### Assessing	the	Effect	of	Five	Gasoline	Properties	on	Exhaust	Emissions	from	Light**** **Duty	Vehicles	certified	to	Tier -**  **2	Standards (EPAct/V2/E**  **- 89:	Phase	3)**  **Part	II:		Data	Analysis	and	Model	Development**



## APPENDIX **E**
**Preliminary	Reduced	Models**

### Development of the models presented below is described in Section 5.3 of the report. All models

are based on the 16
-parameter full model, as shown in Equation 1
. All terms were included at the outset of model fitting, with the exception of T90 × T90. Using the notation for standardized predictors, also shown in Equation 2 , the model is also expressed in Equation 2
. Table E. 1 summarizes the model
- fitting approaches applied to each bag for each emission. Table E. 2 through E. 7 present the coefficients for interim reduced models for THC, NMOG, CH4, CO, NOx and PM, respectively
.

                 

                                         

90 T RVP RVP Arom 90 T 50 T 90 T Arom 50 T Arom T90 etOH T50 etOH RVP etOH Arom etOH etOH 50 T 90 T 50 T RVP Arom etOH ln

16 15 14 13 12 11 10 9 8 2

7 2 6 5 4 3 2 1 0 Y **Equation 1** 



###       

     

    

     

    

     

9 16 15 59 14 9 13 5 12 9 11 5 10 9 8 7 55 6 9 5 5 4 3 2 1 0 

### ln

r ar a a e e er ea ee r a e


### ZZ ZZ ZZ ZZ ZZ ZZ

ZZ ZZ ZZ ZZ ZZ Z

Z Z Z Z Y
**Equation 2** **Table E.**  **1 .**  **Design and	Modeling	Parameters	for	Best** **- fit	models,	by	Compound	and	Bag.**  Com pound Bag n removed Model Type Selection Method 

### THC 1 0 Mixed Minimize BIC

2 0 Mixed Minimize BIC 3 0 Mixed Minimize BIC 

### CO 1 0 Mixed Minimize BIC

2 0 Mixed Minimize BIC 3 0 Mixed Minimize BIC 

### NOx 1 0 Mixed Minimize BIC

2 0 Mixed Minimize BIC 3 0 Tobit Backwards elimination 

### PM 1 2 Tobit Backwards elimination

2 1 Tobit Backwards elimination 3 1 Tobit Backwards elimination 

### NMOG 1 0 Mixed Minimize BIC

2 0 Tobit Backwards elimination 3 0 Tobit Backwards elimination CH4 1 0 Mixed Backwards elimination

2 0 Mixed Backwards elimination 3 0 Mixed Backwards elimination**Table E.**  **2. THC:		Reduced	Models,	starting	from	16**  **- term	full	model.**  

### Model term Notation Bag 1 Bag 2 Bag 3 Intercept Intercept -0.8658
-4.9092
-4.2300 etOH 

### Z e 0.06793 0.06814 0.007879 Arom 

### Z a 0.08343
-0.02281
-0.06120 RVP 

### Z r -0.04669
-0.01423 T50 

### Z 5 0.1490
-0.03953 0.03595 T90 

### Z 9 0.01435 0.07154 0.04904 etOH × etOH 

### ZZ ee 0.04065 0.06681 T50 × T50 

### ZZ 55 0.07555 etOH × Arom 

### ZZ ea 0.02297 0.03054 etOH × RVP 

### ZZ er 0.01666 etOH × T50 

### ZZ e5 0.03426 0.04028
-0.03125 etOH × T90 

### ZZ e9 0.04782 Arom × RVP 

### ZZ ar Arom × T50 

### ZZ a5 0.03386 Arom × T90 

### ZZ a9 0.02264 T50 × T90 

### ZZ 59 0.02886 RVP × T90 

### ZZ r9 **Table E.**  **3. NMOG:		Reduced	Models,	starting	from	16**  **- term	full	model.**  

### Model term Notation Bag 1 Bag 2 Bag 3 Intercept Intercept 0.951 3
- 5.51 66 1

- 5.8449 1 etOH 

### Z e 0.09272 0.0730 0.0339 Arom 

### Z a 0.1051 0.0355 RVP 

### Z r -0.04834
-0.0463
-0.0572 T50 

### Z 5 0.1541 0.0859 0.0783 T90 

### Z 9 0.01124 0.1091 0.1467 etOH × etOH 

### ZZ ee 0.04204
-0.0424 T50 × T50 

### ZZ 55 0.07866 0.0412 etOH × Arom 

### ZZ ea 0.02171 0.0718 etOH × RVP 

### ZZ er -0.0313 0.0707 etOH × T50 

### ZZ e5 0.03576
-0.0728 etOH × T90 

### ZZ e9 0.04763 Arom × RVP 

### ZZ ar 0.02724 Arom × T50 

### ZZ a5 0.0738 Arom × T90 

### ZZ a9 0.02049 0.0327 T50 × T90 

### ZZ 59 0.05437 0.0293 RVP × T90 

### ZZ r9 1 Not fit by Tobit model; calculated manually from intercepts for individual vehicles.**Table E.**  **4. CH**  **4 :		Reduced	Models,	starting	from	16**  **- term	full	model.**  

### Model term Notation Bag 1 Bag 2 Bag 3 Intercept Intercept
- 3.0068
- 5.7076
-4.5979 etOH 

### Z e 0.08877 0.06076 0.03187 Arom 

### Z a -0.09816
-0.09211
-0.1004 RVP 

### Z r -0.02455
-0.02082 T50 

### Z 5 0.1059 0.04477 0.01886 T90 

### Z 9 0.008573 0.02445 0.01856 etOH × etOH 

### ZZ ee 0.03133 T50 × T50 

### ZZ 55 0.05882 0.01398 etOH × Arom 

### ZZ ea 0.03977 0.01047 etOH × RVP 

### ZZ er etOH × T50 

### ZZ e5 0.02883
-0.02007 etOH × T90 

### ZZ e9 0.02655 Arom × RVP 

### ZZ ar 0.02791 Arom × T50 

### ZZ a5 0.02585 Arom × T90 

### ZZ a9 0.03072 T50 × T90 

### ZZ 59 0.0228 0.01374 RVP × T90 

### ZZ r9 -0.00992
**Table E.**  **5. CO:	Reduced	Models,	starting	from	16**  **- term	full	model.**  

### Model term Notation Bag 1 Bag 2 Bag 3 Intercept Intercept 1.3472
- 1.3896
- 1.1409 etOH Z e -0.06967
-0.08154 Arom Z a -0.01156 0.09798 0.07191 RVP Z r 0.02063 0.02838 0.02393 T50 Z 5 0.02159 0.02486 T90 Z 9 -0.1469 0.04180 0.05781 etOH × etOH ZZ ee 0.08535 T50 × T50 ZZ 55 0.07222 etOH × Arom ZZ ea 0.06244 etOH × RVP ZZ er etOH × T50 ZZ e5 0.1117 etOH × T90 ZZ e9 Arom × RVP ZZ ar Arom × T50 ZZ a5 Arom × T90 ZZ a9 0.03861 T50 × T90 ZZ 59 0.02177 RVP × T90 

### ZZ r9**Table E.6**  **. NOx:	Reduced	Models,	starting	from	16**  **- term	full	model.**  

### Model term Notation Bag 1 Bag 2 Bag 3 Intercept Intercept
- 3.01636
-4.7882
- 5.2554 etOH 

### Z e 0.0 3802 0.04112 0.0884 Arom 

### Z a 0.1336 0.03534 0.0667 RVP 

### Z r -0.01418
-0.01464 0.169 T50 

### Z 5 0.01026
-0.0224 T90 

### Z 9 0.02389
-0.0004567 0.085 etOH × etOH 

### ZZ ee -0.05980 T50 × T50 

### ZZ 55 -0.05701 etOH × Arom 

### ZZ ea -0.03038 0.02739 etOH × RVP 

### ZZ er etOH × T50 

### ZZ e5 -0.9774 0.0637 etOH × T90 

### ZZ e9 0.02544 Arom × RVP 

### ZZ ar Arom × T50 

### ZZ a5 0.0894 Arom × T90 

### ZZ a9 -0.04769 T50 × T90 

### ZZ 59 RVP × T90 

### ZZ r9 0.04562
-0.04014 **Table E.**  **7. PM:	Reduced	models,	starting	from	16**  **- term	full	model.**  

### Model term Notation Bag 1 Bag 2 Bag 3 Intercept etOH 

### Z

e 0.1640 0.1158
-0.02120 Arom 

### Z

a 0.3795 0.1988 0.01860 RVP 

### Z

r -0.1275 T50 

### Z

5 0.06650
-0.00370
-0.04110 T90 

### Z

9 0.2882 0.09530 etOH × etOH 

### ZZ ee T50 × T50 

### ZZ 55 0.08560 etOH × Arom 

### ZZ ea 0.08490 etOH × RVP 

### ZZ er etOH × T50 

### ZZ e5 -0.08240 etOH × T90 

### ZZ e9 Arom × RVP 

### ZZ ar -0.1062 Arom × T50 

### ZZ a5 Arom × T90 

### ZZ a9 T50 × T90 

### ZZ 59 0.1059 RVP × T90 

### ZZ r9