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**Assessing	the	Effect	of	Five	Gasoline	Properties	on	Exhaust	Emissions	from	Light******

**Duty	Vehicles	certified	to	Tier -**  **2	Standards Analysis**  **of	Data	from	EPA	Phase	3 (EPAct/V2/E**  **- 89)** 


## Appendix **G.5 Final	Model	Fitting**  **Oxides	of	Nitrogen (**  **NO x** 

## )	( **Bag	3 )** 

No. Observations: 931 No. Vehicles: 15 No. censored measurements: 25 No. missing measurements: 2 No. measurements removed: 1 Model Ty pe: Tobit regression

### 2

**G.5 .1		Model	Fitting	based	on	the	11**  **- term	design	model.** 

**Models fit for NO** **x** 

### (**Bag 3 ): (Grand Intercept not fit by Tobit models).**  Model Term Notation Model Full FM2 1 

### FM3 FM4 FM5 FM6 FM7 etOH Z

e ● ● ● ● ● ● ● 

### Arom Z

a ● ● ● ● ● ● ● 

### RVP Z

r ● ● ● ● ● ● ● 

### T50 Z

5 ● ● ● ● ● ● 

### × T90 Z

9 ● ● ● ● ● ● ● 

### etOH × etOH ZZ ee ● 

### × T50 × T50 ZZ 55 ● ● ● ● 

### × etOH × Arom ZZ ea ● ● ● 

### × etOH × RVP ZZ er ● 

### × etOH × T50 ZZ e5 ● ● ● ● ● 

### × etOH × T90 ZZ e9 ● ● 

### × 1 Indicates “Full minus 2,” etc.


### NO**x** 

### (**Bag 3 ): Model fitting history, starting with the**  **11 -** **term design model.**



### Fit Parameters Test with respect to Previous Model 

### Model p- 1 1



### -2 ln L Dev. d Pr>χ 2 

### Full Model 11 2809.349 FM2 9 2809.676 0.327 2 0.849 FM3 8 2810.499 0.823 1 0.364 FM4 7 2811.808 1.309 1 0.253 FM5 6 2813.571 1.763 1 0.184 FM6 5 2815.925 2.354 1 0.125 FM7 4 2817.195 1.270 1 0.260

1 Total number of terms excludes the intercept, as the Tobit models do not fit intercepts. 2 Best fit with respect to the 16

-term extended model.

### 3

**NO x**  

### (**Bag 3 ):**  **Co efficients and Tests of Effect for the**  **Full and Reduced Models, with respect to the**  **1 1**  **- term**  **design model.**  

### Ef fe ct Fu ll Model Reduced Model (F M7) Es ti mate St d.E

rr. d. f. χ2 - v al

ue Pr>χ2 Es ti

mate St d.E

rr. d. f. χ

2 - v al ue Pr>χ

2 Intercept 1 -5.2561 Z e 0.06820 0.05120 1 1.77 0.18 0.1078 0.0348 1 9.59 0.0020 Z a 0.06770 0.03570 1 3.59 0.058 0.0816 0.0350 1 5.42 0.020 Z r 0.11760 0.04080 1 8.30 0.0040 0.1477 0.0356 1 17.2 <0 .0001 Z 5 -0.05780 0.05140 1 1.26 0.26 Z 9 0.06850 0.03570 1 3.68 0.055 0.0601 0.0353 1 2.90 0.089 ZZ ee -0.01240 0.06870 1 0.03 0.86 ZZ 55 0.05010 0.05150 1 0.95 0.33 ZZ ea -0.04210 0.03490 1 1.45 0.23 ZZ er -0.02020 0.03570 1 0.32 0.57 ZZ e5 0.06420 0.07380 1 0.76 0.38 ZZ e9 0.03450 0.03510 1 0.97 0.33

1.7619

1.05310 1.05750 1 Notfi t by T obitmodel; calculat ed manually from indi vidual vehicle int ercep ts
. 1 2 veh 

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2  

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**G.5 .2	Model	Fitting	based	on	the	16**  **- term	extended	model.** 

**Models fit for NO** **x** 

### (**Bag 3 ): (Grand Intercept not fit by**  **Tobit models).** Model Term Notation Model Full FM4 1 

### FM5 FM6 FM7 FM8 FM9 etOH Z

e ● ● ● ● ● ● ● 

### Arom Z

a ● ● ● ● ● ● ● 

### RVP Z

r ● ● ● ● ● ● ● 

### T50 Z

5 ● ● ● ● ● ● ● 

### T90 Z

9 ● ● ● ● ● ● ● 

### etOH × etOH ZZ ee ● 

### × T50 × T50 ZZ 55 ● ● ● ● ● ● 

### × etOH × Arom ZZ ea ● ● 

### × etOH × RVP ZZ er ● ● ● ● 

### × etOH × T50 ZZ e5 ● ● ● ● ● ● ● 

### etOH × T90 ZZ e9 ● ● ● 

### × T90 × T90 ZZ 99 ● ● ● ● ● ● ● 

### Arom × RVP ZZ ar ● 

### × Arom × T50 ZZ a5 ● ● ● ● ● ● ● 

### Arom × T90 ZZ a9 ● ● ● ● ● 

### × T50 × T90 ZZ 59 ● 

### × RVP × T90 ZZ r9 ● 

### ×

**NO x**  

### (**Bag 3 ): Model fitting history, starting with the**  **1 7** **- t** **erm extended**  **model.**



### Fit Parameters Test with respect to Previous Model 

### Model p- 1 1



### -2 ln L Dev. d Pr>χ 2 

### Full Model 16 2801.073 FM4 12 2801.869 0.796 4 0.939 FM5 11 2802.472 0.603 1 0.437 FM6 10 2803.337 0.865 1 0.352 FM7 9 2804.295 0.958 1 0.328 FM8 8 2806.313 2.018 1 0.155 FM9 7 2808.530 2.217 1 0.136

1 Total number of terms excludes the intercept, as the Tobit Models do not fit intercepts

. 2 Best fit with respect to the 1 7

-term extended model.

### 5

**NO x**  

### (**Bag 3 ):**  **Co efficients and Tests of Effect for the**  **Full and Reduced Models, with respect to the**  **1 6** **- term**  **extended model** **.** 

### Ef fe ct Fu ll Model Reduced Model (F M9) Es ti mate St d.E

rr. d. f. χ2 - v al

ue Pr>χ2 Es ti

mate St d.E

rr. d. f. χ

2 - v al ue Pr>χ

2 Intercept 1 -5.255 Z e 0. 0693 0.0616 1. 0000 1.26 0. 261 0.0884 0.0453 1 3.82 0.051 Z a 0. 0661 0.0387 1. 0000 2.92 0. 088 0.0667 0.0356 1 3.52 0.061 Z r 0. 1737 0.0520 1. 0000 11.1 0. 00080 0.1692 0.0420 1 16.2 <0.0001 Z 5 -0.0508 0.0686 1. 0000 0.55 0.46 -0.0224 0.0488 1 0.21 0. 65 Z 9 0. 1007 0.0398 1. 0000 6.39 0. 012 0.0850 0.0366 1 5.39 0.020 ZZ ee -0.0220 0.0718 1. 0000 0.09 0.76 ZZ 55 0. 0553 0.0586 1. 0000 0.89 0.34 ZZ ea 0. 0477 0.0581 1. 0000 0.67 0.41 ZZ er -0.0516 0.0394 1. 0000 1.72 0.19 ZZ e5 0. 0654 0.0758 1. 0000 0.74 0.39 0.0637 0.0358 1 3.16 0.075 ZZ e9 0. 0464 0.0466 1. 0000 0.99 0.32 ZZ ar 0. 0254 0.0630 1. 0000 0.16 0.69 ZZ a5 0. 1624 0.0701 1. 0000 5.36 0. 021 0.0894 0.0398 1 5.05 0.025 ZZ a9 -0.0444 0.0394 1. 0000 1.27 0.26 ZZ 59 0. 0226 0.0524 1. 0000 0.19 0.67 ZZ r9 0. 0300 0.0446 1. 0000 0.45 0.50
1.7509

1. 0486 1.0527 1 Notfitby T obi

t mo del. 1 2 veh 

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