# ADCO 2 

# Follow - up from April 14, 2011 Meeting

 

# Follow - up included the following:  

# In lieu of acceleration and TRLHP@50 mph as part of the ADCO 2 

# equation study:

 

# Total cycle energy

 

# Total cycle power

 

# F - term s (not officially requested)  

# In lieu of axle ratio as part of the ADCO 2 

# equation study N/V

Date: May 20, 2011 1 

#  

# In lieu of axle ratio as part of the ADCO 2 

# equation study N/V  

# Statistically,

 

# Total cycle and power models had “unacceptable” residuals in 5 of 6 cases

 

# F - term s (with ALVW test weight) produces best m odel fits to date

 

# Axle ratio (vs. N/V) improves mo del fit (perhaps due to the fact only top gear N/V was used for mo del building)

 

# Acceleration and TRLHP@50 mp h (vs. total cycle power or energy) still a good candidate mo del

 

# Fuel type indicator variable produces is NOT statistically significant and produces unacceptable residuals except when included in the model with the Acceleration and TRLHP@50 mp h variable 

#  

# The following slides support the follow - up

# EPA Bag 1

– Energy/Power Calculations

**EPA C**  **ycle - B ag**  **1**

20 40 60 80 100Speed(mph)orPower(kW) F2 50 D yno D ata at 8.5K (kW) Ve hic le Speed (m ph) Ca lc ulated P

ow er (k

W) - N ew M

ethod Ca lc ulated P

ow er (k

W) - Old Method



## Date: May 20, 2011 2 -60 -40 -20 0 0 100 200 300 400 500

Tim e (s ec )Speed(mph)orPower(kW)



## Total Pow **er Positive Time**  **Total Time** ALVW Class F0 F1 F2 Hp MJ Hp MJ Hp MJ kW -hr sec sec **8500** 54.67 1.6218 0.03708 Bag 1 17.4 3.8 14.8 3.3 32.2 7.1 296 505 Bag 2 11.7 4.3 5.7 2.1 17.4 6.3 489 867 Bag 3 17.4 3.8 14.8 3.3 32.2 7.1 296 505 Bag 4 (Hwy) 8.7 4.5 27.4 14.1 36.2 18.6 **5.18** 691 765 City (FTP 75) 49.5 13.4 **3.73 M-**  **H 43.5**  **15.8 4.38** 

**Inertia Roadload**  **Total Energy**

# EPA Bag 1

– 200 to 300 seconds

**EPA C**  **ycl e**  **- B ag**  **1**

60 80 100Speed(mph)orPower(kW) F2 50 D yn o D ata at 8.5K ( kW) Ve hic le Speed ( mp h) Ca lc ul ated P

ow er (k W) - N ew M ethod Ca lc ul ated P

ow er (k W) - O ld M ethod



## Date: May 20, 2011 3 -60 -40 -20 0 20 40

200 210 220 230 240 250 260 270 280 290 300

Tim e ( se c)Speed(mph)orPower(kW)

## 1 0 0 9 9 9 8 9 7 9 6 9 5 9 4 9 3 9 2 N o n T o t a l C y c l e P o w e r o r E n e r g y T o t a l C y c l e P o w e r o r E n e r g y 

# Model Evaluation Chart

[16] [15] [14] The ADCO 2 

# equation from April 14, 201 1 meeting 

# • Bracketed numbers are hypertext linked to the respective model

• Italic brackets [ ] represent Proposed ADCO 2 

# Model

Date: May 20, 2011 4 

# 5 4 3 2 1 9 2 9 1 9 0 8 9 8 8 8 7 8 6 8 5 8 4 8 3 8 2 8 1 8 0 

# T **e r**  **m s**  **i n**  **M o**  **d e**  **l R** **^ 2** **a d** **j** 

# [1] [2]

[3] [4] [5] [6] [7] [8] [1 1] [9] [10] [12] [13] • Italic brackets [ ] represent models with well - behaved residuals

# [1] Base CO 2 

# Model

The regression equation is 

# CO2 = **- 895 + 270 Axle Ratio + 3.12 Accel+TRLHP_50 mph**  Predictor Coef SE Coef T P VIF Constant - 894.55 92.34 - 9.69 0.000 Axle Ratio 270.02 23.24 11.62 0.000 

# 1.047 Accel+TRLHP_50 mph 3.1226 0.2398 13.02 0.000 

# 1.047 **S = 47.6565** R - Sq = 89.0% 

# R **- Sq(adj) = 88.5%** 

Date: May 20, 2011 5 1 0 0 5 0 0 - 5 0 - 1 0 0 - 1 5 0 9 9 9 5 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 5 1 **R E** **S I**  **1 P** **e r** **c e** **n t**  M e a n 3 . 5 3 3 2 0 9 E - 1 3 S t D e v 4 6 . 6 9 N 5 1 A D 0 . 4 6 4 P - V a l u e 0 . 2 4 5 

### P **r o**  **b a**  **b i**  **l i**  **t**

**y P**  **l o**  **t o**  **f R**  **E S**  **I 1**  N o r m a l 

# S = 47.6565 R - Sq = 89.0% 

# R **- Sq(adj) = 88.5%**  Analysis of Variance Source DF SS MS F P Regression 2 877854 438927 193.26 0.000 Residual Error 48 109015 2271 Total 50 986868 Source DF Seq SS Axle Ratio 1 492697 Accel+TRLHP_50 mph 1 385156

Model evaluation chart Residuals well - behaved

# [2] Base ln(CO 2 

# ) Model

The regression equation is 

# ln CO2 = 4.26 + 0.393 Axle Ratio + 0.00426 Accel+TRLHP_50 mph Predictor Coef SE Coef T P VIF Constant 4.2602 0.1145 37.21 0.000 Axle Ratio 0.39324 0.02881 13.65 0.000 

# 1.047 Accel+TRLHP_50 mph 0.0042604 0.0002973 14.33 0.000 

# 1.047 **S = 0.0590850** R - Sq = 91.2% 

# R **- Sq(adj) = 90.8%** 

Date: May 20, 2011 6 

# S = 0.0590850 R - Sq = 91.2% 

# R **- Sq(adj) = 90.8%**  Analysis of Variance Source DF SS MS F P Regression 2 1.73664 0.86832 248.73 0.000 Residual Error 48 0.16757 0.00349 Total 50 1.90421 Source DF Seq SS Axle Ratio 1 1.01968 Accel+TRLHP_50 mph 1 0.71697

0 . 1 5 0 . 1 0 0 . 0 5 0 . 0 0 - 0 . 0 5 - 0 . 1 0 - 0 . 1 5 9 9 9 5 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 5 1 

### R **E S**  **I 2** **P e** **r c** **e n** **t** M e a n - 1 . 0 4 4 9 2 E - 1 5 S t D e v 0 . 0 5 7 8 9 N 5 1 A D 0 . 4 2 7 P - V a l u e 0 . 3 0 1 

### P **r o**  **b a**  **b i**  **l i**  **t**

**y P**  **l o**  **t o**  **f R**  **E S**  **I 2**  N o r m a l



# Model evaluation chart Residuals well - behaved

# [3] CO 2 

# Model

– with N/V in lieu of Axle Ratio

The regression equation is 

# CO2 = **- 527 + 21.6 N/V + 3.41 Accel+TRLHP_50 mph**  48 cases used, 3 cases contain missing values Predictor Coef SE Coef T P VIF Constant - 526.66 80.19 - 6.57 0.000 N/V 21.587 2.360 9.15 0.000 

# 1.014 Accel+TRLHP_50 mph 3.4084 0.2715 12.56 0.000 

# 1.014

Date: May 20, 2011 7 

# S = 54.7812 R - Sq = 85.8% 

# R **- Sq(adj) = 85.2%**  Analysis of Variance Source DF SS MS F P Regression 2 815635 407817 135.89 0.000 Residual Error 45 135044 3001 Total 47 950679 Source DF Seq SS N/V 1 342552 Accel+TRLHP_50 mph 1 473083

1 0 0 5 0 0 - 5 0 - 1 0 0 - 1 5 0 9 9 9 5 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 5 1 

### R **E S**  **I 3** **P e** **r c** **e n** **t** M e a n - 1 . 4 2 1 0 9 E - 1 4 S t D e v 5 3 . 6 0 N 48 A D 0 . 2 4 4 P - V a l u e 0 . 7 5 1 

### P **r o**  **b a**  **b i**  **l i**  **t**

**y P**  **l o**  **t o**  **f R**  **E S**  **I 3**  N o r m a l



# Model evaluation chart Residuals well - behaved

# [4] ln(CO 2 

# ) Model

– with N/V in lieu of axle ratio

The regression equation is 

# ln CO2 = 4.82 + 0.0306 N/V + 0.00469 Accel+TRLHP_50 mph 48 cases used, 3 cases contain missing values Predictor Coef SE Coef T P VIF Constant 4.8188 0.1095 43.99 0.000 N/V 0.030574 0.003223 9.49 0.000 

# 1.014 Accel+TRLHP_50 mph 0.0046905 0.0003708 12.65 0.000 

# 1.014

Date: May 20, 2011 8 

# S = 0.0748206 R - Sq = 86.2% 

# R **- Sq(adj) = 85.6%**  Analysis of Variance Source DF SS MS F P Regression 2 1.57773 0.78886 140.92 0.000 Residual Error 45 0.25192 0.00560 Total 47 1.82964 Source DF Seq SS N/V 1 0.68179 Accel+TRLHP_50 mph 1 0.89594

0 . 2 0 . 1 0 . 0 - 0 . 1 - 0 . 2 9 9 9 5 9 0 8 0 7 0 6 0 5 0 40 3 0 2 0 1 0 5 1 **R E** **S I**  **4 P** **e r** **c e** **n t**  M e a n 9 . 2 5 1 8 5 9 E - 1 7 S t D e v 0 . 0 7 3 2 1 N 4 8 A D 0 . 2 5 2 P - V a l u e 0 . 7 2 4 

### P **r o**  **b a**  **b i**  **l i**  **t**

**y P**  **l o**  **t o**  **f R**  **E S**  **I 4**  N o r m a l



# Model evaluation chart Residuals well - behaved

# [5] CO 2 

# Model

– with N/V and Total Cycle Power

The regression equation is 

# CO2 = **- 302 + 15.1 N/V + 11.7 Total Cycle Power (Hp)**  48 cases used, 3 cases contain missing values Predictor Coef SE Coef T P VIF Constant - 301.62 64.96 - 4.64 0.000 N/V 15.106 2.202 6.86 0.000 

# 1.108 Total Cycle Power (Hp) 11.6857 0.8077 14.47 0.000 

# 1.108

Date: May 20, 2011 9 

# S = 48.8992 R - Sq = 88.7% 

# R **- Sq(adj) = 88.2%**  Analysis of Variance Source DF SS MS F P Regression 2 843078 421539 176.29 0.000 Residual Error 45 107601 2391 Total 47 950679 Source DF Seq SS N/V 1 342552 Total Cycle Power (Hp) 1 500526

1 0 0 5 0 0 - 5 0 - 1 0 0 9 9 9 5 9 0 8 0 7 0 6 0 5 0 40 3 0 2 0 1 0 5 1 **R E**  **S I**  **5 P** **e r** **c e** **n t**  M e a n - 2 . 6 4 0 8 5 E - 1 3 S t D e v 4 7 . 8 5 N 4 8 A D 0 . 7 3 0 P - V a l u e 0 . 0 5 3 

### P **r o**  **b a**  **b i**  **l i**  **t**

**y P**  **l o**  **t o**  **f R**  **E S**  **I 5**  N o r m a l



# Model evaluation chart Residuals NOT well - behaved

# [6] ln(CO 2 

# ) Model

– with N/V and Total Cycle Power

The regression equation is 

# ln CO2 = 5.14 + 0.0220 N/V + 0.0157 Total Cycle Power (Hp) 48 cases used, 3 cases contain missing values Predictor Coef SE Coef T P VIF Constant 5.13789 0.09833 52.25 0.000 N/V 0.021995 0.003333 6.60 0.000 

# 1.108 Total Cycle Power (Hp) 0.015681 0.001223 12.83 0.000 

# 1.108 **S = 0.0740171 R**  **- Sq(adj) = 85.9%** 

Date: May 20, 2011 10 

# S = 0.0740171 R - Sq = 86.5% 

# R **- Sq(adj) = 85.9%**  Analysis of Variance Source DF SS MS F P Regression 2 1.58311 0.79155 144.48 0.000 Residual Error 45 0.24653 0.00548 Total 47 1.82964

0 . 2 0 . 1 0 . 0 - 0 . 1 - 0 . 2 9 9 9 5 9 0 8 0 7 0 6 0 5 0 40 3 0 2 0 1 0 5 1 **R E**  **S I**  **6 P** **e r** **c e** **n t**  M e a n - 5 . 9 2 1 1 9 E - 1 6 S t D e v 0 . 0 7 24 3 N 4 8 A D 0 . 8 1 2 P - V a l u e 0 . 0 3 3 

### P **r o**  **b a**  **b i**  **l i**  **t**

**y P**  **l o**  **t o**  **f R**  **E S**  **I 6**  N o r m a l



# Model evaluation chart Residuals NOT well - behaved

# [7] CO 2 

# Model

– with N/V and Total Cycle Energy *

The regression equation is 

# CO2 = **- 196 + 13.3 N/V + 106 Total Cycle Energy (kW**  **- hr)**  48 cases used, 3 cases contain missing values Predictor Coef SE Coef T P VIF Constant - 195.98 73.18 - 2.68 0.010 N/V 13.262 2.609 5.08 0.000 

# 1.163 Total Cycle Energy (kW - hr) 105.961 8.792 12.05 0.000 

# 1.163 **S = 56.5388 R**  **- Sq(adj) = 84.2%** 

Date: May 20, 2011 11 

# S = 56.5388 R - Sq = 84.9% 

# R **- Sq(adj) = 84.2%**  Analysis of Variance Source DF SS MS F P Regression 2 806830 403415 126.20 0.000 Residual Error 45 143849 3197 Total 47 950679

1 0 0 5 0 0 - 5 0 - 1 0 0 - 1 5 0 9 9 9 5 9 0 8 0 7 0 6 0 5 0 40 3 0 2 0 1 0 5 1 **R E**  **S I**  **7 P** **e r** **c e** **n t**  M e a n - 1 . 8 5 9 2 5 E - 1 3 S t D e v 5 5 . 3 2 N 4 8 A D 0 . 8 5 0 P - V a l u e 0 . 0 2 7 

### P **r o**  **b a**  **b i**  **l i**  **t**

**y P**  **l o**  **t o**  **f R**  **E S**  **I 7**  N o r m a l



## * 

# Note: T otal Cycle Energy in [kW - hr] Model evaluation chart Residuals NOT well - behaved

# [8] ln(CO 2 

# ) Model

– with N/V and Total Cycle Energy *

The regression equation is 

# ln CO2 = 5.28 + 0.0197 N/V + 0.140 Total Cycle Energy (kW **- hr)**  48 cases used, 3 cases contain missing values Predictor Coef SE Coef T P VIF Constant 5.2825 0.1112 47.49 0.000 N/V 0.019717 0.003966 4.97 0.000 

# 1.163 Total Cycle Energy (kW - hr) 0.14043 0.01336 10.51 0.000 

# 1.163 **S = 0.0859402 R**  **- Sq(adj) = 81.0%** 

Date: May 20, 2011 12 

# S = 0.0859402 R - Sq = 81.8% 

# R **- Sq(adj) = 81.0%**  Analysis of Variance Source DF SS MS F P Regression 2 1.49729 0.74864 101.36 0.000 Residual Error 45 0.33236 0.00739 Total 47 1.82964

0 . 2 0 . 1 0 . 0 - 0 . 1 - 0 . 2 9 9 9 5 9 0 8 0 7 0 6 0 5 0 40 3 0 2 0 1 0 5 1 **R E**  **S I**  **8 P** **e r** **c e** **n t**  M e a n - 1 . 0 1 7 7 0 E - 1 5 S t D e v 0 . 0 8 40 9 N 4 8 A D 0 . 8 1 0 P - V a l u e 0 . 0 3 4 

### P **r o**  **b a**  **b i**  **l i**  **t**

**y P**  **l o**  **t o**  **f R**  **E S**  **I 8**  N o r m a l



## * 

# Note: T otal Cycle Energy in [kW - hr] Model evaluation chart Residuals NOT well - behaved

# [9] CO 2 

# Model

– with Fuel indicator variable

The regression equation is 

# CO2 = **- 411 + 15.6 N/V + 3.55 Accel+TRLHP_50 mph + 53.4 Gas=1**  48 cases used, 3 cases contain missing values Predictor Coef SE Coef T P VIF Constant - 411.4 103.1 - 3.99 0.000 N/V 15.561 4.193 3.71 0.001 

# 3.340 Accel+TRLHP_50 mph 3.5481 0.2778 12.77 0.000 

# 1.108 Gas=1 53.36 30.99 1.72 0.092 

# 3.312

Date: May 20, 2011 13 

# S = 53.6231 R - Sq = 86.7% 

# R **- Sq(adj) = 85.8%**  Analysis of Variance Source DF SS MS F P Regression 3 824160 274720 95.54 0.000 Residual Error 44 126519 2875 Total 47 950679

1 0 0 5 0 0 - 5 0 - 1 0 0 - 1 5 0 9 9 9 5 9 0 8 0 7 0 6 0 5 0 40 3 0 2 0 1 0 5 1 **R E**  **S I**  **9 P** **e r** **c e** **n t**  M e a n - 2 . 1 4 3 4 7 E - 1 3 S t D e v 5 1 . 8 8 N 4 8 A D 0 . 6 3 1 P - V a l u e 0 . 0 9 4 

### P **r o**  **b a**  **b i**  **l i**  **t**

**y P**  **l o**  **t o**  **f R**  **E S**  **I 9**  N o r m a l



# Model evaluation chart Residuals NOT well - behaved

# [10] ln(CO 2 

# ) Model

– with Fuel indicator variable

The regression equation is 

# ln CO2 = 4.92 + 0.0253 N/V + 0.00481 Accel+TRLHP_50 mph + 0.0469 Gas=1 48 cases used, 3 cases contain missing values Predictor Coef SE Coef T P VIF Constant 4.9200 0.1436 34.25 0.000 N/V 0.025282 0.005839 4.33 0.000 

# 3.340 Accel+TRLHP_50 mph 0.0048132 0.0003869 12.44 0.000 

# 1.108 Gas=1 0.04686 0.04315 1.09 0.283 

# 3.312

Date: May 20, 2011 14 

# S = 0.0746721 R - Sq = 86.6% 

# R **- Sq(adj) = 85.7%**  Analysis of Variance Source DF SS MS F P Regression 3 1.58430 0.52810 94.71 0.000 Residual Error 44 0.24534 0.00558 Total 47 1.82964

0 . 2 0 . 1 0 . 0 - 0 . 1 - 0 . 2 9 9 9 5 9 0 8 0 7 0 6 0 5 0 40 3 0 2 0 1 0 5 1 **R E** **S I**  **1 0** **P e** **r c** **e n** **t** M e a n 4 . 9 9 6 0 0 4 E - 1 6 S t D e v 0 . 0 7 2 2 5 N 4 8 A D 0 . 3 9 2 P - V a l u e 0 . 3 6 5 

### P **r o**  **b a**  **b i**  **l i**  **t y**  **P l**  **o t**  **o f**  **R E**  **S I**  **1 0** 

N o r m a l



# Model evaluation chart Residuals well - behaved

# [11] CO 2 

# Model

– Model [7] + Fuel indicator variable

The regression equation is 

# CO2 = **- 238 + 12.0 N/V + 11.9 Total Cycle Power (Hp) + 26.8 Gas=1**  48 cases used, 3 cases contain missing values Predictor Coef SE Coef T P VIF Constant - 237.67 92.80 - 2.56 0.014 N/V 11.997 3.901 3.08 0.004 

# 3.471 Total Cycle Power (Hp) 11.8654 0.8294 14.31 0.000 

# 1.166 Gas=1 26.80 27.75 0.97 0.339 

# 3.190

Date: May 20, 2011 15 

# S = 48.9358 R - Sq = 88.9% 

# R **- Sq(adj) = 88.2%**  Analysis of Variance Source DF SS MS F P Regression 3 845312 281771 117.66 0.000 Residual Error 44 105367 2395 Total 47 950679

1 0 0 5 0 0 - 5 0 - 1 0 0 9 9 9 5 9 0 8 0 7 0 6 0 5 0 40 3 0 2 0 1 0 5 1 **R E** **S I**  **1 1** **P e** **r c** **e n** **t** M e a n - 2 . 5 2 2 4 3 E - 1 3 S t D e v 4 7 . 3 5 N 4 8 A D 1 . 0 7 0 P - V a l u e 0 . 0 0 8 

### P **r o**  **b a**  **b i**  **l i**  **t y**  **P l**  **o t**  **o f**  **R E**  **S I**  **1 1** 

N o r m a l



# Model evaluation chart Residuals NOT well - behaved

# [12] ln(CO 2 

# ) Model

– Model [8] + Fuel indicator variable

The regression equation is 

# ln CO2 = 5.16 + 0.0211 N/V + 0.0157 Total Cycle Power (Hp) + 0.0081 Gas=1 48 cases used, 3 cases contain missing values Predictor Coef SE Coef T P VIF Constant 5.1573 0.1419 36.35 0.000 N/V 0.021052 0.005964 3.53 0.001 

# 3.471 Total Cycle Power (Hp) 0.015736 0.001268 12.41 0.000 

# 1.166 Gas=1 0.00814 0.04243 0.19 0.849 

# 3.190

Date: May 20, 2011 16 

# S = 0.0748223 R - Sq = 86.5% 

# R **- Sq(adj) = 85.6%**  Analysis of Variance Source DF SS MS F P Regression 3 1.58331 0.52777 94.27 0.000 Residual Error 44 0.24633 0.00560 Total 47 1.82964

0 . 2 0 . 1 0 . 0 - 0 . 1 - 0 . 2 9 9 9 5 9 0 8 0 7 0 6 0 5 0 40 3 0 2 0 1 0 5 1 **R E** **S I**  **1 2** **P e** **r c** **e n** **t** M e a n 2 . 9 6 0 5 9 5 E - 1 6 S t D e v 0 . 0 7 2 3 9 N 4 8 A D 0 . 8 3 4 P - V a l u e 0 . 0 2 9 

### P **r o**  **b a**  **b i**  **l i**  **t y**  **P l**  **o t**  **o f**  **R E**  **S I**  **1 2** 

N o r m a l



# Model evaluation chart Residuals NOT well - behaved

# [13] CO 2 

# Model

– Coastdown terms + N/V + ALVW

The regression equation is 

# CO2 = **- 234 + 3.02 F0 + 29.9 F1 + 2195 F2 + 12.6 N/V + 0.0202 ALVW (test weight)**  48 cases used, 3 cases contain missing values Predictor Coef SE Coef T P VIF Constant - 234.25 78.88 - 2.97 0.005 F0 3.0208 0.6759 4.47 0.000 

# 3.679 F1 29.87 25.66 1.16 0.251 

# 1.703 F2 2195.2 266.0 8.25 0.000 

# 1.649 N/V 12.550 2.262 5.55 0.000 

# 1.696 Perhaps why drive type (e.g. 4x4) was not statistically significant

Date: May 20, 2011 17 

# N/V 12.550 2.262 5.55 0.000 

# 1.696 ALVW (test weight) 0.020197 0.007671 2.63 0.012 

# 3.956 **S = 40.5908** R - Sq = 92.7% 

# R **- Sq(adj) = 91.9%**  Analysis of Variance Source DF SS MS F P Regression 5 881479 176296 107.00 0.000 Residual Error 42 69200 1648 Total 47 950679

1 0 0 5 0 0 - 5 0 - 1 0 0 9 9 9 5 9 0 8 0 7 0 6 0 5 0 40 3 0 2 0 1 0 5 1 **R E** **S I**  **1 3** **P e** **r c** **e n** **t** M e a n - 2 . 3 9 2 1 6 E - 1 3 S t D e v 3 8 . 3 7 N 4 8 A D 0 . 7 5 4 P - V a l u e 0 . 0

4 6 

### P **r o**  **b a**  **b i**  **l i**  **t y**  **P l**  **o t**  **o f**  **R E**  **S I**  **1 3** 

N o r m a l



# Model evaluation chart Residuals NOT well - behaved

# [14] ln(CO 2 

# ) Model

– Coastdown terms + N/V + ALVW

The regression equation is 

# ln CO2 = 5.18 + 0.00510 F0 + 0.0534 F1 + 2.59 F2 + 0.0190 N/V

**+ 0.000023 ALVW (test weight)** 48 cases used, 3 cases contain missing values Predictor Coef SE Coef T P VIF Constant 5.1765 0.1078 48.02 0.000 F0 0.0051013 0.0009238 5.52 0.000 

# 3.679 F1 0.05342 0.03506 1.52 0.135 

# 1.703 Perhaps why drive type (e.g. 4x4) was not statistically significant

Date: May 20, 2011 18 

# F1 0.05342 0.03506 1.52 0.135 

# 1.703 F2 2.5869 0.3635 7.12 0.000 

# 1.649 N/V 0.018989 0.003091 6.14 0.000 

# 1.696 ALVW (test weight) 0.00002325 0.00001048 2.22 0.032 

# 3.956 **S = 0.0554768** R - Sq = 92.9% 

# R **- Sq(adj) = 92.1%**  Analysis of Variance Source DF SS MS F P Regression 5 1.70038 0.34008 110.50 0.000 Residual Error 42 0.12926 0.00308 Total 47 1.82964

0 . 1 5 0 . 1 0 0 . 0 5 0 . 0 0 - 0 . 0 5 - 0 . 1 0 9 9 9 5 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 5 1 **R E** **S I**  **1 4** **P e** **r c** **e n** **t** M e a n - 2 . 7 7 5 5 6 E - 1 6 S t D e v 0 . 0 5 2 4

4 N 4 8 A D 0 . 5 8 7 P - V a l u e 0 . 1 1 9 

### P **r o**  **b a**  **b i**  **l i**  **t**

**y P**  **l o**  **t o**  **f R**  **E S**  **I 1**  **4** N o r m a l



# Model evaluation chart Residuals near well - behaved

# [15] CO 2 

# Model

– Coastdown terms + Axle Ratio + ALVW

The regression equation is 

# CO2 = **- 570 + 2.18 F0 + 37.4 F1 + 2257 F2 + 189 Axle Ratio**  **+ 0.0222 ALVW (test weight)** Predictor Coef SE Coef T P VIF Constant - 569.73 76.85 - 7.41 0.000 F0 2.1773 0.3921 5.55 0.000 

# 2.699 F1 37.36 18.54 2.01 0.050 

# 1.621 F2 2257.1 184.3 12.25 0.000 

# 1.416 Axle Ratio 189.47 18.63 10.17 0.000 

# 1.650

Date: May 20, 2011 19 

# ALVW (test weight) 0.022198 0.004725 4.70 0.000 

# 2.681 **S = 30.4499** R - Sq = 95.8% 

# R **- Sq(adj) = 95.3%**  Analysis of Variance Source DF SS MS F P Regression 5 945144 189029 203.87 0.000 Residual Error 45 41724 927 Total 50 986868

5 0 0 - 5 0 - 1 0 0 9 9 9 5 9 0 8 0 7 0 6 0 5 0 40 3 0 2 0 1 0 5 1 **R E** **S I**  **1 5** **P e** **r c** **e n** **t** M e a n 1 . 6 1 6 1 3 6 E - 1 3 S t D e v 2 8 . 8 9 N 5 1 A D 0 . 5 5 0 P - V a l u e 0 . 1 4 9 

### P **r o**  **b a**  **b i**  **l i**  **t y**  **P l**  **o t**  **o f**  **R E**  **S I**  **1 5** 

N o r m a l



# Model evaluation chart Residuals well - behaved

# [16] ln(CO 2 

# ) Model

– Coastdown terms + Axle Ratio + ALVW

The regression equation is 

# ln CO2 = 4.66 + 0.00348 F0 + 0.0631 F1 + 2.71 F2 + 0.290 Axle Ratio

**+ 0.000029 ALVW (test weight)** Predictor Coef SE Coef T P VIF Constant 4.65906 0.09337 49.90 0.000 F0 0.0034826 0.0004763 7.31 0.000 

# 2.699 F1 0.06310 0.02253 2.80 0.007 

# 1.621 F2 2.7147 0.2239 12.13 0.000 

# 1.416 Axle Ratio 0.28956 0.02264 12.79 0.000 

# 1.650

Date: May 20, 2011 20 

# ALVW (test weight) 0.00002887 0.00000574 5.03 0.000 

# 2.681 **S = 0.0369938** R - Sq = 96.8% 

# R **- Sq(adj) = 96.4%**  Analysis of Variance Source DF SS MS F P Regression 5 1.84263 0.36853 269.28 0.000 Residual Error 45 0.06158 0.00137 Total 50 1.90421

0 . 1 0 0 . 0 5 0 . 0 0 - 0 . 0 5 - 0 . 1 0 9 9 9 5 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 5 1 **R E** **S I**  **1 6** **P e** **r c** **e n** **t** M e a n - 1 . 1 8 4 2 4 E - 1 5 S t D e v 0 . 0 3 5 1 0 N 5 1 A D 0 . 2 8 3 P - V a l u e 0 . 6 2 1 

### P **r o**  **b a**  **b i**  **l i**  **t**

**y P**  **l o**  **t o**  **f R**  **E S**  **I 1**  **6** N o r m a l



# Model evaluation chart Residuals well - behaved

# [16] ln(CO 2 

# ) Model

– Coastdown terms + Axle Ratio + ALVW

7 . 0 6 . 9 6 . 8 S 0 . 0 3 5 4 5 1 8 R - S q 9 6 . 8 % R - S q ( a d j ) 9 6 . 7 % R e g r e s s i o n 9 0 % P I 1 1 0 0 1 0 0 0 9 0 0 C O 2 L o w e r 9 0 % P I U p p e r 9 0 % P I V a r i a b l e 

# 90% Prediction Intervals for ln(CO 2 

# ) 90% Prediction Intervals for CO 2

Date: May 20, 2011 21 7 . 0 6 . 9 6 . 8 6 . 7 6 . 6 6 . 5 6 . 4 6 . 3 6 . 2 6 . 1 6 . 7 6 . 6 6 . 5 6 . 4 6 . 3 6 . 2 6 . 1 **l n**  **( C** **O 2**  **) F**  **i t**  **s f**  **r o**  **m M**  **o d**  **e l**  **[ 1**  **6 ]** **l n** **( C** **O 2** **)**

1 1 0 0 1 0 0 0 9 0 0 8 0 0 7 0 0 6 0 0 5 0 0 4 0 0 9 0 0 8 0 0 7 0 0 6 0 0 5 0 0 4 0 0 **C O**  **2 F**  **i t**  **s f**  **r o**  **m M**  **o d**  **e l**  **[ 1**  **6 ]** **C O** **2 A** **c t** **u a** **l**

# Application of Model to Analytical Adjustment

**Best Candidate Model: CO2 =**  **- 570 + 2.18 F0 + 37.4 F1 + 2257 F2 + 189**  **Axle Ratio + 0.0222 ALVW (test weight) Subscript**  **[1]**  **Input for Original data point** 

Date: May 20, 2011 22 

# Subscript **[1]**  **Input for Original data point**  **Subscript [2]**   **Input for Data Point to be determined**  **Analytically** 

# CO2[2] = CO2[1] + 2.18(F0[2] **- F0[1])**  **+ 37.4(F1[2] -**  **F1[1]) + 2257(F2[2] -**  **F2[1]) + 189(AR[2]**  **- AR[1])+ 0.0222(ALVW[2]**  **- ALVW[1])** 

New for June 28, 201 1

# Additional Requested Analysis

– Diesel vs. Gas  

# Sufficient data was not available to generate separate accurate and statistically well behaved models for Diesel and gas  

# This question should be revisited as more data becomes available

Date: May 20, 2011 23 

#  

# A Diesel versus gas indicator was tested as a potential input to the combined model, but did not improve the model  

# Likely because other inputs already being used (axle ratio, ALVW) correlate well and work as a surrogate for Diesel/Gas

New for June 28, 201 1

# Additional Requested Analysis

– City and Highway  

# Separate models were generated for city and highway  

# Both models fit the data well and are statistically well behaved, particularly for the ln(CO2)  

# Results appear on next two slides

Date: May 20, 2011 24 

#  

# Results appear on next two slides  

# While these models are useful for development purposes, Ford recommends use of single combined city/highway model for purposes of AD CO2  

# Aligns with exact regulatory requirement for input to fleet average calculation  

# Avoids added variability associated with combining results of two models with associated uncertainties

New for June 28, 201 1

# EPA City CO 2 

# Model

The regression equation is 

## EPA City ln(CO2) = 5.04 + 0.000041 ALVW + 0.247 Axle Ratio + 0.00324 F0 + 0 F1 + 1.03 F2 Predictor Coef SE Coef T P VIF Constant 5.04190 0.09970 50.57 0.000 ALVW (test weight) 0.00004090 0.00000577 7.09 0.000 2.084 Axle Ratio 0.24715 0.02519 9.81 0.000 1.574 F0 0.0032426 0.0005204 6.23 0.000 2.482 F2 1.0307 0.2444 4.22 0.000 1.300 S = 0.0421408 R - Sq = 94.3% R - Sq(adj) = 93.8% **F i**  **t t**  **e d**  **L i**  **n e**  **P l**  **o t**  

# F1 coefficient not statistically significant so set to 0.

Date: May 20, 2011 25 Analysis of Variance Source DF SS MS F P Regression 4 1.34536 0.33634 189.40 0.000 Residual Error 46 0.08169 0.00178 Total 50 1.42705 Source DF Seq SS ALVW (test weight) 1 0.68374 Axle Ratio 1 0.56211 F0 1 0.06792 F2 1 0.03158

7 . 1 7 . 0 6 . 9 6 . 8 6 . 7 6 . 6 6 . 5 6 . 4 6 . 3 7 . 1 7 . 0 6 . 9 6 . 8 6 . 7 6 . 6 6 . 5 6 . 4 6 . 3 **C**

**i t**  **y M**  **o d**  **e l**  **F i**  **t t**  **e d**  **V a**  **l u**  **e s**  **l n**  **( C**  **O 2**  **) E** **P A** **C i** **t y** **l n** **( C** **O 2** **)** S 0 . 0 4 0 8 3 0 4 R - S q 9

4 . 3 % R - S q ( a dj ) 9

4 . 2 % 

## F **i t**  **t e**  **d L**  **i n**  **e P**  **l o**  **t** E P A C i t y l n ( C O 2) = - 0 . 00 00 + 1 . 00 0 FI

TS 4



# New for June 28, 201 1

## The regression equation is



## EPA Hwy ln(CO2) = 4.06 + 0.000015 ALVW + 0.363 Axle Ratio + 0.00358 F0 + 0.128 F1 + 5.34 F2 Predictor Coef SE Coef T P VIF Constant 4.0582 0.1123 36.14 0.000 ALVW (test weight) 0.00001470 0.00000690 2.13 0.039 2.681 Axle Ratio 0.36266 0.02723 13.32 0.000 1.650 F0 0.0035836 0.0005728 6.26 0.000 2.699 F1 0.12846 0.02709 4.74 0.000 1.621 F2 5.3381 0.2692 19.83 0.000 1.416 S = 0.0444883 R - Sq = 97.2% R - Sq(adj) = 96.9% 

# EPA Highway CO 2 

# Model

**F i**  **t t**  **e d**  **L i**  **n e**  **P l**  **o t** 



## Date: May 20, 2011 26 S = 0.0444883 R - Sq = 97.2% R - Sq(adj) = 96.9% Analysis of Variance Source DF SS MS F P Regression 5 3.13995 0.62799 317.29 0.000 Residual Error 45 0.08906 0.00198 Total 50 3.22901 Source DF Seq SS ALVW (test weight) 1 0.83867 Axle Ratio 1 1.47374 F0 1 0.04766 F1 1 0.00181 F2 1 0.77808 6 . 8 6 . 6 6 . 4 6 . 2 6 . 0 6 . 8 6 . 6 6 . 4 6 . 2 6 . 0

**H**

**w y**  **M o**  **d e**  **l F**  **i t** **t e** **d V**  **a l**  **u e** **s l**  **n (**  **C 0** **2 )** **E P** **A H** **w y** **l n** **( C** **O 2** **)** S 0 . 0 4 2 6 33 8 R - S q 9

7 . 2 % R - S q ( a dj ) 9

7 . 2 % 

## F **i t**  **t e**  **d L**  **i n**  **e P**  **l o**  **t** E P A H w y l n ( C O 2) = 0 . 00 00 + 1 . 00 0 FI

TS 6



# New for June 28, 201 1