conventional household surveys.

SELECTED CITIES

Fig-1 selected cities

COLLECTION OF DATA

The data is collected on the basis of home interview survey from dissimilar cities is collected on the basis of:-

1. Comprehensive transportation study

2. Comprehensive development plan

3. Comprehensive mobility study

Comprehensive transportation study

Comprehensive transportation study (CTS) pacts with the study of particular city travel characteristics like Identify travel pattern of residents, Identify for all modes a phased program of appropriate and affordable investments and policy, Development of the predominant mass transit system & road network.

Comprehensive development plan

(CDP) is a comprehensive document outlining the vision and development approach for future development of the city, prepared in consultation with a wide range of stakeholders to recognize the thrust areas to be addressed on priority basis in order to achieve the objectives and the vision.

Comprehensive mobility study

Comprehensive mobility plan is a vision statement of the way urban transport should develop with the prearranged growth of the city. Comprehensive Traffic and Transport studies define and prioritize various projects.

And all the outstanding data is collected from different sources like internet some calculation of parameters, municipal corporation etc.

 Trip rate (or) trip rate (all modes): Number of trips including walk per person of that study area.

 Trip rate (motorized): Number of trips apart from walk per person of that study area

 Trip Length: the distance travelled for a trip in Kilometres

 Congestion Index: CI=1-(observed speed on major corridors/Posted speed limit [i.e. 30kmph])

 City Bus Supply Index is city bus flotilla per lakhs of population.

 Accident fatality index is road accident death per lakhs of population.

 Road safety index: – 1/ (road accident death per lakh population).

 Population density measurement of population per unit area or unit volume.

 Per capita income it is calculated by taking a measure of all sources of income in the aggregate (such as GDP or Gross national income) and dividing it by the total population.

 PTAI (Public transport accessibility index) is a simple, easily calculated approach that hinges on the distance from any point to the nearby public transport stop, and service frequency at those stops. The result is a grade from 1–6 (including sub-divisions 1a, 1b, 6a and 6b), where a PTAL of 1a indicates massively poor access to the location by public transport, and a PTAL of 6b indicates excellent access by public transport.

METHODOLOGY

This project trip rate interaction with travel characteristics is grounded on the multiple regression analysis. For that we have to go through the following steps:-

1. Initially we have to select some cities which we want to consider for our thesis purpose.

2. Then we have to find the parameters values similar trip rate, trip length, population, population density, area, per capita income, walk, public transport, city buses (govt.+pvt.), congestion index, pt. accessibility index, city bus supply index, road safety index, road length for each considered cities.

3. Later with the help of Ms excel software we have to study the variation of those parameters with respect to trip rate for both motorized and all modes separately by drawing graphs among themselves.

4. Then we analyses those graphs and have to observe how they vary with trip rate.

5. After that we have to note those equations which show good relation with trip rate for both motorized and all modes.

6. Later we have to go for multiple linear regression analysis for the better combination and forming good relation.

7. After getting the best relation we should check whether those formed equation is giving the correct value or not.

8. And then we will plot graphs for the value obtained by home interview survey and the values formed by the equations.

9. If those will match than, we can consider those formed equation for the calculation of trip rate for cities.

8.1 REGRESSION ANALYSIS

In statistics, regression analysis is a statistical process for approximating the relationships among variables. It includes many techniques for modelling and investigating several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More exactly, regression analysis helps one understand how the typical value of the dependent variable fluctuations when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis approximations the conditional expectation of the dependent variable given the independent variables – that is, the middling value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quintile, or other position parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the self-governing variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable all over the place the regression function which can be described by a probability distribution.

Regression analysis is used to understand which between the independent variables are related to the dependent variable, and to discover the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables.

Many techniques for carrying out regression analysis have been established. Familiar methods such as linear regression and ordinary least squares regression are parametric, in that the regression function is defined in terms of a fixed number of unknown parameters that are estimated from the data.

The performance of regression analysis methods in practice depends on the form of the data generating process, and how it narrates to the regression approach being used. Since the true form of the data-generating process is generally not known, regression analysis often be subject to to some extent on making assumptions about this process. These assumptions are sometimes testable if a adequate quantity of data is available. Regression models for prediction are often useful even when the assumptions are abstemiously violated, although they may not perform optimally.

8.2 SIMPLE LINEAR REGRESSION ANALYSIS

In simple linear regression, we predict scores on one variable from the scores on a second variable. The variable we are predicting is called the criterion variable and is referred to as Y. The variable we are grounding our predictions on is called the predictor variable and is referred to as X. When there is only one predictor variable, the prediction technique is called simple regression. In simple linear regression, the topic of this section, the predictions of Y when prearranged as a function of X form a straight line.

Y=bX1 + a

Where, b = constant

X1= predictor variable

a = regression coefficient

Analyzing an equation which is having only one unknown variable, there will be one independent variable and one dependent variable in an equation.

Here the independent variables are travel parameters and dependent variable is trip rate, for this we have to analyze for both trip rate (motorised) and trip rate (all modes) separately.

With the help of MS excel software we start analyzing the parameters. The statistical analysis is done by advanced software technique like MAT LAB. The graphs are generated by considering travel parameters on x – axis and trip rate on y – axis.

12 travel parameters with trip rate (all modes) generate 12 graphs and for trip rate (motorized) another 12 graphs. Total 24 graphs plotted for this simple linear regression analysis

All the 24 graphs plotted are listed below with the observations

8.3 Graphs for simple linear regression analysis

Graph-1 Area (Sq. km) vs. Trip rate (all modes)

As from the above graph-1 plotted between Area (sq. km) vs. Trip rate (all modes), as the area increasing from 0 to 4500 trip rate (all modes) also increasing from 0.9 to 1.6, no trip rate (all modes) for cities in between 2000 to 4500 (sq. km) area, max trip rate (all modes) are for considered cities in between 0 to 1000 (sq. km) area, hence it is clear that the trip rate (all modes) increases as area increases.

Graph-2 City buses (govt.+pvt.) vs. Trip rate (all modes)

As from the above graph-2plotted between city buses (gov.+pvt.) vs. Trip rate(all modes),as the city buses (gov.+pvt.) increasing from 0 to 4500 trip rate (all modes) also increasing from 0.94 to 16, no trip rate (all modes)for considered cities in between 1000 to 2500 city buses (gov.+pvt.) , max trip rate (all modes) are in between 0 to 1000 city buses (gov.+pvt.) hence it is clear that the trip rate (all modes) increases as city buses (gov.+pvt.) increases.

Graph-3 City bus supply index vs. Trip rate (all modes)

As from the above graph-3 plotted between City buses supply index vs. Trip rate (all modes),as the city buses supply index increasing from 0 to 45trip rate (all modes) decreasing from 1.5to 0.8, no trip rate (all modes) for considered cities in between 20 to 30 city buses supply index, max trip rate (all modes) for considered cities are in between 10 to 20city buses supply index hence it is clear that the trip rate(all modes) decreases as city buses supply index increases.

Graph-4 Congestion index vs. Trip rate (all modes)

As from the above graph-4 plotted between Congestion index vs. Trip rate(all modes),as the Congestion index increasing from 0 to 0.5 trip rate (all modes) also increasing from 0.57 to 16.9, clearly shows that more cities have trip rate (all modes) in between 0.2 to 0.5 of congestion index, hence it is clear people are travelling more in those cities, in overall trip rate (all modes) varying gradually, so the trip rate (all modes) increases as Congestion index increases.

Graph-5 Per capita income (Rs) vs. Trip rate (all modes)

As from the above graph-5 plotted between Per capita income (Rs) vs. Trip rate (all modes),as the per capita income increasing from 2×104 to 13 x104 (Rs) trip rate (all modes) also increasing from 0.8 to 15.2, clearly shows that cities have trip rate (all modes) gradually whole among for considered cities for per capita income and more cities have trip rate (all modes) in between 2×104 to 8x104for per capita income, hence it is clear that the trip rate (all modes) increases as Per capita income increase.

Graph-6 Population (in lakhs) vs. Trip rate (all modes)

As from the above graph-6 plotted between Population (lakhs) vs. Trip rate (all modes), as the Population increasing from 0 to 180 (lakhs) trip rate (all modes) also increasing from 0.41 to 1.2, no trip rate (all modes) are there for considered cities in between 100 to 170 of population, means in between this income group transportation is not much required and max required in between 0 to 110 population (lakhs) cities as at that particular interval more trip rate (all modes) are noticed, hence it is clear that the trip rate (all modes) increases as population increase

Graph-7 Population density per (sq km) vs. Trip rate (all modes)

As from the above graph-7plotted between Population density per (sq km) vs. Trip rate(all modes),as the population density increasing from 0 x104 to 24 x104per (sq km), trip rate (all modes) also increasing from 0.92 to 17, no trip rate (all modes) for considered cities in between 1.3 to 1.8, and max are in between 0 x104 to 13 x104population density per (sq km), hence it is clear that the trip rate (all modes) increases as population density increase.

Graph-8 Public transport (%) vs. Trip rate (all modes)

As from the above graph-8 plotted between Public Transport (%) vs. Trip rate (all modes),as the public transport (%)increasing from 0 to 60 trip rate (all modes) also increasing from 0.9 to 16.9, clearly shows that more cities have trip rate (all modes) in between 0 to 2.5 of public transport (%), hence it is clear people are travelling more in those cities, so the trip rate (all modes) increases as public transport (%) increases.

Graph-9 Road length (km) vs. Trip rate (all modes)

As from the above graph-9 plotted between Road length (km) vs. Trip rate (all modes), as the road length increasing from 0 to 3×104 trip rate (all modes) also increasing from 0.45 to 1.1, clearly shows that more considered cities have trip rate (all modes) in between 0 to 0.4×104 of road length and then very few are there in between 0.5 to 3×104, hence it is clear that cities have less road length are more, the trip rate (all modes) increases as road length (km) increases.

Graph-10 Road safety index vs. Trip rate (all modes)

As from the above graph-10 plotted between Road safety index vs. Trip rate (motorised), as the road safety index increasing from 0 to 0.35 trip rate (all modes) also increasing from 0.9 to 1.7, trip rate (all modes) for considered cities are varying gradually according to road safety index, means in between this city group transportation is required equally, but in between 0 to 0.16 road safety index trip rate (all modes) are more for considered cities, hence it is clear that the trip rate (all modes) increases as road safety index increase.

Graph-11 Trip length (km) vs. Trip rate (all modes)

As from the above graph-11 plotted between Trip length (km) vs. Trip rate (all modes), as the trip length (all modes) increasing from 3 to 13 (km) trip length (all modes) also increasing from 0.84 to 1.79, clearly shows that cities have trip length (all modes) gradually whole among the trip length, but more considered cities are in between 3 to 7.2 trip length (km) have more trip length (all modes) , hence it is clear that the trip length (all modes) increases as trip length increase.

Graph-12 walk (%) vs. Trip rate (all modes)

As from the above graph-12 plotted between Walk (%) vs. Trip rate (all modes),as the walk (%)increasing from 15 to 45 trip rate (all modes) also increasing from 0.9 to 15.6, clearly shows that cities have trip rate (all modes) gradually whole among the walk (%), but more cities have trip rate (all modes) in between 20 to 30 of Walk (%),hence it is clear that the trip rate (all modes) increases as Walk (%) increase.

Graph-13 Area (sq. km) vs. Trip rate (motorised)

As from the above graph-13 plotted between Area (sq. km) vs. Trip rate (motorised), as the area increasing from 0 to 1500 trip rate (motorised) also increasing from 0.49 to 11.2, no trip rate (motorised)for considered cities in between 1000 to 1500 (sq. km) area, maximum trip rate (motorised) are for considered cities in between 0 to 500 (sq. km) area, hence it is clear that the trip rate (motorised) increases as area increases.

Graph-14 City bus supply index vs. Trip rate (motorised)

As from the above graph-14 plotted between city buses supply index vs. Trip rate (motorised), as the city buses supply index increasing from 0 to 45 trip rate (motorised) increasing from 0.5 to 1.1, very less no of trip rate (motorised) of considered cities in between 20 to 30 city buses supply index, maximum trip rate (motorised) for considered cities are in between 5 to 20 city buses supply index hence it is clear that the trip rate (motorised) increases as city buses supply index increases.

Graph-15 City buses (govt.+pvt.) vs. Trip rate (motorised)

As from the above graph-15 plotted between city buses (gov.+pvt.) vs. Trip rate (motorised) ,as the city buses (gov.+pvt.) increasing from 0 to 4500 trip rate (motorised) also increasing from 0.58 to 1.05, no trip rate (motorised) for considered cities in between 1000 to 2500 city buses (gov.+pvt.) , maximum trip rate (motorised) for considered cities are in between 0 to 500 city buses (gov.+pvt.), hence it is clear that the trip rate (motorised) increases as city buses (gov.+pvt.) increases.

Graph-16 Congestion index vs. Trip rate (motorised)

As from the above graph-16 plotted between Congestion index vs. Trip rate (motorised),as the Congestion index increasing from 0 to 0.5 trip rate (motorised) also increasing from 0.37 to 1.09, , clearly shows that more considered cities have trip rate (motorised) in between 0.2 to 0.4 of congestion index, hence it is clear people are traveling more in those cities, so the trip rate (motorised) increases as Congestion index increases.

Graph-17 Per capita income (Rs) vs. Trip rate (motorised)

As from the above graph-17 plotted between Per capita income (Rs) vs. Trip rate (motorised), as the per capita income increasing from 2×104 to 13 x104 (Rs) trip rate (motorised) also increasing from 0.4 to 1, clearly shows that considered cities have trip rate gradually whole among the per capita income and more cities have ttrip rate (motorised) in between 2 to 7 of per capita income, hence it is clear that the trip rate (motorised) increases as per capita income increase.

Graph-18 Population density per (sq km) vs. Trip rate (motorised)

As from the above graph-18 plotted between Population density per (sq km) vs. Trip rate (motorised), as the population density increasing from 0 x104 to 2.4 x104 per (sq km), trip rate (motorised) also increasing from 0.4 to 1.09, no trip rate (motorised) are there among the considered cities in between 1.3 to 2, and maximum trip rate (motorised) for considered cities are in between 0 x104 to 13 x104 per (sq km), hence it is clear that the trip rate (motorised) increases as population density increase.

Graph-19 Population (in lakhs) vs. Trip rate (motorised)

As from the above graph-19 plotted between Population (lakhs) vs. Trip rate (motorised), as the population increasing from 0 to 180 (lakhs) trip rate (motorised) also increasing from 0.41 to 1.2, no trip rate (motorised) are there for considered cities in between 100 to 170 of population, means in between this income group transportation is not much required and maximum required in between 0 to 110 population (lakhs) cities as at that particular interval more trip rate (motorised) are noticed, hence it is clear that the trip rate (motorised) increases as Population increase

Graph-20 Public transport (%) vs. Trip rate (motorised)

As from the above graph-20 plotted between Public Transport (%) vs. Trip rate (motorised), as the public transport (%) increasing from 0 to 60 trip rate (motorised) also increasing from 0.5 to 1.09, clearly shows that more considered cities have trip rate (motorised) in between 0 to 2.5 of public transport (%), and remaining vary gradually, hence it is clear people are traveling more in those cities, so the trip rate (motorised) increases as Public Transport (%) increases.

Graph-21 Road length (km) vs. Trip rate (motorised)

As from the above graph-21 plotted between Road length (km) vs. Trip rate (motorized), as the Road length increasing from 0 to 3x104trip rate (motorised) also increasing from 0.45 to 1.1, clearly shows that more considered cities have trip rate (motorised) in between 0 to 0.4×104 of road length and then very few are there in between 0.5 to 3×104, hence it is clear that cities have less road length are more, the trip rate (motorised) increases as road length (km) increases.

Graph-22 Road safety index vs. Trip rate (motorised)

As from the above graph-22 plotted between Road safety index vs. Trip rate (motorised), as the road safety index increasing from 0 to 0.35 trip rate (motorised) also increasing from 0.36 to 1.2, trip rate (motorised) for considered cities are varying gradually according to road safety index, means in between this city group transportation is required equally, but in between 0 to 0.16 road safety index trip rate (motorised) are more for considered cities, hence it is clear that the trip rate (motorised) increases as road safety index increase.

Graph-23 Trip length (km) vs. Trip rate (motorised)

As from the above graph-23 plotted between Trip length (km) vs. Trip rate (motorised), as the trip length increasing from 3 to 13 (km) trip rate (motorised) also increasing from 0.4 to 1.09, clearly shows that cities have trip rate (motorised) gradually whole among the Trip length, but more considered cities are in between 3 to 7 trip length (km) have more trip rate (motorised) , hence it is clear that the trip rate (motorised) increases as trip length increase.

Graph-24 walk (%) vs. Trip rate (motorised)

As from the above graph-24 plotted between Walk (%) vs. Trip rate (motorised), as the walk (%) increasing from 15 to 45 trip rate (motorised) also decreasing from 1.5 to 0.3, clearly shows that cities have trip rate (motorised) gradually whole among the Walk (%), but more cities in between 20 to 35 of Walk (%), hence it is clear that the trip rate (motorised) decreases as Walk (%) increase so special care has to be taken for this.

As simple linear regression method is carried out for various cities we plotted the graphs according to that. After studying the variation for different cities trip rate for both motorised and all modes with different travel parameters all the equations are tabulated below in table

As the simple linear regression equations are not sufficient for the consideration of equations because it has a lot of variations. Our next step is to go for multiple linear regression analysis.

For that purpose we find the R2value with the help of Ms excels for all the parameters which we considered among them. After finding all the R2 value the values are tabulated in matrix format which is shown below.

TABLE-7 Matrix sheet with all r2 values

A B C D E F G H I J K L M N

A 1 0.053 0.343 0.387 0.829 0.123 0.425 0.629 0.579 0.313 0.433 0.304 0.865 0.195

B 1 0.018 0.016 0.006 0.01 0.081 0.019 0 0 0.033 0.001 0.034 0.002

C 1 0.054 0.394 0.036 0.17 0.084 0.46 0.249 0.241 0.113 0.427 0.654

D 1 0.459 0.042 0.104 0.29 0.312 0.134 0.128 0.381 0.473 0.026

E 1 0.264 0.267 0.586 0.771 0.486 0.44 0.396 0.874 0.245

F 1 0.006 0.083 0.106 0.221 0.012 0.044 0.192 0.004

G 1 0.155 0.09 0.108 0.105 0.11 0.382 0.031

H 1 0.55 0.139 0.564 0.139 0.456 0.118

I 1 0.392 0.573 0.149 0.563 0.536

J 1 0.072 0.092 0.371 0.105

K 1 0.03 0.361 0.273

L 1 0.421 0.017

M 1 0.164

N 1

A-Trip rate motorised, B-Area(sq. km), C-population(in lakhs), D-Population density(sq. km), E-Trip length(kms), F-Per capita income(Rs), G-Walk (%), H-Public Transport(%), I-City Buses (Govt.+Pvt.), J-Congestion Index, k-City Bus Supply Index , L-Road Safety Index , M-Trip rate (all modes), N-Road length(km).

8.4 MULTIPLE LINEAR REGRESSION ANALYSIS

Analyzing an equation which is having only one unknown variable, there will be more than one independent variable and one dependent variable in and equation.

A statistical technique that uses several explanatory variables to forecast the outcome of a response variable. The goal of multiple linear regressions (MLR) is to model the connection between the explanatory and response variables.

MLR takes a group of random variables and tries to find a mathematical connection between them. The model creates a relationship in the form of a straight line (linear) that best estimates all the individual data point.

In many cases, the contribution of a single independent variable does not alone work for to explain the dependent variable Y. If this is so, one can perform a multivariable linear regression to study the influence of multiple variables on the dependent variable.

In the multivariable regression model, the dependent variable is pronounced as a linear function of the independent variables Xi, as follows: Y = a + b1 × X1 + b2 × X2 +…+ bn × Xn. The model licenses the computation of a regression coefficient bi for each independent variable Xi

Regression line for a multivariable regression

Y= a + b1 × X1 + b2 × X2+ …+ bn × Xn,

Where

Y = dependent variable

Xi = independent variables

a = constant (y-intersect)

bi= regression coefficient of the variable Xi

From the above table-3 the top five R2value are noticed and coloured in red colour and the next top five values are coloured in blue colour and with help of multi regression analysis those parameters are analysed among themselves similarly the next 5 values are also analysed and by studying those we got the best 3 equations which is best matched among the considered value those are-

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