Empirical Understanding of Traffic Data Influencing Roadway PM2.5 Emission Estimate
A Paper Submitted to the NSF 2012 Academic-Year REU Program
Part of NSF Type 1 STEP Grant
Sponsored By
The National Science Foundation
Grant ID No.: DUE-0756921
Justin Cox*, Sr. Electrical Engineering,
College of Engineering and Applied Sciences
University of Cincinnati, Cincinnati, OH 45221-0071
Tel: (803)354-2404; E-mail: coxc5@mail.uc.edu
Zachary D. Johnson* Sr. Mechanical Engineering,
College of Engineering and Applied Sciences
University of Cincinnati, Cincinnati, OH 45221-0071
Tel: (513)284-9766; E-mail: Johnson.Zachary.D@gmail.com
Heng Wei, Ph.D., P.E.
Associate Professor, Director, ART-Engines Transportation Research Laboratory
College of Engineering and Applied Science, 792 Rhodes Hall,
University of Cincinnati, Cincinnati, OH 45221-0071
Tel: (513)556-3781; Fax: (513)556-2599; E-mail: heng.wei@uc.edu
Zhuo Yao, Ph.D. Candidate
College of Engineering and Applied Science,735 ERC,
University of Cincinnati, Cincinnati, OH 45221-0071
Tel: (513)556-5420; Fax: (513)556-2599; E-mail: yaozo@mail.uc.edu
Hao Liu, Ph.D. Candidate
College of Engineering and Applied Science
University of Cincinnati, Cincinnati, OH 45221-0071
Tel: (513)556-5420; Fax: (513)556-2599; E-mail: liuh5@mail.uc.edu
Qingyi Ai, Ph.D. Candidate
College of Engineering and Applied Science
University of Cincinnati, Cincinnati, OH 45221-0071
Tel: (513) 556-5420; Fax: (513) 556-2599; E-mail: aiqi@mail.uc.edu
Submitted on: December 3rd, 2012
_____________________
Dr. Heng Wei, Ph.D., P.E.
*Corresponding Author
____________
Date
Cox, Johnson, Wei, Yao, Liu, Ai
ABSTRACT
Within Traffic Engineering, understanding emission output of a roadway during various traffic conditions
is a topic of great interest. PM2.5 is a particulate matter emission that is less than 2.5 micrometers in
diameter. These particles pose the greatest health risk because of their capability to lodge deeply in to
the lungs. Therefore, it is necessary to study the relationship between the quantity of PM2.5 and
surrounding traffic conditions. REMCAN is used to quickly extract vehicle parameters relating virtual
video data with vehicle speeds and acceleration. The field data collected shows 1.5 times more PM2.5
being emitted than the EPA’s MOVES software. EPA’s MOVES software shows a greater increase of
PM2.5 with greater traffic than the field data. The Organic Carbon pollutant accounts for the greatest of
the PM2.5 pollutants. The total emissions from our site throughout one day yielded 14.73 micrograms of
PM2.5 , which is 55% greater than the MOVES model predicted, but less than EPA’s 60 micrograms daily
average max. [6] The field data result being 55% times greater than the MOVES model promotes further
research into traffic and emissions studies.
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Cox, Johnson, Wei, Yao, Liu, Ai
Table of Figures
FIGURE 1 METHODOLOGY FLOW CHART ........................................................................................................... 6
FIGURE 2 VEVID SCREENSHOT ....................................................................................................................... 8
FIGURE 3 SYSTEM FLOWCHART FOR (REMCAN) SYSTEM ................................................................................. 9
FIGURE 4 REMCAN SCREENSHOTS .............................................................................................................. 10
FIGURE 5: EXPERIMENTAL AND MOVES PM DATA ......................................................................................... 13
FIGURE 6: EPA'S MOVES SOFTWARE COMPARING PM2.5 AND NUMBER OF VEHICLES ..................................... 14
FIGURE 7:OCT3&9 METEOROLOGICAL DATA .................................................................................................. 15
FIGURE 8: OP MODE DISTRIBUTION ................................................................................................................ 16
FIGURE 9: POLLUTANT EMISSIONS FOR STUDY SITE........................................................................................ 16
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Cox, Johnson, Wei, Yao, Liu, Ai
Introduction
Traffic Engineering is an important field of study as traffic problems continue to be identified caused by
the increasing amount of automobiles on the road. One problem associated with traffic engineering has
to deal with the particulate matter emitted from each automobile. The particulate matter less than 2.5
micrometers in diameter, - henceforth referred to as PM2.5 - is a cause for particular concern because of
their very small size and capability to lodge deeply in to the lungs causing respiratory difficulties.
Therefore it is crucial to maximize the capability of localized traffic emission models in maximizing their
capability to accurately reflect the energy consumption and greenhouse gases (GHGs) emission
associated with transportation.[7] The EPA’s newest Emissions Simulator (MOVES) greatly increases the
accuracy of emission modeling, however, the various traffic service levels have not been incorporated
into MOVES. Therefore, it is possible that a roadway contains an emergency situation causing all traffic
to stand-still, while the schools and places of work neighboring this road are exposed to the idling vehicle
traffic emissions for as long as the traffic stays congested. Higher pollutant levels are expected with such
a situation and this research tries to identify the relationship between traffic and PM2.5.
Current models for emissions composition research vary greatly due to several factors including:
rapidly changing emission output composition, weather, and automobile variations. Results from each
model will vary anywhere from 5-15%. [1] MOVES tends to be the best modeling per appropriate use,
however it is known that emission model simulators have great difficulty in modeling exact emissions of
vehicles. MOVES uses operating modes identified by using the speed and the VSP of vehicles. [7]
Conventional methods of data collection in order to identify operating modes is expensive and time
consuming. In this experiment, REMCAN is utilized in quickly identifying each vehicles belongs in the
available operating modes.
The results from MOVES are compared with the field data results. Finally, conclusions are drawn
and recommendations for further research are provided.
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Cox, Johnson, Wei, Yao, Liu, Ai
LITERATURE REVIEW
Particulate matter (PM) in general (also called fine particles) is a mixture of either tiny solid particles or
liquid particles or a mixture of both. PM2.5 is particulate matter that is less than or equal to a diameter of
2.5 μm (micro-meters). Particularly because of its very small size, this pollutant can be inhaled through
the respiratory tract and cause adverse health impacts. [1] Besides traffic conditions, wind speed and
directions also affect near-road PM2.5 concentrations. Other contributions in traffic air pollution include the
traffic volume, fleet composition, as well as factors such as the presence of a noise barrier. [2]
Depending on how much an individual is exposed to the emission of PM 2.5 is the basis for how much it
can affect someone’s health. Long-term exposure to concentrations of PM2.5 increases the risk of acute
and chronic respiratory infection, lung cancer, arteriosclerosis, and other cardiovascular diseases. Short
term exposure can make worse existing problems that are related to pulmonary and cardiovascular
diseases. [1]
Tests for PM2.5 emissions have been going on for many years now in a variety of different
locations because traffic conditions continue to get more complex and models continue to be made which
can make up for the complexity. Also, studies are often conducted for specific local traffic situations over
short periods of time (hours/days compared to the necessary weeks or months) so studies only partially
validate traffic emission models. [3] Therefore, information from single studies has not been able to be
used for an overall evaluation of PM2.5. Ultimately, the goal in researching this topic is to get a sufficient
correlation between traffic conditions and the emission of the particulate matter.
Due to an increasing number of vehicle types and fuel types, models for monitoring the emission
of PM2.5 are becoming more comprehensive over time and they also are made to show results for a
higher quantity of vehicle (thousands as compared to previous models used before the 1980s which were
meant for ~100). [3] Many households (approximately 11%) are located within 100 meters of 4-lane
highways, where vehicle emissions are the major source of PM2.5. [5] Because monitoring PM2.5
concentrations cannot be done for all of these near-road regions, use of appropriate models with vehicle
and meteorological information to estimate near-road PM2.5 concentrations is important. [1] There are
advantages and disadvantages of different models, but for this particular research project, VEVID,
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Cox, Johnson, Wei, Yao, Liu, Ai
REMCAN and MOVES were the appropriate models to use for data analysis due to the rapid data input
attribute. VEVID calculates the speed of the vehicle as well as their classification, REMCAN is a rapid
traffic emission and energy consumption analysis system, and MOVES (Motor Vehicle Emission
Simulator) generates emission rates.
METHODOLOGY
Goals of this research project were to gain insights on how dynamic traffic operating conditions affect the
PM2.5 emission estimation, gain concept and experience to experiment design and field data collection,
and finally to develop a regression model from field data that was collected. This was done through
meeting objectives that include researching project relevant articles covering traffic operation and
emission characteristics, becoming experienced with the data collection instruments, and by modeling the
data using VEVID, REMCAN and MOVES successfully. These objectives were further broken down into
several tasks for a final result. Figure 1 shows the step by step process of this experiment.
DESIGNING AND PLANNING OF FIELD
DATA
A. Location
a. I-275 selected based on
traffic flow and air quality
concerns
B. Equipment
a. Meteorology station
b. Video camera
c. Air sampler
C. Distance Markings on Highway
A.
B.
C.
PROBLEM
Regional Air Quality Concerns from
PM2.5
Contribution of On-road Transportation
Activity to PM2.5 Emission


FIELD DATA COLLECTION
Measure wind speed, temperature,
direction of wind, and humidity
b. Record the incoming and outgoing
traffic
c. Sample the PM2.5 emission
a.
DATA ACQUISITION AND PROCESSING
A. Split video for software usage
a. VEVID
B. REMCAN
a. Calibration
b. Data Processing
DATA ANALYSIS & MODELING
MOVES Emission Estimate
Regression
Comparison of Measured vs. Modeled
Figure 1 Methodology Flow Chart
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Cox, Johnson, Wei, Yao, Liu, Ai
Understanding basic traffic flow fundamentals and emission characterization was the first task
accomplished during this project. Different literature was read for better understanding of the subject
matter.
Designing and planning of field data collection was the next task of this research project. The
main location for the field data collection site was at a highway located on interstate 275. This location
was selected particularly because of access to a loop detector (AKA automatic traffic recorder). The Ohio
department of transportation sponsors this ongoing UC project and supplies the loop detector.
It
measures how many cars pass, the speed, and the classification of the car to name a few things. This
location was also convenient because of the traffic flow and air quality concerns in the area. Other
equipment used for the design and plan of field collection data include a meteorology station, video
cameras, and air samplers on each side of the highway. The meteorology station has a weather tracker
that measures wind speed, temperature, direction of wind, and humidity. Video cameras were used to
record the incoming and outgoing traffic. The video cameras are able to stay on for so long (14 hour data
collecting periods) because of a generator which is fueled with gasoline. Lastly, an air sampler, which
also samples carbon dioxide, is what actually samples the PM2.5.
Task three includes the actual field participation in the data collection. A time span of three
weeks was spent collecting data.
The activity required included setting up and tearing down the
equipment, making sure the equipment is collecting correctly, keeping the equipment secure, and
recording any significant traffic events. Figure 7 in the results shows meteorological data for October 3
and October 9.
The fourth task of this research project involved preparing camcorder data and also cutting the
videos into chapters. Preparing the camcorder data was done with the help of Mr. Zhuo Yao, who is a
graduate mentor on the team. The first step to this task was to find days where sufficient field data was
collected. This was achieved with a combination of camcorder results and air sampler results. The goal
was to find days where good quality video was recorded for the hours of 16:30 to 18:30 (4:30 – 6:30
p.m.). This time was convenient because this is a time where typically a lot of cars are on the road and
therefore a higher emission rate might be recorded. It was a requirement that adequate PM2.5 results from
the air sampler were recorded as well for these times of the day. After the videos were observed and two
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Cox, Johnson, Wei, Yao, Liu, Ai
days were found that met this criteria using Microsoft Excel, video editing software was used to cut the
videos into smaller pieces. Two days were used (October 3 and October 9) and these videos were initially
cut into two hour periods from 16:30 to 18:30. Video results were used for traffic flow going east and west,
so a total of four two hour videos were edited. After this, the two hour videos were cut into five minute
sections which gave the videos better quality and these videos were used in REMCAN. One of the five
minute videos from each day for both directions were then cut into one minute videos for the convenience
of extracting data using VEVID, which is a type of software developed by the Civil Engineering
department at UC.
The fifth task included the data analysis and modeling. The data gathered is analyzed using
several applications, the first being VEVID. Graduate students designed this program and it is a graphical
user interface which uses distance markings on the highway to calculate the speed of vehicles.
Classification of the vehicle is determined by VEVID as well. Figure 2 below shows the graphical user
interface as well as the distance markings which were originally placed on the highway.
Figure 2 VEVID Screenshot
The next application for the gathered data was for REMCAN. REMCAN stands for the computer
vision-based Rapid traffic Emission and Energy Consumption Analysis. REMCAN is an automated
computer vision-based computer system for ground truth (which allows image data to be related to real
features and materials on the ground) vehicle detection and tracking. This video acquisition module
enhances, splits, and resizes raw video data into a common standard size and length so MOVES can
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Cox, Johnson, Wei, Yao, Liu, Ai
read. It uses VEVID data to extract data for the purpose of vehicle speed calibration and validation. A
possible error for REMCAN might be that the angle at which vehicles are recorded can cause phantom
cars in other lanes. Also, the sun can cause shadows in other lanes as well. The methodology along with
Trajectory
Extraction
Foreground
Segmentation
Vehicle
Tracking
Vehicle
Detection
Vehicle Locations in
Detection
Zone
Sequential Frames
Video Acquisition
REMCAN Development with C++
Video
Background
Initialization
Segmentation
Calibration Module
Vehicle Parameter Extraction Module
case studies from previous experiment is shown in figure 3. [6]
Video Selection Base on
Time of Day/Location
Interest
Video Enhance, Split and
Resize
Distance Markings on
Highway
VEVID Trajectory Data
Extraction
Calibration and
Validation
MOVES Emission and
Energy Consumption
Estimation
Operating Mode Distribution
Link Source Types
MOVES Traffic Activity Inputs
Generation
Traffic Volume
Other MOVES Inputs
MOVES Input Generation/Conversion Module
Figure 3 System flowchart for (REMCAN) system
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Cox, Johnson, Wei, Yao, Liu, Ai
Figure 4 REMCAN Screenshots
With the data collected from REMCAN which includes operation mode and number of vehicles,
the MOVES input generation/conversion module generates the operating mode distribution, link source
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Cox, Johnson, Wei, Yao, Liu, Ai
types, and volume that are ready for MOVES model run. Volume describes the total amount of vehicle
traffic flow through the recorded data. Link Source allows the MOVES program to identify the amount of
car versus truck vehicles moving through the recorded data.
Operation mode is found initially in
REMCAN with the use of Vehicle Specific Power (VSP). VSP reveals the impact of vehicle operation
conditions on emission and energy consumption estimates that are dependent upon the speed roadway
grade and acceleration or deceleration on the basis of the second-by-second cycles. [7]
The VSP values for light-duty vehicles (cars) are calculated by the following equation:
Equation 1: VSP Calculation
𝑉𝑆𝑃 = 𝑣 x [1.1𝑎 + 9.81 x 𝑔𝑟𝑎𝑑𝑒(%) + 0.132] + 0.000302 x 𝑣 3
The VSP values for heavy-duty vehicles (trucks) are calculated by the following equation:
Equation 2: VSP Calculation for Trucks
𝑉𝑆𝑃 = 𝑣 𝑥 [𝑎 + 9.81 𝑥 𝑔𝑟𝑎𝑑𝑒(%) + 0.09199] + 0.000169 𝑥 𝑣 3
(v = vehicle speed (m/s); a = vehicle acceleration/deceleration rate (m/s2) ;grade = vehicle vertical rise
divided by the horizontal run (%)) . With the combinations of speed and VSP representing real-world
vehicle operating mode, MOVES adapted the 23 operating mode bins, plus additional operating modes
for starts and evaporative emissions which is shown in Table 1. [7]
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Cox, Johnson, Wei, Yao, Liu, Ai
Table 1 Operating Mode Bins for MOVES Running Emissions
Age distribution, meteorological data, fuel type, fuel supply, and formulation are the other inputs
MOVES uses in addition to the global inputs to project level emission analysis. MOVES results are based
on EPA standards. Further, a regression model was also found using REMCAN data. The significance of
a regression model is to prediction the emission estimate of PM 2.5 due to different traffic conditions.
Typically, this is what an automatic traffic recorder (loop detector) is used for however there can be many
potential errors with a loop detector that involve it not functioning correctly due factors such as weather
conditions so the method was used for more accurate results.
Equation 3 below is an example of the linear regression model. Tolerances include error from the
modeling software, meteorological differences between the place of collection and the place of
experimentation, and averaging errors. Reduction in error is attempted using linear regression. Linear,
Quadratic and a poly linearization techniques were used and the resulting models increases the accuracy
greatly, but the number of terms in the equation increases also - Table 2 Regression Models.
Equation 3 Linear Regression Model
𝑌(𝑚𝑖𝑐𝑟𝑜𝑔𝑟𝑎𝑚𝑠 𝑜𝑓 𝑃𝑀2.5 ) = 0.054 − 0.000015 ∗ 𝐴𝑙𝑙 𝑉𝑒ℎ𝑖𝑐𝑙𝑒𝑠 + 0.000016 ∗ 𝐶𝑎𝑟𝑠 + 0.000015 ∗ 𝑇𝑟𝑢𝑐𝑘𝑠 −
0.0000267 ∗ 𝑊𝑖𝑛𝑑𝑆𝑝𝑒𝑒𝑑(𝑚𝑝ℎ) − 0.000106 ∗ 𝑂𝑢𝑡𝑠𝑖𝑑𝑒𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒(𝐹) − 0.000163 ∗
𝑘𝑔
𝑊𝑖𝑛𝑑𝐷𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑅𝑎𝑑𝑖𝑎𝑛𝑠 − 6.127 ∗ 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦 − 0.0403 ∗ 𝑊𝑖𝑛𝑑 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 ( 3 )
𝑚
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Cox, Johnson, Wei, Yao, Liu, Ai
Results and Discussion

PM2.5 Emission Comparison between the EPA’s MOVES software results used to calculate PM2.5
and the Experimental calculation technique using meteorological PM2.5 data vehicles.
Figure 5: Experimental and MOVES PM Data
As seen in Figure 5, the field data has much higher PM2.5 emission results than the MOVES software
calculated. The EPA’s limits on PM2.5 emission are as follows: “The new PM2.5 standards limit PM2.5
concentrations to 15 micrograms per cubic meter based on an annual average, and 65 micrograms per
cubic meter based on a 24 hour average.”[6]
13
Cox, Johnson, Wei, Yao, Liu, Ai

PM2.5 Emission Comparison between the EPA’s MOVES software and the number of vehicles.
Figure 6: EPA's MOVES Software comparing PM2.5 and number of vehicles
Data in Figure 6 show the EPA’s PM2.5 emission predictions for the given experimental meteorological
variables.
14
Cox, Johnson, Wei, Yao, Liu, Ai

Meteorlogical Data
Blue:
Oct9
Red:
Figure 7: October 3 & 9 Meteorological Data
Oct3
Neither temperature nor wind speed is shown to have a direct correlation with the amount of PM 2.5
emission collected.
15
Cox, Johnson, Wei, Yao, Liu, Ai

Operating Mode Distribution
Figure 8: Op Mode Distribution
The majority of vehicles were allocated into Bin 33. This is the Bin representing a VSP anywhere
from 3 to less than zero and greater than 50 mph.

Pollutant Emissions from Study Site
Figure 9: Pollutant Emissions for Study Site
The data that is available shows the primary contributor to PM2.5 emission is Organic Carbon.
This is the same material that makes up hydrocarbons and un-burnt fuel.
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Cox, Johnson, Wei, Yao, Liu, Ai
Table 2 Regression Models
Regression Type
R-squared
Terms
Linear
0.107
8
Quadratic
0.59
45
Poly
0.863
165
Further detail can be found in the appendices.
Conclusions
A collection of meteorological and PM2.5 emissions data was collected and modeled using Vevid,
REMCAN and MOVES traffic modeling software. MOVES is maintained by the Environmental Protection
Agency and is used to predict emissions in the United States of America.
The model of the field data
demonstrates 1.5 times more PM2.5 being emitted than the EPA’s MOVES software as seen in Figure 5.
A possible cause for this difference is the intentional collection of data during and throughout rush hour
(16:30 – 18:30). Depending on which regression model is used to model the field data – See
Table 2-, it is possible that MOVES is underestimating the output of PM2.5. Another point of interest is
that the MOVES software does not differentiate between each individual workday of Monday through
Friday. Therefore MOVES is unable to identify if one day of the work week receives greater traffic flow
than another.
When there is a greater vehicle flow rate, EPA’s MOVES software shows a greater increase
number in PM2.5 than the experimental model. It is possible that the MOVES model recuperates the
difference between the field model and MOVES as the traffic flow increases. An interesting avenue of
further research would be analyzing this trend in MOVES in order to identify whether the positive
correlation is consistent with higher traffic flows.
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Cox, Johnson, Wei, Yao, Liu, Ai
Organic Carbon (hydrocarbons) accounts for the greatest of the PM 2.5 pollutants. The carbons
represented 3 and 4 times the amounts of other pollutants – Brakewear and Tirewear – and this identifies
a key pollutant particulate that would be the most beneficial in reducing. Our research results promote
further traffic emissions studies in identifying whether the EPA model attains greater accuracy within
higher traffic volume areas or the EPA model remains inconsistent with results attained from field data
collection.
Acknowledgements
The authors would like to thank the NSF CEAS Research Experiences for Undergraduates (REU)
Program, Dr. Urmila Ghia, Dr. Heng Wei P.E. PhD, Mr. Zhuo Yao Ph.D. Candidate, Hao Liu, Ph.D.
Candidate, Qingyi Ai Ph.D. Candidate and Dr. Kukreti.
CITATIONS
1. Chen, Hao., Bai, Song., Eisinger, Douglas., Niemeier, Deb., and Claggett, Michael. (2009).
“Predicting Near-Road PM2.5 Concentrations Comparative Assessment of CALINE4, CAL3QHC,
and AERMOD”. Environment 2009, pp. 26-37.
2. Karner, Lexa., Eisinger, Douglass., and Niemeier, Deba. (2010). “Near-Roadway Air Quality:
Synthesizing the Findings from Real-World Data”. ENVIRONMENTAL SCIENCE &
TECHNOLOGY, /VOL. 44, NO. 14, pp. 5334-5343.
3. Smit, Robin., Ntziachristos, Leonidas., Boulter, Paul. (2010). “Validation of road vehicle and traffic
emission models e A review and meta-analysis). Atmospheric Environment, 44 pp. 2943-2953.
4. Riediker, Michael. (2007). “Cardiovascular Effects of Fine Particulate Matter Components in
Highway Patrol Officers.” Inhalation Toxicology, Supplement 1, Vol. 19, p99-105.
5. Brugge, D., J. L. Durant, and C. Rioux. Near-Highway Pollutants in Motor Vehicle Exhaust: A
Review of Epidemiologic Evidence of Cardiac and Pulmonary Health Risks. Environmental
Health, Vol. 6, No. 23, Aug. 9, 2007.
6. EPA. "EPA’s Designations for PM2.5 Nonattainment Areas in New England Questions and
Answers." United States Environmental Protection Agency. Environmental Protection Agency, 2
Dec. 2011. Web. 2 Dec. 2012. <http://www.epa.gov/region1/airquality/pdfs/pm25_qa.pdf>.
7. Yao, Zhuo, Heng Wei, Tao Ma, Qingyi Ai, and Hao Liu. Developing Operating Mode Distribution
Inputs for MOVES Using Computer. Tech. no. 13-4899. N.p.: n.p., n.d. Web. 3 Dec. 2012.
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Appendix
The following represents the equations associated with each Polynomial, Quadratic, and Linear
Regression:
Polynomial Linear regression model:
y ~ [Linear formula with 165 terms in 8 predictors]
Estimated Coefficients:
Estimate
SE
pValue
(Intercept)
tStat
0
0
NaN
NaN
x1
0
0
NaN
NaN
x2
0
0
NaN
NaN
x3
0
0
NaN
NaN
x4
0
0
NaN
NaN
x5
0
0
NaN
NaN
x6
0
0
NaN
NaN
x7
0
0
NaN
NaN
x8
0
0
NaN
NaN
x1^2
7.4055e-05
7.0896e-05
x1:x2
0
x2^2
-0.00012147
0.00010513
-1.1555
x1:x3
0
0
NaN
NaN
x2:x3
0
0
NaN
NaN
x3^2
0.00011055
x1:x4
-0.001872
x2:x4
0
0
NaN
NaN
x3:x4
0
0
NaN
NaN
x4^2
0
0
NaN
NaN
x1:x5
0.00092405
x2:x5
0
x3:x5
-0.00044592
x4:x5
0.0039179
x5^2
x1:x6
x2:x6
0
NaN
0.00026371
0.0017314
0.00084139
0
NaN
0.0023561
1.0446
NaN
NaN
0.41922
-1.0812
1.0982
NaN
NaN
NaN
NaN
NaN
-0.18926
NaN
0.0062831
0.62356
-0.0011255
0.001161
-0.96948
NaN
-0.0018238
0.0016069
-1.135
NaN
0
0
NaN
NaN
x3:x6
0
0
NaN
NaN
x4:x6
0
0
NaN
NaN
x5:x6
0
0
NaN
NaN
19
NaN
Cox, Johnson, Wei, Yao, Liu, Ai
x6^2
0
x1:x7
-0.001612
x2:x7
0.00084171
x3:x7
0
NaN
0.0034347
NaN
-0.46932
0.0036786
0.22882
0
0
NaN
NaN
x4:x7
0
0
NaN
NaN
x5:x7
0
0
NaN
NaN
x6:x7
0
0
NaN
NaN
x7^2
0.0018655
x1:x8
0
0
NaN
NaN
x2:x8
0
0
NaN
NaN
x3:x8
0
0
NaN
NaN
x4:x8
0
0
NaN
NaN
x5:x8
0
0
NaN
NaN
x6:x8
0
0
NaN
NaN
x7:x8
0
0
NaN
NaN
x8^2
0
0
NaN
NaN
x1^3
-1.0391e-06
x1^2:x2
2.0718e-06
x1:x2^2
0
x2^3
-1.0327e-06
x1^2:x3
2.7441e-06
x1:x2:x3
0
x2^2:x3
x1:x3^2
x2:x3^2
x3^3
x1^2:x4
-3.7554e-06
0
-4.4659e-06
-1.7551e-06
-9.2843e-07
0.0023218
1.2747e-05
0.80347
-0.081518
2.5519e-05
0
0.081188
NaN
1.2773e-05
0.077752
NaN
4.8091e-05
0
5.7863e-05
2.2547e-05
NaN
NaN
NaN
NaN
NaN
NaN
-0.077181
NaN
-0.077845
NaN
-0.9831
NaN
9.4439e-07
x1:x2:x4
0
x2^2:x4
1.4224e-06
x1:x3:x4
0
0
NaN
NaN
x2:x3:x4
0
0
NaN
NaN
x3^2:x4
3.9426e-06
2.8447e-06
1.3859
NaN
x1:x4^2
2.3942e-05
8.7784e-05
0.27274
NaN
x2:x4^2
-2.8359e-05
0.00011535
-0.24586
x3:x4^2
x4^3
x1^2:x5
0
NaN
1.4636e-06
0
NaN
NaN
0.97184
0.00085651
-1.087
-4.7765e-07
3.3565e-07
-1.4231
0
x2^2:x5
5.7874e-07
x1:x3:x5
0
0
0
NaN
4.4782e-07
0
NaN
0
NaN
NaN
NaN
NaN
-0.00093105
x1:x2:x5
x2:x3:x5
0
NaN
NaN
-0.07809
NaN
NaN
NaN
-0.080848
3.5292e-05
0
NaN
NaN
NaN
NaN
1.2924
NaN
NaN
NaN
x3^2:x5
-5.2801e-07
5.7526e-07
-0.91787
NaN
x1:x4:x5
-1.9538e-06
6.9869e-06
-0.27964
NaN
20
Cox, Johnson, Wei, Yao, Liu, Ai
x2:x4:x5
0
x3:x4:x5
2.1998e-05
x4^2:x5
-0.00026188
0.00040532
x1:x5^2
-1.6214e-06
x2:x5^2
-2.1888e-06
x3:x5^2
0
x4:x5^2
-6.3416e-05
x5^3
6.1301e-05
x1^2:x6
-3.7925e-06
x1:x2:x6
0
x2^2:x6
5.313e-06
x1:x3:x6
0
x2:x3:x6
0
0
NaN
3.8699e-05
NaN
0.56843
NaN
-0.6461
NaN
6.1305e-06
-0.26448
NaN
9.4186e-06
-0.23239
NaN
0
NaN
0.00016358
5.1915e-05
4.3053e-06
0
NaN
6.258e-06
0
NaN
0
NaN
NaN
-0.38767
1.1808
NaN
NaN
-0.8809
NaN
NaN
0.84899
NaN
NaN
NaN
x3^2:x6
-7.2633e-06
7.8242e-06
-0.92832
NaN
x1:x4:x6
-6.3384e-05
0.00019525
-0.32464
NaN
x2:x4:x6
0.0001561
0.00029279
0.53315
NaN
x3:x4:x6
0
x4^2:x6
0.0017849
0.0022976
0
0.77684
NaN
x1:x5:x6
-3.0413e-05
9.1132e-05
-0.33373
NaN
x2:x5:x6
-2.6326e-05
0.00012272
-0.21453
NaN
0
x4:x5:x6
0.00078832
0.00087048
0.90562
NaN
x5^2:x6
-0.00030961
0.0011077
-0.27951
NaN
x1:x6^2
2.4643e-05
0.00015495
0.15904
NaN
0
x3:x6^2
-0.00031388
x4:x6^2
0
x5:x6^2
-0.0021815
x6^3
x1^2:x7
0
-3.0173e-06
x1:x2:x7
0
x2^2:x7
3.0308e-06
0
NaN
NaN
x3:x5:x6
x2:x6^2
0
NaN
NaN
NaN
NaN
0.00042889
-0.73184
0
NaN
NaN
0.0027786
0
NaN
4.415e-05
0
NaN
4.4106e-05
x1:x3:x7
0
x2:x3:x7
6.6667e-06
8.8429e-05
0
NaN
x3^2:x7
4.0395e-06
x1:x4:x7
-0.78513
NaN
NaN
NaN
-0.068343
NaN
NaN
0.068717
NaN
NaN
0.07539
NaN
4.418e-05
0.091433
NaN
-2.7226e-05
3.8485e-05
-0.70745
NaN
x2:x4:x7
2.0776e-05
4.1243e-05
0.50374
NaN
x3:x4:x7
0
x4^2:x7
0.00030588
0.00051255
0.59678
x1:x5:x7
7.8457e-06
7.3189e-06
1.072
x2:x5:x7
0
x3:x5:x7
2.248e-06
x4:x5:x7
0.00014716
0
0
NaN
NaN
1.2522e-05
0.00044886
NaN
NaN
NaN
NaN
0.17953
0.32785
21
NaN
NaN
Cox, Johnson, Wei, Yao, Liu, Ai
x5^2:x7
-0.00019789
x1:x6:x7
4.9233e-05
x2:x6:x7
0
x3:x6:x7
9.0537e-05
x4:x6:x7
-0.0014151
x5:x6:x7
0.0015355
x6^2:x7
0.0033432
x1:x7^2
-3.5093e-06
x2:x7^2
0
0.00014463
5.2744e-05
0
NaN
9.146e-05
-1.3683
NaN
0.93344
NaN
NaN
0.98991
NaN
0.0012504
-1.1317
NaN
0.0027812
0.55209
NaN
0.0042409
0.78831
NaN
2.8513e-06
-1.2308
NaN
0
NaN
NaN
x3:x7^2
-4.0157e-06
5.8788e-06
-0.68308
NaN
x4:x7^2
-2.9934e-05
0.0003038
-0.098531
NaN
x5:x7^2
0.00018503
0.00015943
1.1606
NaN
x6:x7^2
x7^3
x1^2:x8
-0.0014718
-4.5436e-05
-3.9214e-05
0.0018665
-0.78851
NaN
8.1301e-05
-0.55886
NaN
4.409e-05
-0.88943
NaN
x1:x2:x8
0
0
NaN
x2^2:x8
6.8808e-05
x1:x3:x8
0
0
NaN
NaN
x2:x3:x8
0
0
NaN
NaN
6.4982e-05
NaN
1.0589
x3^2:x8
-6.519e-05
x1:x4:x8
0.0016232
x2:x4:x8
0
x3:x4:x8
0.00027266
x4^2:x8
0
x1:x5:x8
-0.00053212
x2:x5:x8
0
x3:x5:x8
0.00022432
0.0019181
0.11695
NaN
x4:x5:x8
-0.0041764
0.0056042
-0.74522
NaN
x5^2:x8
0.00062293
0.00087074
x1:x6:x8
0.0021484
0.0027462
x2:x6:x8
0
0
NaN
NaN
x3:x6:x8
0
0
NaN
NaN
0
NaN
x4:x6:x8
0
x5:x6:x8
-0.0031064
x6^2:x8
0
x1:x7:x8
0.00083864
x2:x7:x8
-0.00049635
x3:x7:x8
0
x4:x7:x8
0
x5:x7:x8
0.00021497
-0.30326
0.001704
0.95257
NaN
0
NaN
0.15538
0
NaN
0.00056345
0
NaN
0.0068088
0
NaN
NaN
NaN
0.0017547
NaN
NaN
-0.9444
NaN
NaN
NaN
0.7154
NaN
0.78232
NaN
NaN
-0.45624
NaN
NaN
0.0028203
0.29735
NaN
0.0029346
-0.16914
NaN
0
NaN
NaN
0
NaN
NaN
0
0
NaN
NaN
x6:x7:x8
0
0
NaN
NaN
x7^2:x8
-0.00063818
0.0018606
-0.343
x1:x8^2
-0.00022043
0.0029143
-0.07564
22
NaN
NaN
Cox, Johnson, Wei, Yao, Liu, Ai
x2:x8^2
0
0
NaN
NaN
x3:x8^2
0
0
NaN
NaN
x4:x8^2
0
0
NaN
NaN
x5:x8^2
0
0
NaN
NaN
x6:x8^2
0
0
NaN
NaN
x7:x8^2
0
0
NaN
NaN
x8^3
0
0
NaN
NaN
Number of observations: 96, Error degrees of freedom: 11
Root Mean Squared Error: 0.00027
R-squared: 0.863, Adjusted R-Squared -0.184
F-statistic vs. constant model: 0.824, p-value = 0.709
Linear regression model:
y ~ 1 + x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8
Estimated Coefficients:
Estimate
SE
tStat
(Intercept)
0.0055505 0.0066789
0.40822
pValue
0.83106
x1
-3.4703e-06
9.541e-06
-0.36373
0.71695
x2
3.5278e-06
9.6525e-06
0.36548
0.71564
x3
3.8913e-06
9.4252e-06
0.41285
0.68073
x4
4.3707e-05
4.7966e-05
0.9112
0.36471
x5
-1.9423e-05
1.6488e-05
-1.178
0.24202
x6
-8.0623e-05
4.8714e-05
-1.655
0.10152
x7
2.5804e-05
1.446e-05
1.7845
0.077831
x8
-0.0044867
0.0059756
-0.75084
0.45478
Number of observations: 96, Error degrees of freedom: 87
Root Mean Squared Error: 0.000245
R-squared: 0.107, Adjusted R-Squared 0.0252
F-statistic vs. constant model: 1.31, p-value = 0.251
Quadratic Linear regression model:
y ~ [Linear formula with 45 terms in 8 predictors]
Estimated Coefficients:
23
Cox, Johnson, Wei, Yao, Liu, Ai
Estimate
SE
tStat
pValue
(Intercept)
-2.0322
1.913
-1.0623
0.2931
x1
-0.0002758 0.00046282 -0.59592
0.55387
x2
0.000224 0.00059692
0.37525
0.70903
x3
0
x4
x5
0.84595
x6
0.92346
x7
0.52938
0.020224
0.0016576
0.013883
0.008488
1.4567 0.15132
0.19528
0.0069732
0.072219
0.096557
0.0046139
0.0072858
0.63328
x8
x1:x2
0.014381
x1:x3
0.014063
x1:x4
0.66168
x1:x5
0.17692
x1:x6
0.20101
x1:x7
0.016215
x1:x8
0.79657
x2:x3
0.014097
3.3049
3.3488
0.98687 0.32837
0.00020818 8.2146e-05
2.5343
x2:x4
0
NaN
NaN
0.00028576
0.00011237
4.1636e-07
9.4593e-07
0.44016
-7.9133e-07
5.7793e-07
-1.3693
1.149e-05
8.8701e-06
2.5431
1.2954
-0.00034029
0.00013685
-2.4865
0.00010742
0.00041453
0.25915
-0.00033763
0.00013281
-2.5422
0
x2:x5
x2:x6
0.064191
x2:x7
0.016109
x2:x8
0.99541
x3:x4
0.55189
x3:x5
0.034246
0
-2.2525e-05
0
NaN
NaN
0
NaN
NaN
1.1906e-05
-1.8919
0.00034077
0.0001369
2.4891
3.0783e-06
0.00053246
0.0057813
2.3862e-06
3.9844e-06
0.5989
3.9324e-06
1.8075e-06
2.1756
x3:x6
x3:x7
0.016774
0
0.00033851
0
NaN
0.00013689
x3:x8
x4:x5
0.037404
x4:x6
0.1315
0
-9.3971e-05
0
NaN
NaN
4.3971e-05
-2.1371
-0.00054663
0.00035661
NaN
2.4729
-1.5328
24
Cox, Johnson, Wei, Yao, Liu, Ai
x4:x7
0.041577
x4:x8
0.25812
x5:x6
0.93304
x5:x7
0.29553
x5:x8
0.77491
x6:x7
0.048384
x6:x8
0.82468
x7:x8
0.5615
x1^2
0.01426
x2^2
0.014523
x3^2
0.014021
x4^2
0.076092
x5^2
0.26293
x6^2
0.15966
x7^2
0.92248
x8^2
8.6579e-05
4.1416e-05
-0.014008
0.012249
2.0905
-1.1436
-1.0704e-05
0.00012677
-0.08444
-2.2662e-05
2.1442e-05
-1.0569
-0.0021056
0.0073244
-0.28748
0.00022624
0.00011186
-0.014634
0.065719
-0.0036427
0.0062327
-0.58445
-7.8185e-05
3.081e-05
-2.5376
-0.00013
2.0225
-0.22268
5.1375e-05
-2.5304
-0.00020758
8.1586e-05
-2.5443
-0.00016758
9.2552e-05
-1.8106
1.4837e-05
1.3107e-05
1.132
0.00031093
0.00021788
9.0109e-07
9.2146e-06
-1.3158
1.4837
1.427
0.097789
-0.88687
0.37931
Number of observations: 96, Error degrees of freedom: 56
Root Mean Squared Error: 0.000207
R-squared: 0.59, Adjusted R-Squared 0.305
F-statistic vs. constant model: 2.07, p-value = 0.0063
25