MEMORANDUM

SUBJECT: Regression Analysis of Nitrous Oxide and Oxides of Nitrogen from Motor 

Vehicles 

FROM: David Choi 

 Assessment and Standards Division 

 Office of Transportation and Air Quality 

TO: Docket Number EPA-HQ-OAR-2011-0135 

DATE: February 27, 2014 

The purpose of this memorandum is to document the regression analysis examining the 

relationship between nitrous oxide (N2O) and oxides of nitrogen (NOx) from motor vehicles. 

The result from the analysis was used to estimate the reductions in N2O emissions projected from 

gasoline cars and trucks due to the Tier 3 vehicle and sulfur standards. 

Nitrous oxide (N2O) is a potent greenhouse gas with 100-year global warming potential 298 

times greater than carbon dioxide (CO2).A N2O is not formed during combustion, but in the 

catalyst, during catalyst warm-up, before the catalyst reaches the temperatures required for full 

effectiveness (known as “light-off”). Improvements to catalyst technology required to meet 

lower emission standards reduce the time required for the catalyst to reach light-off, which 

reduces the window of N2O formation. 

Several studies have established that reductions in tailpipe standards for NOx result in reductions 

in N2O. Studies conducted by EPA and Environment Canada found that N2O emission are lower 

on vehicles certified to more stringent NOx emission standards.1,2 A study by Meffert, et al. 

established a strong correlation between improvements in NOx catalytic conversion efficiency 

and reductions in N2O emissions.3 A study published by Behrentz, et al. in 2004 examined the 

relationship between N2O and NOx from data collected by the California Air Resources Board 

(CARB) on 37 passenger cars and light-duty trucks ranging from the mid-1980s through early 

2000’s Low Emission Vehicle (LEV) technology.4

 Another study by Winer, et al (2005) tested 

134 light-duty vehicles, including passenger cars and light-duty trucks, as part of the CARB’s 

                                                           

A 2007 Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) 
vehicle surveillance program, varying from Tier 0 to ULEV in emissions standards.5

 These two 

studies reported N2O: NOx ratios of 0.06 and 0.095, respectively, and supported the application 

of N2O: NOx ratios to NOx emissions as a reasonable method for estimating N2O emission 

inventories. Meszler, et al. subsequently analyzed the dataset by Behrentz and found that for 

vehicles equipped with more modern controls, N2O emissions increased with vehicle mileage, 

suggesting deterioration in N2O emissions as vehicles age.6 The study by Winer, et al (2005) 

also found that as the emissions standards became more stringent, the N2O: NOx ratios increased. 

The MOVES model used to generate emissions inventory is based on a limited sample of N2O 

emissions data and currently does not associate N2O emissions to NOx emissions as suggested by 

Winer and Behrentz. Therefore, the model does not estimate the potential N2O reduction 

concurrent with the Tier 3 program since it does not account for the factors affecting light-duty 

NOx emissions, such as deterioration, aggressive driving, and lower NOX standards. 

In an effort to estimate the N2O inventory accounting for the factors that affect N2O emissions, 

EPA analyzed the data collected by California Air Resources Board (CARB) at El Monte 

laboratory facilities from 2000 to 2007, as a part of CARB’s vehicle surveillance program. The 

data described in Winer and Behrentz were also collected as a part of the same program. 

However, the data we analyzed, available as a part of this memorandum to the docket, is the 

most comprehensive since it includes additional tests that CARB collected, since the studies 

conducted by Winer and Behrentz. The same dataset was used to examine the association 

between N2O and NOx emissions and to apply the relationship to estimate the N2O benefits from 

the LEV III program.7

 

Regression Analysis 

A total of 174 vehicles were included in the analysis, ranging in model years from 1981 to 2004. 

For this analysis, weighted FTP was calculated based on the individual bag results and the 

regression analysis was performed on the weighted FTP results. 

Before proceeding with the analysis of the data, EPA performed a number of tests to assess 

whether the data meets the assumptions of linear regression. First, the assumption of normality 

was tested. Both visual inspection of the QQplot (Figure 1) and the Shapiro-Wilk W test of 

normality (p-value < .0001) indicated that the null hypothesis that it is normally distributed need 

to be rejected. However, the failure to meet the normality assumption is not likely to affect the 

validity of estimation of coefficients. 
Figure 1. Test for normality: QQplot of Raw Data 

Next, the test for heteroskedasticity was performed. One of the main assumptions for the 

ordinary least squares regression is the homogeneity of variance of the residuals, and if the 

constant variance assumption is not met, it can affect the model fit. The visual inspection of the 

residual vs. predicted plot (Figure 2) indicates that there is a potential heteroskedasticity showing 

the pattern is very narrow towards the left end. The White test was performed to confirm the 

finding and the test showed that the p-value is very small (p=0.0118) indicating that the null 

hypothesis that the variance of the residual is homogeneous needs to be rejected. 
Figure 2. Plot of Residual vs. Predicted: Raw Data 

In an effort to fulfill the assumptions of the ordinary least squares regression, EPA has logtransformed both the dependent and independent variables, which is a well-established method in 

modeling of emissions data. The QQplot testing for normality in Figure 3 shows that the 

distribution of the residual has improved. Furthermore, the homogeneity of the variance of the 

residuals is confirmed both by visual inspection of Figure 4 and by the White test with p-value of 

0.5706. 
Figure 3. Test for Normality: QQplot of Log-Transformed Data 
Figure 4. Plot of Residual vs. Predicted: Log-Transformed Data 

After confirming the assumptions of the ordinary least squares regression have been satisfied, a 

regression analysis was performed to examine the relationship between N2O and NOX. A number 

of different methodologies were considered including performing regression analysis by bags, 

technology groups, and fuel types. However, the analysis did not find improvement in the model 

fit due to increased variability from reduced sample size. No statistically significant difference 

in N2O: NOx ratio was observed between different vehicle types. 

The resulting regression model correlating N2O emissions to NOx emissions is shown in 

Equation 1. 

Equation 1. Regression Model Correlating N2O Emissions to NOX Emissions 

In order to evaluate the performance of the regression, the data vs. model prediction was plotted 

(Figure 5). The model shows reasonable accuracy in predicting the data (R2

=0.57). 
Figure 5. Plot of Data vs. Predicted – Regression with log-transformation 

Conclusion 

N2O emissions are known to be dependent on catalyst control technology, age of the technology, 

operating conditions such as the drive cycle, and the fuel sulfur levels. The many factors 

involved make it difficult to accurately estimate the N2O emissions inventory. Because the 

dataset the regression was based on included vehicles with different emission standards, it may 

not be reasonable to apply the regression to estimate N2O emissions on a per-vehicle basis. 

However, since the purpose of the analysis was to examine the relationship between N2O and 

NOx to be applied in estimating the fleet-wide N2O emissions inventory, the analysis has merits. 

Furthermore, the future fleet to which N2O: NOx emissions ratio is being applied is much cleaner 

than the test fleet the regression is based on, and considering the previous findings that N2O: 

NOx emissions ratios increase with more stringent emission standards, the estimation of the 

future N2O emissions inventory and the reductions in N2O from the Tier 3 standards, using the 

regression presented in this memorandum, would likely be a conservative estimates. 
References 

                                                           

1

 Michaels, H. (1998) Emissions of Nitrous Oxide from Highway Mobile Sources, U.S. EPA EPA420-R-98-009. 

2

 Graham, L. (2006) Greenhouse Gas Emissions from 1997-2005 Model Year Light Duty Vehicles Environment 

Canada ERMD Report #04-44. 

3

 Meffert, et al (2000) Analysis of Nitrous Oxide Emissions from Light Duty Passenger Cars, SAE 2000-01-1952. 

4

 Behrentz, et al. (2004) Measurements of nitrous oxide emissions from light-duty motor vehicles: a pilot study, 

Atmospheric Environment 4291-4303. 

5

 Winer, et al. (2005) Estimates of Nitrous Oxide Emissions and the Effects of Catalyst Composition and Aging, 

State of California Air Resources Board 02-313. 

6

 Meszler, D. (2004) Light Duty Vehicle Methane and Nitrous Oxide Emissions: Greenhouse Gas Impacts Study for 

Northeast States Center for a Clean Air Future. 

7

 LEVIII Mobile Source Emissions Inventory Technical Support Document – Appendix T, January 2012. 

http://www.arb.ca.gov/regact/2012/leviiighg2012/levappt.pdf