MEMORANDUM

FROM: James Warila 

United States Environmental Protection Agency

Office of Air and Radiation

Office of Transportation and Air Quality

Assessment and Standards Division

TO: Tier 3 Docket EPA-HQ-OAR-2011-0135

DATE: February 28, 2013

RE: Statistical Analysis of the Effects of Changing Fuel Properties on CO2

Emissions from Light-Duty Gasoline-Powered Vehicles based on EPAct/V2/E-89

Test Program Results

The proposed change in test fuel, if finalized, could have implications for the CAFE and GHG 

emissions compliance programs, as well as the fuel economy labeling program. Therefore, it is 

important to characterize the potential impact on CO2 emissions from the change in certification 

test fuel proposed in this rule. As outlined in the preamble to the 2017 and Later Model Year 

Greenhouse Gas Emissions and Corporate Average Fuel Economy (CAFE) final rule, if the EPA 

test fuel used for certification and fuel economy vehicles changes to include ethanol, EPA is 

committed to address whether the fuel change has a potential to affect the stringency of 

Greenhouse Gas and CAFE standards.1 As a result, we used data from the EPAct Program to 

examine the effects of changing fuel properties on CO2 emissions. 

Based on results from Phase 3 of the EPAct Program, we performed a statistical analysis of the 

effects of five fuel properties on the CO2 emissions of 15 late-model light-duty vehicles. To our 

knowledge, this is the most comprehensive study of fuel effects of CO2 emissions available. 

The project was conducted as a controlled experiment, in which the design can be characterized 

as “randomized block with repeated measures”, in which vehicles are treated as blocks and fuel 

properties as “treatments.” A statistically optimal study design was developed to represent 

variation in five fuel properties: ethanol volume (%), aromatic content (%), RVP (psi), T50 (°F) 

and T90 (°F). These five parameters were selected based on previous studies as having potential 

to affect exhaust emissions, and were included in the design at the levels shown in Table 1. A 

critical feature of the study design is that the properties of the test fuels are assigned to span the 

ranges of in-use fuel properties, with the intent of providing a basis for the development of 

statistical models capable of predicting emissions for the majority of in-use fuels. Following a 

process in which statistical power, fuel-blending feasibility and budget were balanced, the final 

design included 27 test fuels.

A set of 15 test vehicles, all in model year 2008, with the majority certified to Tier-2/Bin-5 

standards, was selected on the basis of sales levels, vehicle and engine sizes, and representation 

of manufacturers. Emissions were measured on the LA92 test cycle at a nominal temperature of 

 

1

77 FR 62624, 62777-62778 (October 15, 2012).
75°F. Emissions measured include carbon dioxide (CO2), carbon monoxide (CO), total 

hydrocarbons (THC), methane (CH4), non-methane hydrocarbons (NMHC), oxides of nitrogen 

(NOx), and particulate matter (PM2.5). Following the completion of data collection, in June 

2010, construction of the dataset involved intensive evaluation and quality assurance. 

The conduction and analysis of the EPAct Phase-3 project are discussed in greater detail in the 

EPA project Report2.

Table 1. Levels assigned to Experimental Factors (Fuel parameters) for the Phase-3 EPAct 

program.

Factor No. Levels Levels

Low Middle High

Ethanol (%) 4 0 10, 15 20

Aromatics 2 15 35

RVP (psi) 2 7 10

T50 (°F) 5 150 165, 190, 220 240

T90 (°F) 3 300 325 340

Analysis

Each of the vehicles was measured on each of the 27 fuels, with replication. On most vehicle 

fuel combinations two replicates were performed, whereas on some combinations, 3 replicates 

were performed. The total dataset includes 956 observations. More details on the vehicles, fuels, 

and test procedures can be found in the program report.3

For purposes of this analysis, we used cycle composites for the LA92 results. Results for the 3 

phases of the cycle (cold start, hot running and hot start) were averaged in the same manner as a 

composite calculated on the FTP cycle.

Data Review

Error! Reference source not found. shows a summary of the entire dataset as the common 

logarithm of the cycle composites, presented by vehicle and fuel. As expected, measurements are 

consistent and precise for each vehicle, with variability among vehicles considerably larger than 

variability within vehicles. Overall, the measurements range from 290 to 600 g CO2/mi.

 

2 USEPA. Assessing the Effect of Five Gasoline Properties on Exhaust Emissions from Light-Duty Vehicles 

certified to Tier-2 Standards: Data Analysis and Model Development (EPAct/V2/E89). Office of Transportation and 

Air Quality, Ann Arbor, MI. 

3

See memorandum to Tier 3 Docket # EPA-HQ-OAR-2011-0135, “EPAct/V2/E-89: Assessing the Effect of Five 

Gasoline Properties on Exhaust Emissions from Light-Duty Vehicles Certified to Tier 2 Standards Test Program.”

(March, 2013)
Figure 1. Common logarithms of CO2 measurements (Composites on LA92 cycle).

As a next step, we averaged the data across all levels of each of the fuel properties in turn, and by 

vehicle, as shown in Error! Reference source not found. through Error! Reference source 

not found.. The plots make it clear that, at the scales shown, visible effects are apparent only for 

aromatics. Effects may be present for the other properties, but would be too small to be visible at 

the scale shown.
Figure 2. CO2 (Composite): Results averaged by four levels of ethanol and by vehicle.

Figure 3. CO2 (Composite): Results averaged by two levels of aromatics and by vehicle.
Figure 4. CO2 (Composite): Results averaged by two levels of RVP and by vehicle.

Figure 5. CO2 (Composite): Results averaged by five levels of T50 and by vehicle.
Figure 6. CO2 (Composite): Results averaged by three levels of T90 and by vehicle.

In addition, we investigated whether graphing the results might indicate the possibility of an 

interaction effect between aromatics and ethanol. In this case we averaged the data by both its 

four ethanol and two aromatics levels and plotted the means, as shown in Error! Reference 

source not found.. In this plot we show trends against aromatics with a different series for each 

ethanol level. As in Error! Reference source not found., the effect of aromatics is visible, but it 

is not apparent that the aromatics effect differs systematically by ethanol level.

Figure 7. CO2 (Composite): Emissions vs. Aromatics by Ethanol Level.
Statistical Modeling

We followed up on the graphical presentation of the data by performing statistical modeling. 

Response variable: As mentioned above, the response variable was CO2 emissions, as the cycle 

composite on the LA92 cycle. Unlike other emissions, such as NOx, PM or NMOG, it was not 

necessary to perform a natural log transformation of the data before modeling, as the CO2 results 

are approximately normally distributed with respect to the fuel properties.

Design Model: The properties of the test fuels form a five-dimensional study design optimized 

to estimate emissions as efficiently as possible for set of pre-specified model terms. These terms 

include a linear term for each of the five fuel properties, two squared terms for ethanol and T50, 

and four interaction terms, for combinations of ethanol with each of the remaining four 

properties. A model including this set of 11 terms is shown in Error! Reference source not 

found..

etOH Arom etOH RVP etOH T50 etOH T90

etOH etOH T50 T50

CO etOH Arom RVP T50 T90

8 9 10 11

6 7

2 0 1 2 3 4 5

      

   

      

   

 

     

Equation 1

The model including all 11 terms will be referred to as a “full model,” indicating that it contains

all available candidate terms.

Standardization: Prior to modeling, all terms were “standardized.” That is, each fuel property 

measurement was “centered” by subtracting its mean (for all measurements), and then “scaled” 

by dividing the difference by its corresponding standard deviation (for all measurements). For 

the five linear terms, this process was performed using individual fuel property measurements. 

The resulting “Z score” has a mean of 0.0 and a standard deviation of 1.0. For 2nd–order terms, 

cross products terms were constructed not from the original measurements, but rather from the Z

scores for the applicable linear terms. Then the standardization process was repeated, after 

calculating the means and standard deviations of the cross products of the Z scores. Thus, these 

“two-stage” standardized values for the 2nd-order terms will be referred to using the notation 

“ZZ.” For example, the term for the etOH×etOH quadratic term is notated as ZZee, and that for 

the etOH×Aromatics interaction as ZZea. This process is performed to neutralize any remaining 

correlations among terms, particularly between linear effects and corresponding 2nd-order terms, 

and is described in greater detail in section 2.3.1 of the EPAct analysis report. Thus the models 

actually fit are represented in Error! Reference source not found., in which each term 

corresponds to its counterpart in Error! Reference source not found..

8 ea 9 er 10 e5 11 e9

6 ee 7 55

CO2 0 1 e 2 a 3 r 4 5 5 9

ZZ ZZ ZZ ZZ

ZZ ZZ

Z Z Z Z Z

   

 

     

  

 

      

Equation 2
Model Fitting: Starting with a “full model” including all 11 terms in Error! Reference source 

not found., we performed model fitting to identify and remove terms not contributing to the fit 

of the model to the dataset. This process was performed by backwards elimination. In the first 

step, after fitting the full model, any terms with p-values for their Type-III tests greater than 0.10 

were removed and the model refit without them. The model with fewer terms is termed a 

“reduced model,” which is said to be “nested” in the full model. Then, as a test of goodness of fit 

between the two models, a likelihood ratio test was performed. The test statistic was the 

difference in the -2 log likelihood statistics between the nested and full models (known as the 

“reference model” for purposes of the test). This statistic is assumed to follow a χ

2

distribution 

with degrees of freedom equal to the difference in the number of parameters between the two 

models. If the test gave a p-value greater than 0.10, the null hypothesis of no difference in fit 

between the two models was retained, and the term(s) under consideration were dropped in 

subsequent model-fitting steps, under the assumption that they did not make a statistically

significant improvement in the model fit. On the other hand, if the p-value was < 0.10, the null 

hypothesis was dropped, and one or more of the term(s) would be retained in the model, pending 

successive fitting steps. In this circumstance, one or more of the terms is assumed to make a 

statistically significant improvement in model fit.

If terms dropped in the first step are not retained, the “reduced model” with fewer terms becomes 

the “reference model” and the process is repeated. Successive model fitting steps are performed 

until a significant result is obtained and all remaining terms have p-values < 0.10.

Results

The process is summarized in Error! Reference source not found. to Error! Reference source 

not found.. Error! Reference source not found. shows the set of reduced models fit. Error! 

Reference source not found. shows the results of successive tests fit during the process. Error! 

Reference source not found. shows the coefficients, standard errors and tests of effect for the 

full model and the reduced model having the best fit to the dataset.

Table 2. Models fit for CO2 (composite): (all models include an intercept term).

Model Term Notation Model

Full FM61FM7 FM8

etOH Ze ● ● ● ●

Arom Za ● ● ● ●

RVP Zr ● ● ● ×

T50 Z5 ● ● ● ●

T90 Z9 ● ×

etOH × etOH ZZee ● ×

T50 × T50 ZZ55 ● ×

etOH × Arom ZZea ● ● ×

etOH × RVP ZZer ● ×

etOH × T50 ZZe5 ● ×

etOH × T90 ZZe9 ● ×

1

denotes “full minus 6.”
Table 3. CO2 (Bag 1): Model Fitting History, starting with the 11-term Full model.

Fit Parameters Test with respect 

to

Previous Model

Model p -2lnL BIC 

1 Dev. d Pr>χ2

Full 12 -7591.08 -7553.17

FM6 6 -7582.70 -7561.03 8.380 6 0.212

FM7 5 -7580.88 -7561.92 1.820 1 0.177

FM8 24 -7578.22 -7561.97 2.660 1 0.103

1

A lower value indicates a better fit.

2

Best fit with respect to the 11-term design model.

Table 4. CO2 (Composite): Coefficients and Tests of Effect for the Full and Reduced Models, with 

respect to the 11-term design model.

Effect Full Model Reduced Model (FM8)

Estimate1Std.Err.1d.f. t-value Pr> t Estimate1Std.Err.1d.f. t-value Pr> t

Intercept 433.7 25.59 15 16.95 0.000000 433.7 25.59 15 16.95 0.000000

Ze 0.9796 0.2043 941 4.795 0.000002 0.9877 0.1678 941 5.886 0.000000

Za 7.784 0.1424 941 54.67 0.000000 7.766 0.1414 941 54.92 0.000000

Zr-0.1993 0.1626 941 -1.225 0.22 0.8249 0.1730 941 4.768 0.000002

Z5 0.7546 0.2051 941 3.679 0.00025

Z9 -0.0243 0.1424 941 -0.170 0.86

ZZee 0.2269 0.2741 941 0.8276 0.41

ZZ55 -0.2038 0.2053 941 -0.993 0.32

ZZea 0.2050 0.1393 941 1.472 0.14

ZZer -0.1770 0.1421 941 -1.246 0.21

ZZe5 -0.0867 0.2942 941 -0.295 0.77

ZZe9 -0.0459 0.1398 941 -0.328 0.74

2  veh 9,822 9,821

2  18 18

1

Expressed in units of g/mi per a change in the fuel property of 1.0 standard deviation (g/mi-σ).

Interpretation

The results presented in Error! Reference source not found. are presented graphically below 

in Figure 8, in which the bars represent the magnitude and signs of the coefficients, excluding the 

intercept (434 g/mi). Error bars on the coefficients represent 90% confidence intervals based on 
the standard errors shown in the table. The terms dropped from the reduced model are clearly 

seen as those with error bars spanning 0.0.

Figure 8. CO2 (Composite): Standardized Model Coefficients for Full and Reduced Models (Error 

bars represent 90% confidence intervals).

The reduced model is simple, retaining only three linear effects and no 2nd-order terms. It 

contains three linear terms, for ethanol, aromatics and T50, with the values for ethanol and T50 

being similar in size, with values of approximately 1.0 g/mi-σ. The term for aromatics is 

considerably larger, at approximately 8.0 g/mi-σ. 

Because, as mentioned above, the fuel properties are “standardized” before model fitting, and 

because the response variable is CO2 emissions (g/mi), as a composite on the LA92, the 

coefficients represent a change in CO2 emissions corresponding to changes in the fuel properties 

of 1.0 standard deviation (σ), as calculated for the fuel matrix used in the study. In addition, the 

coefficients represent the effect on the emission rate for each fuel property, as though the 

remaining properties would be held constant while varying the property under consideration. 

This assumption is entirely artificial but very useful in assessing the behavior of emissions in 

relation to changing fuel properties.

An interpretation of each of the terms is provided below:

Ethanol: The coefficient takes a value of 0.98 g/mi-σ. As the σ for ethanol is 7.9 vol.%, the 

coefficient indicates an increase of ~0.124 g CO2/mi per % increase in ethanol volume, assuming 

aromatics and T50 are held constant. For example, with the other two properties constant, we 

would predict a 1.25 g/mi increase in CO2 from an E10 blend relative to an E0 blend. Note, 
however, that the change is very small, e.g., an average rate of 350 g/mi on E0 would increase to 

351.24 g/mi on E10, which represents an increase of 0.4%.

Aromatics: This coefficient takes a value of 7.8 g/mi-σ. The σ for aromatics is 10.0 vol.%. 

Thus, the coefficient indicates an increase of 0.78 g CO2/mi per % increase in aromatics volume, 

assuming ethanol and T50 are held constant. For example, with the other two properties 

constant, we would predict a 7.8 g/mi increase in CO2 from a 15% aromatics to one with 25% 

aromatics. While larger than the ethanol effect, this change is also small relative to the base 

level, e.g., an average rate of 350 g/mi on a fuel with 15% aromatics would increase to 357.8 

g/mi on a fuel with 25% aromatics, which represents an increase of 2.2%. 

T50: This coefficient takes a value of 0.83 g/mi-σ. The σ for T50 is 28.6°F. The coefficient 

thus indicates an increase of 0.029 g CO2/mi per an increase in T50 of 1.0 F°, assuming ethanol 

and aromatics are held constant. For example, with the other two properties held constant, we 

would predict a 0.88 g/mi increase in CO2 from a fuel with T50 at 220°F relative to a fuel with 

T50 at 190°F. An average rate of 350 g/mi on a fuel with T50 at 220°F would increase to 350.88 

g/mi on a fuel with T50 at 190°F, which represents an increase of 0.3%.

Conclusion

The analysis of results from the EPAct program indicates that changes in fuel properties are 

associated with measurable changes in CO2 emissions. In particular, three fuel properties, 

ethanol, aromatics and T50 are associated with statistically significant changes in CO2 emissions 

that are, however, small to very small in absolute terms. 

Of the three properties, the effect for aromatics is clearly the most important, with the aromatics 

coefficient 8 times and 9.4 times larger than those for ethanol and T50, respectively (based on 

the standardized coefficients shown above in Figure 8).

While it is useful to consider the coefficients in isolation, it is critical to remember that in 

practice the fuel properties cannot be cleanly separated. Thus, when applying the models, it is 

necessary to account for the effects of multiple properties varying simultaneously. 

For example, while noting that the ethanol coefficient predicts that a shift from E0 to E10 blends 

would result in a small increase in CO2 emissions, accounting for simultaneous decreases in 

aromatics (and possibly T50) due to dilution and/or octane match-blending by refiners, we would 

expect the aromatics effect would be opposite the ethanol effect and of an equal or greater 

magnitude. For example, the model suggests that the increase in CO2 due to an increase in

ethanol from 0 to 10 vol% (1.25 g/mi CO2 increase) would be offset by a reduction in aromatics 

of 1.6 vol% (1.25 g/mi CO2 decrease), not accounting for potential changes in T50. Stated 

differently, the model predicts that a gasoline with 0 vol% ethanol and 25 vol% aromatics would 

have the same CO2 emissions as a fuel with 10 vol% ethanol and 23.4 vol% aromatics.

In general, we conclude that the data and analysis support a conclusion that, aside from 

improbable cases in which ethanol and aromatics increase simultaneously, the addition of 

ethanol to gasoline is expected to have no appreciable effects on CO2 emissions.