Calspan
Technical Report
STUDY TO DETERMINE EMISSION DETERIORA TION
FROM EMISSION FACTOR PROGRAM DA TA
TASK III FINAL REPORT
Calspan Report No. NA-5542-V-3
Calspan Corporation
Buffalo, New York 14221
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Calspan
STUDY TO DETERMINE EMISSION DETER/OR A TION
FROM EMISSION FACTOR PROGRAM DA TA
TASK III FINAL REPORT
Calspan Report No. NA-5542-V-3
Prepared for:
ENVIRONMENTAL PROTECTION AGENCY
NATIONAL ENVIRONMENTAL RESEARCH CENTER
CINCINNATI, OHIO 45268
SEPTEMBER 1976
CONTRACT NO. 68-03-0486
FINAL REPORT
Prepared by: Approved by: AjhiXLC. *
A.C. Keller, Task Engineer M.W. Hall, Head
Systems Evaluation Dept. Systems Evaluation Dept.
Calspan Corporation
Buffalo, New York 14221
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EPA-420-R-76-108
This report was furnished to the Environmental Protection
Agency by Calspan Corporation, in fulfillment of Task III of
Contract No. 68-03-0486. The opinions, findings, and conclusions
expressed are those of the author and not necessarily those of
the Environmental Protection Agency.
ii
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ABSTRACT
This report on emission deterioration was prepared for the
Environmental Protection Agency, Emission Control Technology Division,
Ann Arbor, Michigan, under EPA Contract No. 68-03-0486. The purpose
of this study is to estimate emission deterioration of in-use vehicles
as they accumulate age and mileage. The analysis uses data collected
on vehicles tested in the FY 71, FY 72, and FY 73 Emission Factor
Programs.
This study assesses the differences in deterioration rates
between (a) Model years, over the three fiscal years, (b) Fiscal years,
for a specified model year, (c) Fiscal years, over all model years, and
(d) Test sites, for a specific model year. This study also includes
investigations to determine the best form of the deterioration curve
and the most appropriate independent variable, age or mileage. Changes
in the SDS Modal Emissions Model as related to mileage are also evaluated.
This report reviews the problems of predicting emissions with
available EFP data, including the statistical and engineering significance
of the predictions, the danger of extrapolating beyond age and/or mileage
ranges, and the shortcomings of the EFP format for predictive purposes.
iii
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ACKNOWLEDGEMENTS
Support and encouragement by the Environmental Protection
Agency are gratefully acknowledged. Particular thanks go to
Lois A. Platte for her guidance and suggestions.
A number of individuals at Calspan Corporation contributed
significantly to this effort. These include William R. Fairchild and
Jeffrey C. Bernard, who performed the computer analysis, and H.T. McAdams
who provided guidance and helpful comments throughout the entire program.
iv
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TABLE OF CONTENTS
Section Title Page
1 INTRODUCTION 1
1.1 Background 1
1.2 Purpose and General Approach 2
2 SUMMARY 3
2.1 Choice of Deterioration Curve Form and
Independent Variable 3
2.2 Deterioration Analysis Results -- FTP Data .... 3
2.3 Deterioration Analysis Results — SDS Data .... 5
2.4 Problems and Recommendations 5
3 DETERIORATION ANALYSIS 7
3.1 Data 7
3.2 Data Analysis and Statistical Tests 7
3.3 Form of the Deterioration Curves 9
3.4 Independent Variable Investigation 18
4 DETERIORATION ANALYSIS RESULTS 23
4.1 FTP Data Analysis 23
4.1.1 Model Year Effects 24
4.1.2 EFP Fiscal Year Effects for a Given
Model Year 24
4.1.3 EFP Fiscal Year Effects for all Model Years. 28
4.1.4 Test Site Effects 28
4.1.5 CID Effects 28
4.1.6 Mileage Accumulation Rate Effects 34
4.2 SDS Data Analysis 34
4.2.1 Observed Bag Values -- Model Year and
Test Site Effects 34
4.2.2 Emission Deterioration as Reflected in the
Modal Emission Model Coefficients 42
4.2.3 Observed Idle Mode Bag yalues Changes
with Mileage 50
v
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TABLE OF CONTENTS (cont.)
Section Title Page
5 PROBLEMS AND RECOMMENDATIONS 53
5.1 Using EFP Data to Determine Historical Emission Trends . 53
5.2 Using EFP Deterioration Estimates to Predict Overall
Emission Levels 55
5.3 Using EFP Deterioration Estimates to Predict Emission
Levels of Individual Vehicles 58
5.4 Recommendations for Future Studies 58
REFERENCES 60
APPENDIX I T-TEST FOR THE EQUALITY OF TWO SLOPES 1-1
II LINEAR REGRESSION RESULTS FOR FTP DATA II-l
III LINEAR REGRESSION RESULTS FOR SDS BAG VALUE DATA
AND FOR SELECTED MODAL EMISSION MODEL PARAMETERS . . . . III-l
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LIST OF ILLUSTRATIONS
Figure Title Page
1 Linear and Quadratic HC vs. Mileage Regressions for 1971
Model Year Data 11
2 Linear and Quadratic CO vs. Mileage Regressions for 1971
Model Year Data 12
3 Linear and Quadratic NOXC vs. Mileage Regressions for 1971
Model Year Data 13
4 Linear and Quadratic HC vs. Age Regressions for 1971
Model Year Data 14
5 Linear and Quadratic CO vs. Age Regressions for 1971
Model Year Data IS
6 Linear and Quadratic NOXC vs. Age Regressions for 1971
Model Year Data 16
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LIST OF TABLES
Table Title Page
1 Comparison of Linear and Quadratic Models of
Emission Deterioration 17
2 Correlation Matrix for 1971 Model Year Emissions 20
3 Stepwise Regression Results; Significant Independent
Variables for 1971 Model Year Emissions 22
4 Significant Deterioration Factors by Model Years (All FY) . 25
5 Significant Deterioration Differences: Model Year Effects
(All FY) 26
6 Significant Deterioration Factors by EFP Fiscal Year
(Model Year 1971) 27
7 Significant Deterioration Differences: Fiscal Year Effects
(Model Year 1971) 29
8 Significant Deterioration Factors by EFP Fiscal Year
(All Model Years) 30
9 Significant Deterioration Differences: Fiscal Year Effects
(All Model Years) 31
10 Significant Deterioration Factors by Test Site
(Model Year 1971) 32
11 Significant Deterioration Differences: Test Site Effects
(Model Year 1971) 33
12 Significant Deterioration Factors by CID
(Model Year 1971) 35
13 Significant Deterioration Differences: CID Effects
(Model Year 1971) 36
14 Significant Deterioration Factors by Mileage Accumulation
Rate (Model Year 1971) 37
15 Significant Deterioration Differences: Mileage Accumulation
Rate Effects (Model Year 1971) 38
16 SDS Significant Deterioration Factors by Model Year for
Low-Altitude, Non-Californi^ Cities , 39
17 SDS Significant Deterioration Factors by Model Year
for Denver 40
viii
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LIST OF TABLES (cont.)
Table Title Page
18 SDS Significant Deterioration Factors by Model Year for
Los Angeles 41
19 SDS Significant Deterioration Differences: Model Year Effects
(Low-Altitude, Non-California Cities) 43
20 SDS Significant Deterioration Differences: Test Site Effects
(Model Years 1972-1974) 44
21 Significant Changes with Mileage in the Modal Emission Model
Coefficient A1 (Constant Term) 46
22 Significant Changes with Mileage in the Modal Emission Model
Coefficient A2 (Velocity Term) 47
23 Significant Changes with Mileage in the Modal Emission Model
Coefficient A3 (Acceleration Term) 48
24 Comparison of SDS Bag Value Deterioration Factors with Modal
Emissions Model Component Trends 49
25 SDS Significant Deterioration Factors in Idle Mode Bag
Values by Test Site (Model Years 1972-1974) 51
26 SDS Idle Mode Significant Deterioration Differences:
Test Site Effects (Model Years 1972-1974) 52
27 Prediction Error for 1971 Model Year Emissions 56
11 -1 Regression Results by Model Year (EFP FY 71-73) II-2
II-2 Regression Results by Fiscal Year (Model Year 1971) .... II-4
II-3 Regression Results by Fiscal Year (All Model Years) II-5
I1-4 Regression Results for All Model Years (EFP FY 71-73) . . . II-6
II-5 Regression Results by Test Site 11 - 7
II-6 Regression Results by CID (EFP FY 71-73) II-8
II-7 Regression Results by Accumulated Mileage Range
(EFP FY 71-73) II-9
II-8 Age and Mileage Regression Results (EFP FY 71-73) 11-10
IX
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LIST OF TABLES (cont.)
Table Title Page
III-1 Bag Value Regression Results for Pre-1968 Vehicles III-2
II1-2 Bag Value Regression Results for Model Years 1968 and 1969 . . 111-3
111-3 Bag Value Regression Results for Model Years 1970 and 1971 . . III-4
II1-4 Bag Value Regression Results for Model Years 1972-1974 .... 111-5
II1-5 Regression Results for Modal Emission Model Coefficient A1 . III-6
II1-6 Regression Results for Modal Emission Model Coefficient A2 . II1-7
111-7 Regression Results for Modal Emission Model Coefficient A3 . 111-8
111-8 Regression Results for Idle Mode Bag Values (EFP FY 73) . . 111-9
x
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Section 1
INTRODUCTION
1.1 BACKGROUND
The Emission Factor Programs (EFP) are a series of projects,
conducted annually, to measure exhaust emissions of in-use motor vehicles
tested in as-received condition. The purpose of the EFP is to estimate
total emissions of in-use vehicles by model year and region for the
current calendar year. The results of the programs have also been used
to develop linear emission deterioration curves based upon accumulated
mileage. The deterioration curves have been used for projecting average
emissions in order to assess how well vehicles are expected to perform
in relation to the Federal standards over their useful life.
Accurate determination of emission deterioration levels has
recently become more critical with the delay of new and more stringent
standards. Moreover, the potential benefits of more stringent Federal
standards, as opposed to implementation of Inspection/Maintenance, is
in large part dependent on the performance of in-use vehicles. The
important policy questions which depend on an assessment of the effec-
tiveness of current Federal standards suggest that additional and
thorough investigations of available EFP data be undertaken in order
to develop the best emission deterioration estimates and to determine
if these estimates can be expected to provide a meaningful and reliable
assessment of vehicle emissions in successive years.
Modal emissions taken over the Surveillance Driving Sequence
(SDS) are also collected in the EFPs in order to obtain a sound data
base for the modal emission model. The model enables the user to pre-
dict emissions over any specified driving sequence. A precise estimate
of modal emission deterioration is needed in order to accurately estimate
the modal emissions of older vehicles which may not be tested over the
SDS in successive EFPs.
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1.2 PURPOSE AND GENERAL APPROACH
The purpose of this study is to estimate emission deterioration
of in-use vehicles as they accumulate age and mileage. The analysis
uses data collected on vehicles tested in the FY 71, FY 72, and FY 73
EFPs. Deterioration estimates are made using emissions measured from
the Federal Test Procedure (FTP) and the SDS. The estimates are used to
assess differences in deterioration rates between --
a. Model years, over the three fiscal years
b. Fiscal years, for a specific model year
c. Fiscal years, over all model years
d. Test sites (Denver, Los Angeles, and low
altitude, non-California cities), for a
specific model year.
This study includes investigations to determine the best form
of the emission versus age and/or mileage curve (linear, quadratic, etc.)
and to identify the most appropriate independent variable, age or mileage,
or combinations, on which the emission deterioration rate estimates should
be based. Also included is the identification of other vehicle and
driving parameters (CID, mileage accumulation rate, etc.) which may affect
deterioration.
This study also investigates changes in the SDS data modal
emissions model coefficients as related to accumulated mileage. These
coefficients have previously been determined for each vehicle in the
FY 71 and FY 73 EFPs (see References 1 and 2).
In addition to the above specific investigations, this report
also reviews the problems of predicting emissions with available EFP
data, including the statistical and engineering significance of the pre-
dictions, the danger of extrapolating beyond age and/or mileage ranges,
and the shortcomings of the EFP design and format for predictive purposes.
Section 2 of this report summarizes the study findings. Section
3 describes the emission deterioration analysis procedures and discusses
the choice of deterioration curve form and independent variable. Dete-
rioration analysis results are presented in Section 4. Problems and
recommendations are included in Section 5.
2
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Section 2
SUMMARY
The results of this study are summarized below in terms of
general observations and conclusions regarding the appropriate form of
the deterioration curves and the choice of an independent variable,
specific deterioration analysis results, and a review of problems and
recommendations. The results apply only to the test data generated in
the FY 71-73 Emission Factor Programs. Extrapolation of data trends
or application to newer vehicles may not be valid. In much of the analyses,
Model Year 1971 vehicles have been used as a data base. These vehicles
are the latest models to have been tested in all three EFPs.
2.1 CHOICE OF DETERIORATION CURVE FORM AND INDEPENDENT VARIABLE
1) For regressions of emission rate vs. Mileage, linear
functions are adequate; higher order polynomials are not necessary to
model any of the three pollutant trends. For regressions of emission
rate vs. Age, quadratic functions appear to be necessary, but this may
be a result of the inherent error in assigning a single Age value to all
vehicles from one model year.
2) Accumulated Mileage appears to be preferable to Age as
the independent variable in deterioration analysis. Either parameter can
be used, but since emission deterioration as a function of Mileage can
be assumed to be linear, the analysis is less complex than for Age
deterioration analysis. Furthermore, the mileage parameter allows
distinguishing between vehicles of the same model year. A combination
of Mileage and Age does not appear to be warranted for the EFP data.
3) CO and NOX emissions for Model Year 1971 are more highly correlated
with Weight and CID than with either deterioration parameter. This correlation
is expected to decrease as newer vehicles meet more stringent standards.
2.2 DETERIORATION ANALYSIS RESULTS -- FTP DATA
1) Model Year Effects -- Model Years 1970-72 have essentially indis-
tinguishable deterioration rates with mileage. The HC and CO deterioration
3
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rates of this group are greater than those of earlier models (pre-1968).
Apparent differences between this group and 1973 Models are due to the
limited data and the short mileage span represented by the data for 1973
Models in the FY 73 EFP. NOX deterioration is essentially insignificant
for all Model Years. [Analysis of Model Years 1968 and 1969 was not made.
2) Fiscal Year Effects -- Data for 1971 vehicles shows
significant HC and CO deteriorations in FY 73 EFP only. This trend is more
indicative of the increased range of mileage represented in the test data
than of actual changes in deterioration rates. The data for all model years
combined does exhibit significant differences from one EFP to the next;
but these differences are probably as much due to the changing model year
population as they are to a change in deterioration rates of specific
vehicle groups.
3) Overall Emission Deterioration -- The overall emission rate
regressions for all models (pre-68 to 1973) over the three EFPs are listed below.
The second term in each equation is the estimated deterioration rate for each
pollutant:
HC = 3.01 (gm/mi) + 0.666 (gm/mi) per 10,000 miles
CO = 43.41 (gm/mi) + 7.170 (gm/mi) per 10,000 miles
NOXC = 4.41 (gm/mi) - 0.029 (gm/mi) per 10,000 miles
4) Test Site Effects (Model Year 1971) -- The only significant
difference in emission rate deterioration is exhibited in CO emissions. The
deterioration rate is statistically greater for vehicles tested at low alti-
tude, non-California sites than for vehicles tested at either Denver or
Los Angeles.
5) CID Effects (Model Year 1971) -- Statistically significant
differences are shown for the deterioration rates of vehicles grouped by
engine size. CO deterioration rates are greater for medium engines (250-360
CID) than for smaller or larger engines. Both HC and NOX deterioration rates
are higher for small engines than for large engines.
6) Mileage Accumulation Rate Effects (Model Year 1971) --
CO deterioration rates for low annual mileage accumulation vehicles are
lower than for the higher accumulation rate vehicles (10,000 miles/year
and up). HC and NOX differences are also exhibited.
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2.3 DETERIORATION ANALYSIS RESULTS -- SDS DATA
1) Observed Bag Values, Model Year Effects -- The results
are, in general, consistent with the FTP data results.
2) Observed Bag Values, Test Site Effects (Model Years 1972-74) --
The statistically significant results are not at all consistent with those
for Model Year 1971 from the FTP Data: HC and CO deterioration rates were
highest for vehicles tested in Denver. The low altitude, non-California
site vehicles had the lowest CO deterioration rates.
3) Modal Emission Model Coefficients (Model Years 1972-74) --
Statistically significant changes in model parameters a^ (constant term),
a^ (velocity term), and a^ (acceleration term) with mileage accumulation
are evident. Analysis of these trends shows several patterns:
a. Wherever significant trends exist in both the a^
and components, these trends are of opposite sign.
b. Wherever significant factors exist for both the bag
value and a^ component, the a^ trend has the same sign
as the HC and CO deteriorations and the opposite sign
from the NOX deterioration.
c. CO deterioration does not show up as an a^ (acceleration
trend; CO deterioration is always exhibited as an a^
(constant) trend.
d. Both bag value emission deterioration and emission model
coefficient changes are less evident in the Los Angeles
tested vehicles than in vehicles from other test sites.
4) Observed Idle Mode Bag Values, Test Site Effects (Model Years
1972-74) -- Deterioration rate differences are quite consistent with those
observed for the total bag values (item (2) above).
2.4 PROBLEMS AND RECOMMENDATIONS
This study shows that the EFP data can be used to characterize the
tested vehicles in terms of historic emission trends with mileage and age.
The applicability of such characterizations to the overall population depends
highly on the number and stratification of vehicles used in the test samples.
Serious problems exist, moreover, if these historical trends are used to
predict emission levels or if emission deterioration of individual vehicles
is required. r
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Recommendations to address the prediction problems include --
1) Consideration of historical, current, and postulated
vehicle mixes in terms of model years, engine types,
emission control equipment, and expected accumulated
mileage levels per year.
2) Consideration of the number of vehicles from a specific
group which are required to be tested over a period of
time to yield emission predictions of specified precision.
3) Consideration of the form of the emission deterioration
curves for newer vehicles.
4) Comparison of emission level predictions derived from
the FY 71-73 EFP data as contained in this study with
actual emission levels measured at this time (1976).
The analysis and comparison of emission deterioration for
individual vehicles requires additional tests or a redesign of the EFP
test format. Deterioration rates must be determined for individual vehicles
over a period of time. Since deterioration is a consequence of vehicle
maintenance, it is necessary to monitor the deterioration of vehicles
maintained under various inspection and service schedules. It will be
necessary to trade off the costs of such a test program with the expected
gains in information.
An additional advantage in measuring emission characteristics for
individual vehicles is that it becomes possible to analyze the correlation
among the deteriorations of the three pollutants. Just as there exists a
correlation between emission levels at any one time, it is suspected that
the rates of change in these levels over a period of time are also correlated.
It may be possible to develop a theory of composite deterioration by applying
Principal Component Analysis and Factor Analysis procedures to emission
deterioration data from individual vehicles.
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Section 3
DETERIORATION ANALYSIS
This section describes the data used in this study and the
data analysis and statistical techniques employed. Two primary inves-
tigations- -the choice of the deterioration curve form, and the choice
of the independent variable—are also presented as necessary first steps,
prior to the actual data analysis given in Section 4.
3.1 DATA
The exhaust emissions data used in this study was collected
on vehicles tested in the FY 71, FY 72, and FY 73 Emission Factor Pro-
grams (EFP). References 3, 4 and 5 summarize the analysis of the test
data from these EFPs. The test data collected includes total HC, CO,
and NOX (corrected) emissions for vehicles driven through the 1975 Federal
Test Procedure, in units of grams/mile. Vehicle parameters include make,
model year, CID, inertia weight, mileage, and emission control type.
Similar emission data exist for vehicles driven over the first
1024 seconds of the Surveillance Driving Sequence (SDS) for the FY 71
and FY 73 EFPs. In addition, emissions are available mode-by-mode (37
modes in all) for each vehicle in the SDS. These modal emissions form
the basis for a modal emission model (References 1 and 2). The coefficients
used in the model for each vehicle—weighting values for each of the
velocity/acceleration terms--are analyzed in this study to estimate
changes in the coefficients as a function of time and/or mileage.
Idle mode bag value deteriorations are also analyzed.
3.2 DATA ANALYSIS AND STATISTICAL TESTS
The regression analyses conducted in this study—linear,
polynomial, stepwise linear—have employed the BMD Biomedical Computer
Programs (Health Sciences Computing Facility, UCLA). These or similar
statistical analysis routines are widely available and are not documented
here.
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Testing for the significance of a term in an emission deterioration
equation involves an F-test (sometimes called a partial F-test) as des-
cribed in Reference 6. This standard procedure is used, for example, to
test for the significance of the quadratic term when investigating the
form of the deterioration equation. The procedure is also used to test
the hypothesis that a deterioration factor is not statistically different
from zero. The 1 -ot level of significance for which the hypothesis
can be rejected is a measure of how much of an age or mileage trend is
exhibited in the emission data. The engineering significance of this
trend is a matter of judgment.
Testing for statistically significant differences between two
deterioration slopes (in the linear case), due to model year or test
site for example, involves a special T-test as described in Reference 7.
Again, the 1 -oL level of significance is a measure of the confidence
with which one can reject the hypothesis that two deterioration rates
are not statistically different. The direction of any difference
can be ascertained from the two slope estimates. The magnitude of the
difference (and its engineering significance), however, cannot be implied
from the test. Appendix I briefly describes the test computations.
The method of least squares for obtaining estimates of slopes
and intercepts does not depend upon any assumption about the distribution
of emissions. Statements about the confidence in these estimates, however,
require knowledge of (or assumptions about) the distribution of these
estimates. This requirement in turn implies the need for specifying the
distribution form of the emission data. Throughout this study the emission
data has been assumed to have a normal distribution. Consequently, the
intercept and slope estimates are also assumed to be normally distributed.
Inasmuch as the emissions distributions often appear to have an asymmetric,
e.g., log-normal, form, the assumption of normality can lead to errors in
some of the results. A more exact method would have been to normalize the
data by taking the log of the emissions data, for example. These considera-
tions indicate, however, that the approximate method (assuming normality)
yields sufficient accuracy for this study:
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1) In all cases involving tests on the significance of deterioration
factors, the data set has "outliers" removed. These outliers appear in the
high emissions "tail" of the distribution. Their removal reduces the degree
of asymmetry in the emissions distribution.
2) A relatively large number of sample points are used in any one
regression analysis; so the resulting confidence intervals for intercept and
slope estimates are small and concentrated near the mean where any asymmetry
in the actual distribution has only a minor effect. As the confidence
interval gets wider as a result of decreased sample sizes, the effect of the
asymmetric tails becomes more important.
3) When establishing confidence limits on the sample mean emission
level for a specified mileage or age (see Section 5), there is relief from
the distribution form assumption in that the distribution of the sample mean
can be considered to be normal. By the Central Limit Theorem the distribution
of means of samples taken from any distribution approaches a normal distribu-
tion as the number of samples approaches infinity. The sample number which
can be considered "sufficiently close to infinity" depends on the shape of
the distribution of the original variables. Even when the underlying distribu-
tion is rectangular or triangular, the distribution of mean values from
samples as small as four is approximately normal.
3.3 FORM OF THE DETERIORATION CURVES
Deterioration curves have commonly been assumed to be linear
with age or mileage, in some cases due to lack of sufficient data to
justify more complex functions, and in other cases merely in order to
avoid the complexities of determining and analyzing a nonlinear function.
The choice of the form of the curves is, of course, closely tied to the
choice of the independent variable. In this section, it is assumed that
either age or mileage alone will be the choice for the independent
variable. Further refinement of this assumption is presented in
Section 3.4.
The procedure for investigating the form of the deterioration
curves involves a combination of statistical and practical considerations.
First, the FTP Emissions data from all three EFPs for 1971 model year
vehicles in low altitude, non-California was chosen as the data base for
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the analysis. This data set is, therefore, based on the latest vehicle
model year which has been tested in all three EFPs. The three year span
and associated mileage range for the vehicles is necessary to point out
possible nonlinear deterioration effects. The data set did not include
data collected at the Denver or Los Angeles test sites in order to avoid
any confounding with altitude effects or California emission control
equipment differences.
The data was first analyzed assuming linear models:
HC, CO, or NOXC - &i + bi x MILEAGE(miles).
and
HC, CO, or NOXC ¦ a. + b.. x AGE(months).
Figures 1 through 6 indicate the data points and the linear regressions
(solid lines) for the six cases. The age values (in months) for vehicles
in Figures 4 through 6 are approximated by considering the time over which
the EFP was conducted and the average production date for vehicles of the
specified model year (1971). Time age—in terms of day of production or
sale to day of testing for each vehicle--was not available.
Also shown on Figures 1 through 6 are the regression results
(dashed curves) when quadratic models are assumed:
HC, CO, or NOXC - ^ x MILEAGE + c± x (MILEAGE)2
and
2
HC, CO, or NOXC - a. + b. x AGE + c. x (AGE)
J ^ J
From these figures it is apparent that in most cases the quadratic model is
unwarranted. Table 1 gives the results of F-tests which indicate the relative
significance of the terms in the two models. Consistent with the plots,
the statistical tests show that none of the pollutant deteriorations as
functions of mileage warrant a quadratic term. As functions of age, all of
the pollutant deteriorations exhibit some nonlinear effects--NOXC quite
significantly (even to the exclusion of the linear term); HC and CO moderately
(the linear term is more Significant, in a statistical sense, than the quadratic
term). It must be emphasized, however, that these nonlinear effects are more
likely to be a result of the error in assigning a specific age to all vehicles
of one model year than they are a result of actual deterioration rate patterns.
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DISTANCE(MILES)
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DISTANCE(MILES)
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o_,
Figure 3 LINEAR AND QUADRATIC NOXC VS. MILEAGE REGRESSIONS FOR 1971 MODEL YEAR DATA
FTP Data
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AGE(MONTHS)
Figure 4 LINEAR AND QUADRATIC HC VS. AGE REGRESSIONS
FOR 1971 MODEL YEAR DATA
14
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AGE(MONTHS)
Figure 5 LINEAR AND QUADRATIC CO VS. AGE REGRESSIONS FOR
1973 MODEL YEAR DATA
IS
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o.
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RGE(MONTHS)
60
Figure 6 LINEAR AND QUADRATIC NOXC VS. AGE REGRESSIONS
FOR 1971 MODEL YEAR DATA
16
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Table 1
COMPARISON OF LINEAR AND QUADRATIC MODELS
OF EMISSION DETERIORATION
FTP Data Model Year 1971, EFP FY 71-73
Low Altitude Non-California Cities
F
-TEST
SIGNIFICANCE
MODEL
TERM
POLLUTANT
RATIO
LEVEL
LINEAR
LINEAR
HC
12.89
.999
CO
11.63
.999
NOXC
0.20
QUADRATIC
LINEAR
HC
12.89
.999
CO
11.61
.999
NOXC
.20
...
QUAD
HC
1.12
— . ¦
CO
0.49
—
NOXC
0.22
LINEAR
LINEAR
HC
15.12
.999
CO
7.88
.99
NOXC
.80
—
QUADRATIC
LINEAR
HC
15.12
.999
CO
7.92
.99
NOXC
.82
¦
QUAD
HC
1.05
.75
CO
2,47
.75
NOXC
8.55
.995
17
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An extension of this investigation to higher order polynomials
or more complex functions is unnecessary—it is not warranted with the
mileage functions, and it is impossible with the age functions since a
maximum of only three values of the independent variable for any one model
year are available in this study.
3.4 INDEPENDENT VARIABLE INVESTIGATION
Emission deterioration can be a function of vehicle mileage,
as a result of engine wear, for example; and it can be a function of
vehicle age, as a result of corrosive surface aging, for example. One
of the investigations conducted in this study considered which variable,
mileage or age (or a combination of the two), is the more appropriate
independent variable (explains more of the variability about the deterio-
ration curve) within the EFP emission data.
A stepwise linear regression program was used as a "shotgun"
approach for comparing the contributions of the age and mileage parameters,
along with several others, toward accounting for the overall variability
exhibited in the emissions data. Once again the 1971 Model Year data from
the three EFPs was used. The variables allowed to "enter" the stepwise
regression process for each pollutant were:
• Age
• Mileage
• CID
• Weight
• Make Code
• Mileage/CID
• Mileage/Age
• Mileage/Weight
Some of these variables were not expected to emerge as important.
The "Make Code," for example, is a rather arbitrary integer coding used
for data identification purposes only. The "Mileage over CID" and "Mileage
over Weight" tatios are also somewhat arbitrary, unless one suspected a
strong correlation between miles driven and the size or type of vehicle. The
18
-------
"Mileage over Age" ratio, on the other hand, carries the implication of
"mileage accumulation rate" which, indeed, might be a secondary factor
in emission deterioration.
The first output of the stepwise regression program is the
correlation matrix which identifies the correlation between each of the
eleven variables (the eight listed above, plus the three pollutants).
The important patterns which emerged are listed below; the complete
correlation matrix is given in Table 2.
1. HC emissions are most highly correlated with
CO emissions (0.496); then with AGE (0.217)
and MILEAGE (0.201).
2. CO emissions are most highly correlated with HC
emissions (0.496); then with CID (0.283) and WEIGHT
(0.228); then with MILEAGE (0.191) and AGE (0.158).
3. NOXC emissions are most highly correlated with
WEIGHT (0.367) and CID (0.319); NOXC emissions
are negatively correlated with CO emissions (-.224)
and HC emissions (-.131); they are essentially
uncorrelated with AGE (-.051) and MILEAGE (-.026).
Without even going to the stepwise regression results, several
important, albeit not new, observations can be made;
A. The emission levels of the pollutants are closely
correlated to each other. This implies that a
mechanism to analyze the deterioration rates of all
three pollutants simultaneously, e.g. Factor Analysis,
could yield benefits beyond those attained by analyzing
each pollutant deterioration separately.
B. AGE and MILEAGE (closely correlated to each other)
are approximately equal in importance as independent
variables.
19
-------
Table 2
CORRELATION MATRIX FOR 1971 MODEL YEAR EMISSIONS
FTP DATA, EFP FY 71-73
Low Altitude, Non-California Cities
Variable Name
Variable Name
1. MAKE
2. CID
3. AGE
4. WEIGHT
5. MILEAGE
6. HC
7. CO
8. NOXC
9. MILEAGE/CID
10. MILEAGE/AGE
11. MILEAGE/WEIGHT
Variable
1 2
3
4
5
6
7
8
9
10
11
I
1.000 -.209
0.050
-.217
0.026
-.021
-.055
-.024
0.230
-.013
0.169
2
1.000
0.014
0.939
0.115
0.044
0.283
0.319
-.640
0.079
-.389
3
1.000
-.030
0.594
0.217
0.158
-.051
0.317
-.369
0.527
4
1.000
0.096
0.008
0.228
0.367
-.583
0.107
-.412
S
1.000
0.201
0.191
-.026
0.481
0.413
0.825
6
1.000
0.496
-.131
0.120
-.014
0.200
7
1.000
-.224
-.103
-.008
0.030
8
1.000
-.281
0.044
-.227
9
1.000
0.179
0.847
10
1.000
0.316
11
1.000
-------
C. CID and WEIGHT (closely correlated to each other)
account for more of the CO and NOXC emissions variability
than do either AGE or MILEAGE. This implies that any
changes in the sampling distribution of vehicles by
weight or CID from one test year to the next could
easily confound the analysis of emission changes with
age or mileage. (This correlation should diminish for
newer vehicles subject to more stringent controls.)
The stepwise regression output lists the order in which the
variables "enter" the linear model, most important first. Table 3 shows
those variables which were "significant" in explaining emission variability
for each pollutant. In the stepwise regression process, the pollutants
themselves were restricted to be only dependent variables; i.e., they could
not enter the regression of another pollutant. The resulting lists in
Table 3 indicate that MILEAGE is the overall better choice for an
independent variable to describe emission deterioration. A combined
function of AGE and MILEAGE does not seem warranted. Even in the HC
emissions where both variables are significant, the first variable to
enter the regression is more important by a factor of about 5 to 1.
MILEAGE did not enter first in this case since it was slightly less
correlated than AGE with HC emissions.
Other considerations point to MILEAGE as the better choice.
For those late Model Years where testing in only one EFP has occurred,
AGE would be useless as a variable since all vehicles of one Model Yea,r
have nominally the same age. On the other hand, AGE is a much easier
parameter to use when characterizing a vehicle population. The cost of
this simplicity is apparently, however, a loss of some precision in
estimating emission deterioration. Furthermore, from Section 3.3 it is
evident that nonlinear AGE deterioration curves may be necessary (or the
associated error in the AGE value accounted for) when estimating emission
deteriorations; whereas, linear MILEAGE deterioration curves are adequate
for all three pollutants,
21
-------
Table 3
STEPWISE REGRESSION RESULTS; SIGNIFICANT INDEPENDENT
VARIABLES FOR 1971 MODEL YEAR EMISSIONS
FTP DATA EFP FY 71-73 Low Altitude, Non-California Cities
HC Emissions
1. AGE
2. MILEAGE
3. MILEAGE/WEIGHT
4. CID
CO Emissions
1. CID,
2. MILEAGE
3. MILEAGE/AGE
4. WEIGHT
NOXC Emissions
1. WEIGHT
2. MILEAGE
3. MILEAGE/WEIGHT
4. CID
22
-------
Section 4
DETERIORATION ANALYSIS RESULTS
This section discusses the results of the deterioration analyses
conducted on the FTP and SDS data from the FY 71 - 73 Emission Factor
Programs (EFP). The analyses are based on linear regressions of emissions
vs. mileage, in keeping with the results of Section 3. Thus the term
deterioration factor or slope is appropriate.
The regressions were conducted in two ways. First the regressions
were performed using the complete basic set of vehicles as listed on the
EFP data tapes. Second, the regressions were performed on a "cleaned up"
data set which remained after "outlier" vehicles had been eliminated.
"Outliers" in this case are any vehicles whose vector of HC, CO and NOXC
emission levels falls outside of the 1.65 (T (90%) ellipsoid. Thus, any
vehicle whose HC emissions are greater than 1.650^ is eliminated. More-
over, a vehicle which has two or three high levels, although all within
the individual 1.65(T limits, might also be eliminated if its 3-dimensional
emission vector falls outside the 1.65ff" joint distribution emission ellipsoid.
Outliers were found to occur throughout the .mileage range not just at the
high mileages.
The data analysis is presented in this section for the corrected,
or cleaned up, data since it better represents the, expected deterioration
effects in the whole population. The regression results for both the basic
and corrected data are presented in Appendices II and III.
Tests for significance of deterioration factors and for differences
between two factors use level of significance cutoffs of .75 and .80,
respectively. These cutoffs have been chosen somewhat low to assure that if
there is indeed a finite difference, it will be detected. Had the cutoff
level been chosen higher, say at .99, fewer significant differences would
have been noted. The cutoff values are slightly different (.75 and .80)
as a result of the available F- and t-tables.
4.1 FTP DATA ANALYSIS
The chart below indicates the EFP Fiscal Year, Model Year, and
Test Site data groups which were used in the regression analysis. X's
indicate that the particular model year did not exist for that EFP Fiscal Year.
23
-------
Additional regressions were also conducted to evaluate secondary effects
due to CID and mileage accumulation rate.
MODEL YEAR
EFP
FY
Pre '68
68, 69
70
71
72
73
All
Available
71
—
Low
X
X
Low
72
—
—
Low
(Low)
X
Low
73
—
Low
(Low)
Low
All Available
Low
—
Low
Low, LA, Den
Low
Low
Low
Low = Low Altitude, Non-California LA ® Los Angeles Den = Denver
Deterioration factor data in tables which follow is presented in
scientific notation with the power of ten listed after the four-place
characteristic.
4.1.1 Model Year Effects
Table 4 shows the deterioration factors which axe significantly
different from zero for the Model Year groups listed. Data from every
applicable EFP Fiscal Year was used. The fact that Model Year 1973 has no
significant deterioration factors is more an indication of the short
mileage span represented by the data (EFP FY 73 only) than of the absence
of emission deterioration.
Table S indicates the significant differences in deterioration
factors between model years. Model Years 1970-72 have essentially
indistinguishable factors. Each exhibits greater HC and CO deterioration
than Model Year 1973, again, due to the lack of significance in the 1973
data.
4.1.2 EFP Fiscal Year Effects for a Given Model Year
In the section above it was shown that over a three year-period
Model Year 1971 vehicles exhibited (statistically) significant deteriora-
tion rates in HC and CO (see Table 4). Table 6 shows the results when
24
-------
Table 4
SIGNIFICANT DETERIORATION FACTORS
BY MODEL YEARS (ALL FY)
FTP Data
Low-Altitude, Non-California Cities
Deterioration Factors Significantly
Different from Zero
MODEL
YEAR
Pollutant
Deterioration
Factor
(Gm/Mi per Mile)
Significance
Level
Pre-1968
HC
0.1486 -04
.90
CO
0.2754 -03
.975
1970
HC
0.2267 -04
.999
CO
0.4332 -03
.999
NOXC
-.8343 -05
.75
1971
HC
0.3018 -04
.999
CO
0,5137 -03
.999
1972
HC
0.2536 -04
.999
(FY 72 § 73)
CO
0.4710 -03
.999
1973
None
--
(FY 73)
25
-------
Table 5
SIGNIFICANT DETERIORATION DIFFERENCES:
MODEL YEAR EFFECTS (ALL FY)
FTP Data
Low-Altitude, Non^California Cities
Significant Differences
Between Deterioration Factors
Model Year
Test
Pollutant
Deterioration Difference
Significance
Level
1971
vs.
Pre-1968
"71
>
HCPre-68
.80
C071
>
C0Pre-68
.80
1971
vs.
1970
No significant differences
—
1971
vs.
1972
No significant differences
--
1971
vs.
1973
HC71
>
HC73
.98
C071
>
C073
.98
1972
vs.
1973
HC72
>
HC73
.90
C072
>
»
CO,,
73
.95
1970
vs.
1973
HC70
>
HCyj
.80
C070
>
C073
.95
26
-------
Table 6
SIGNIFICANT DETERIORATION FACTORS
BY EFP FISCAL YEAR (MODEL YEAR 1971)
FTP Data
Low-Altitude, Non-California Cities
Deterioration Factors Significantly
Different from Zero
EFP
•FISCAL YEAR
Pollutant
Deterioration
Factor
(Gm/Mi per Mile)
Significance
Level
1971
None
--
—
1972
None
—
—
1973
HC
0.2280 -04
.975
CO
0.8169 -03
.999
27
-------
the data for only one EFP Fiscal Year is used at a time. For FY 71 and 72
no significant factors appear. This result does not necessarily imply
that the deterioration rate for Model Year 1971 vehicles suddenly increased
in 1973 after two initial years with no significant deterioration. In
fact, such a nonlinear effect has already been discounted in Section 3.3
for this same three year data set.
Table 7 indicates the significant differences in deterioration
between the EFP Fiscal Years for Model Year 1971. Only CO deterioration
shows differences at a level greater than 0.75.
4.1.3 EFP Fiscal Year Effects for All Model Years
Table 8 lists the significant deterioration rates for all vehicles
by EFP Fiscal Year. Also shown are the results for the total data set —
0
all Fiscal Years and all Model Years. The large data sets provide significant
factors in every case. It is not clear why the 73 EFP shows a positive NOXC
deterioration factor.
Table 9 indicates that NOX deterioration rates are increasing from
year to year (from negative to positive, in fact) over all Model Years. HC and
CO deterioration rates show the opposite trend. This pattern is probably due
as much to the changing Model Year population from one fiscal year to the next
as it is to a change in the deterioration rates of the constant elements of the
population. The fact that emission standards also changed in some years implies
that these "overall" deterioration rates are somewhat meaningless.
4.1.4 Test Site Effects
Table 10 lists the significant deterioration factors for Denver,
Los Angeles, and the other low altitude, non-California city test sites.
Table 11 shows that the only significant difference occurs with
CO deterioration. It is statistically greater in the low, non-California
cities than in either Denver or Los Angeles.
4.1.5 CID Effects
The fact that CO and NOX emissions were highly correlated to
CID in the stepwise regression analysis (see Section 3.4) prompted the
28
-------
Table 7
SIGNIFICANT DETERIORATION DIFFERENCES:
FISCAL YEAR EFFECTS (MODEL YEAR 1971)
FTP Data
Low-Altitude, Non-California Cities
EFP
Fiscal Year
Test
Significant Differences
Between Deterioration Factors
Pollutant
Deterioration Difference
Significance
Level
FY 71 vs. FY 72
No significant differences
--
FY 71 vs. FY 73
C071 < C073
.90
FY 72 vs. FY 73
C072 < C073
.98
29
-------
Table 8
SIGNIFICANT DETERIORATION FACTORS
BY EFP FISCAL YEAR (ALL MODEL YEARS)
FTP Data
Low-Altitude, Non-California Cities
Deterioration Factors Significantly
Different from Zero
EFP
•FISCAL YEAR
Pollutant
Deterioration
Factor
(Gm/Mi per Mile)
Significance
Level
1971
HC
0.6542 -04
.999
CO
0.7634 -03
.999
NOXC
-.2066 -04
.999
1972
HC
0.5899 -04
.999
CO
0.6868 -03
.999
NOXC
-.1183 -04
.999
1973
HC
0.3585 -04
.999
CO
0.5909 -03
.999
NOXC
0.1542 -04
.999
1971 - 1973
HC
0.5243 -04
.999
CO
0.6678 -03
.999
NOXC
-.2870 -05
.90
30
-------
Table 9
SIGNIFICANT DETERIORATION DIFFERENCES:
FISCAL YEAR EFFECTS (ALL MODEL YEARS)
FTP Data
Low^Altitude, Nont-California Cities
EFP
Fiscal Year
Test
Significant Differences
Between Deterioration Factors
Pollutant
Deterioration Difference
Significance
Level
FY
71 vs. FY
72
noxc?1
<
N0XC__
72
.90
FY
71 vs. FY
73
HC71
>
HC73
.999
C071
>
C073
.90
NOXC?1
<
N0XC73
.999
FY
72 vs. FY
73
hc72
>
HC73
.999
C072
>
C073
.80
noxc72
<
noxc?3
.999
31
-------
Table 10
SIGNIFICANT DETERIORATION FACTORS
BY TEST SITE (MODEL YEAR 1971)
FTP Data
EFP FY 71-73
Deterioration Factors Significantly
Different from Zero
TEST
SITE
Pollutant
Deterioration
Factor
(Gm/Mi per Mile)
Significance
Level
Low Altitude,
HC
0.3018 -04
.999
Non-Calif. Cities
CO
0.5137 -03
.999
Denver
None
—
—
Los Angeles
HC
0.1958 -04
.975
CO
0.2180 -03
.75
NOXC
-.1411 -04
.95
32
-------
Table 11
SIGNIFICANT DETERIORATION DIFFERENCES:
TEST SITE EFFECTS (MODEL YEAR 1971)
FTP Data
EFP FY 71-73
Low-Altitude, Non-California Cities
Significant Differences
Between Deterioration Factors
Test Site
Test
Pollutant
Deterioration Difference
Significance
Level
Low Altitude, Non-Calif,
vs.
Denver
C^Low ^ ^Denver
.95
Low Altitude, Non-Calif,
vs.
Los Angeles
C0Low > C°LA
.80
Denver
vs.
Los Angeles
No significant differences
U
-------
suspicion that deterioration rates might also be affected by CID. Table 12
indicates that 1971 Model vehicles tested over all three EFPs, indeed, have
significant deterioration rates when broken down by CID.
Table 13 shows that the CO deterioration rate is (statistically)
significantly greater for the medium engines (250-360 CID) than for the
small or large engines. Both HC and NOXC deterioration rates are higher
for the small engines than for the large engines.
4.1.6 Mileage Accumulation Rate Effects
The rate at which mileage is accumulated is likely to be a factor
in emission deterioration. Many short trips for example can result in
greater engine wear than several long trips. Table 14 shows the significant
deterioration factors for the 1971 Model vehicles (all three EFPs) broken
down by an overall miles per year range. The three ranges were chosen to
provide approximately equal sample sizes. The statistical significance
between these factors is indicated in Table 15. CO deterioration rates for
the low accumulation vehicles are lower than for the medium (up to 14,000
miles/year) or the high accumulation (14,000 to 100,000 miles/year) vehicles.
Deterioration factors for the medium rate group are significantly higher
than the other two groups for both HC and NOX emissions. The reasons behind
these patterns are not evident.
4.2 SDS DATA ANALYSIS
The Surveillance Driving Sequence (SDS) data from EFP FY 71 and
FY 73 includes observed bag values of emissions after the first 1024 seconds
of the SDS and mode-by-mode emission values. These modal data form the
basis for a modal emissions model (References 1 and 2). The coefficients
used in the model for each vehicle -- weighting values for each of the
velocity/acceleration terms -- are analyzed in this section to estimate
changes in the model coefficients as a function of mileage. Deterioration
factors are presented in scientific notation with the power of ten listed
after the four-place characteristic.
4.2.1 Observed Bag Values -- Model Year and Test Site Effects
Tables 16-18 list the statistically significant deterioration
factors by Model Year groups for data from the three test site categories
34
-------
Table 12
SIGNIFICANT DETERIORATION' FACTORS
BY CID (MODEL YEAR 1971)
FTP Data
EFP FY 71-73
Low-Altitude, Non-California Cities
Deterioration Factors Significantly
Different from Zero
CID
RANGE
Pollutant
Deterioration
Factor
(Gra/Mi per Mile)
Significance
Level
0 - 249
HC
0.4312 -04
.995
NOXC
-.4295 -04
.99
2SO - 360
HC
0.2533 -04
.999
CO
0.6518 -03
.999
361 - 500
HC
0,1510 -04
.75
31
-------
Table 13
SIGNIFICANT DETERIORATION DIFFERENCES
CID EFFECTS (MODEL YEAR 1971)
FTP Data
EFP FY 71-73
Low-Altitude, Non-California Cities
Significant Differences
Between Deterioration Factors
CID Range
Test
Pollutant
Deterioration Difference
Significance
Level
Small vs. Medium
C0Small COMed
.95
Small vs. Large
"SmaU ^Large
.80
N0XCSaall > N0XClarge
.95
Medium vs. Large
C0Med > C0Large
.90
36
-------
Table 14
SIGNIFICANT DETERIORATION FACTORS
BY MILEAGE ACCUMULATION RATE (MODEL YEAR 197.1)
FTP Data
EFP FY 71-73
Low-rAltitude, Non-California Cities
Deterioration Factors Significantly
Different from Zero
MILEAGE
ACCUMULATION
RATE
(Miles per Year)
Pollutant
Deterioration
Factor
(Gm/Mi per Mile)
Significance
Level
0 - 9,999
HC
0.3768 -04
.975
NOXC
-.2751 -04
.75
10,000 - 13,999
HC
0.5100 -04
.999
CO
0.7030 -03
.999
NOXC
0.1754 -04
.75
14,000 - 100,000
HC
0.2051 -04
.95
CO
0.5820 -03
.995
NOXC
-.1340 -04
.75
37
-------
Table 15
SIGNIFICANT DETERIORATION DIFFERENCES:
MILEAGE ACCUMULATION RATE EFFECTS (MODEL YEAR 1971)
FTP Data
EFP FY 71-73
Low-Altitude, Non-California Cities
Mileage
Accumulation Rate
Test
Significant Differences
Between Deterioration Factors
Pollutant
Deterioration Difference
Significance
Level
Low vs. Medium
C0Low < C0Med
NOXCLow < NOXCMed
O O
00 Oi
Low vs. High
CO. < CO„. .
Low High
.80
Medium vs. High
HC ' , > HC„. .
Med High
NOXC,. . > NOXCu. ,
Med High
.95
.90
38
-------
Table 16
SDS SIGNIFICANT DETERIORATION FACTORS
BY MODEL YEAR FOR LOW-ALTITUDE, NON-CALIFORNIA CITIES
Deterioration Factors Significantly
Different from Zero
MODEL
YEARS
Pollutant
Deterioration
Factor
(Gm/Mi per Mile)
Significance
Level
Pre-1968
NOXC
-.7901 -05
.90
1968, 1969
HC
0.1621 -04
.95
CO
0.2632 -03
.95
1970, 1971
HC
0.1974 -04
.995
CO
0.1679 -03
.75
1972 - 1974
CO
-.2411 -03
.95
NOXC
0.4119 -04
.999
39
-------
Table 17
SDS SIGNIFICANT DETERIORATION FACTORS
BY MODEL YEAR FOR DENVER
Deterioration Factors Significantly
Different from Zero
MODEL
YEARS
Pollutant
Deterioration
Factor
(Gm/Mi per Mile)
Significance
Level
Pre-1968
None
—
1968, 1969
NOXC
0.1888 -04
.75
1970, 1971
CO
-.8214 -03
.90
1972 - 1974
HC
0.4890 -04
.99
CO
0.1020 -02
.75
NOXC
0.3875 -04
.995
40
-------
Table 18
SDS SIGNIFICANT DETERIORATION FACTORS
BY MODEL YEAR FOR LOS ANGELES
Deterioration Factors Significantly
Different from Zero
MODEL
YEARS
Pollutant
Deterioration
Factor
(Gn/Mi per Mile)
Significance
Level
Pre-1968
HC
0.2841 -04
.90
CO
0.3829 -03
.99
NOXC
-.2461 -04
.995
1968, 1969
HC
0.3026 -04
.95
CO
0.3118 -03
.75
NOXC
-.5515 -04
.75
1970, 1971
HC
0.3772 -04
.975
NOXC
0.7016 -04
.975
1972 - 1974
NOXC
0.5057 -04
.999
41
-------
(Denver, Los Angeles, and low-altitude, non-California cities). In Table 16,
it is not clear why the newer model (1972-74) exhibited a negative CO deteriora-
tion factor. Table 19 shows the significant differences between the 1972-1974
Model Year group and the earlier Model Years for the low-altitude, non-California
sites. The results in general are consistent with those of Table 5 showing
Model Year differences in the FTP data and are, in part, due to the lack of
deterioration data for the late model vehicles.
Table 20 shows the significant deterioration differences between
the test sites for the 1972-1974 Model Years. These trends do not correspond
at all with the differences experienced in the FTP data for 1971 vehicles
(Table 11).
4.2.2 Emission Deterioration as Reflected in the Modal Emission
Model Coefficients
The modal emission model relates emission rate e to a linear
combination of velocity and acceleration terms. The general form of the
model is
e(V,A) = h(a) e^D + [l-h(a)] egs
where
®A/D = al + a2V + a3A + a4VA + a5y2 + a6A2 + s7Va2 + &8Va2 +
for acceleration/deceleration modes;
2
ess * a10 + allV + a12V for steady-state modes (A®0);
h(a) is a linear weighting function which combines the two
portions in the region close to A»0 .
The a^^ coefficients or weighting factors in the model have been
determined for each vehicle in the FY 71 and FY 73 EFP's (References 1 and 2).
The emission rate over any specified driving sequence can be estimated using
these functions. Further analysis under EPA Contract No. 68-03-0435 indicates,
however, that the constant term (a^ and the acceleration term (a3) may
account for more than 80% of the variance in the data, In addition, the
velocity term (aj) nay account for up to another 5%. Thus, it may be possible
to provide an estimate of emission rate over a specified driving sequence
using a simpler model without much loss in precision.
42
-------
Table 19
SDS SIGNIFICANT DETERIORATION DIFFERENCES:
MODEL YEAR EFFECTS (LOW-ALTITUDE, NON-CALIFORNIA CITIES)
Significant Differences
Between Deterioration Factors
Model Year
Test
Pollutant
Deterioration Difference
Significance
Level
Pre-1968 vs. (1972-1974)
CO > CO
Pre-68 72-74
.75
N0XCPre-68< NOXC72-74
.975
(1968, 1969)
HC68, 69 > HC72-74
.90
vs.
C068, 69 > C072-74
.998
(1972 - 1974)
N0XC68,69< NOXC72-74
.999
(1970, 1971)
HC70, 71 >HC72-74
.98
vs.
C070, 71 >C072-74
.98
(1972 - 1974)
NOXC70,71^ NOXC72-74
.99
43
-------
Table 20
SDS SIGNIFICANT DETERIORATION DIFFERENCES:
TEST SITE EFFECTS (MODEL YEARS 1972-1974)
Test Site
Test
Significant Differences
Between Deterioration Factors
Pollutant
Deterioration Difference
Significance
Level
Low Altitude, Non-Calif,
vs.
Denver
HC. < HCn
Low Denver
CO, < C0»
Low ^ Denver
.75
.75
Low Altitude, Non-Calif,
vs.
Los Angeles
CO. < CO..
Low LA
.75
Denver
vs.
Los Angeles
^Denver > HCU
C0Denver ^ C0LA
.75
.75
44
-------
The observations above indicate that emission deterioration due
to age or mileage accumulation should also be reflected as changes in the
important model coefficients over comparable age or mileage periods.
Consequently, linear regression analysis was conducted on the a^, a
and a^ coefficients as functions of the mileage of the 1972-1974 vehicles.
This analysis was done for each of the test site groups. Statistically
significant changes in these model parameters with mileage are listed in
Tables 21-23. To aid in relating these mileage trends in model parameters
to the bag value emissions deterioration, Table 24 summarizes the comparable
bag value factors and component factors. Several patterns emerge:
1. Wherever significant trends exist in both the a^
and components, these trends are of opposite sign.
2. Wherever significant mileage effects exist for both
the bag value and a^ coefficient, these effects have
the same sign in the case of HC and CO emissions, but
the opposite sign in the case of NOX emissions.
3. CO deterioration does not show up as a change in the
(acceleration) term; significant trends in the aj
(constant) term, however, are exhibited for CO in
each case.
4. Both bag value emission deterioration and emission
model coefficient changes are less evident in the
Los Angeles tested vehicles than in vehicles from other
test sites.
These observations are tentative at best; their significance is
not understood at this point. Under less stringent time and funding constraints,
further studies of the model emissions data might yield additional relation-
ships. Such analysis could include that half of the test vehicles with
low accumulated mileage as an observation set to model emissions and predict
how the vehicles with higher mileage will perform. Comparison of the predic-
tions with the actual emission levels of the higher mileage set would indi-
cate the feasibility of using a "mileage adaptive" modal emissions model to
predict vehicle emissions over any specified driving sequence, at some future time,
45
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Table 21
SIGNIFICANT CHANGES WITH MILEAGE IN THE MODAL EMISSION
MODEL COEFFICIENT A1 (CONSTANT TERM)
Coefficient Changes Significantly
Different from Zero
TEST
SITE
Pollutant
Coefficient
Change
(Aa., per Mile)
Significance
Level
Low Altitude,
HC
0.1859 -06
.90
Non-Calif. Cities
CO
-.2983 -05
.90
Denver
HC
0.9960 -06
.999
' CO
0.2393 -04
.995
NOXC
-.3079 -06
.975
Los Angeles
CO
0.3688 -05
.75
NOXC
-.2306 -06
.75
46
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Table 22
SIGNIFICANT CHANGES WITH MILEAGE IN THE MODAL EMISSION
MODEL COEFFICIENT A2 (VELOCITY TERM)
Coefficient Changes Significantly
Different from Zero
TEST
SITE
Pollutant
Coefficient
Change
(Aa2 per Mile)
Significance
Level
Low Altitude,
HC
-.9885 -08
.75
Non-Calif. Cities
CO
0.3213 -06
.975
NOXC
0.9473 -08
.75
Denver
HC
-.3379 -07
.95
CO
-.1028 -05
.90
NOXC
0.2333 -07
.90
Los Angeles
None
--
—
47
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Table 23"
SIGNIFICANT CHANGES WITH MILEAGE IN THE MODAL EMISSION
MODEL COEFFICIENT A3 (ACCELERATION TERM)
Coefficient Changes Significantly
Different from Zero
TEST
SITE
Pollutant
Coefficient
Change
(Aol3 per Mile)
Significance
Level
Low Altitude,
HC
0.2617 -07
.90
Non-Calif. Cities
NOXC
-.2150 -07
.75
Denver
NOXC
0.3929 -07
.75
Los Angles
HC
0.5672 -07
.90
48
-------
Table 24
COMPARISON OF SDS BAG VALUE DETERIORATION FACTORS
WITH MODAL EMISSIONS MODEL COMPONENT TRENDS
Significant
Bag Value
Deteriorations
Emissions Model Component Trends with Mileage
Test Site
Pollutant
al
(constant)
a2
(velocity)
a3
(acceleration)
Low Altitude,
HC
—
0.1859 -06
-.9885 -08
0.2617 -07
Non-California
CO
-.2411 -03
-.2983 -05
0.3213 -06
—
Cities
NOXC
0.4119 -04
0.9473 -08
-.2150 -07
HC
0.4890 -04
0.9960 -06
-.3379 -07
Denver
CO
0.1020 -02
0.2393 -04
-.1028 -05
NOXC
0.3875 -04
-.3079 -06
0.2333 -07
0.3929 -07
HC
— —
0.5672 -07
Los Angeles
CO
NOXC
0.5057 -04
0.3688 -05
-.2306 -06
-------
4.2.3 Observed Idle Mode Bag Values -- Changes with Mileage
A separate analysis of idle mode bag values was made to compare
with the total bag value emission deterioration rates. Table 25 shows
those deterioration factors for each test site which were statistically
different from zero. Table 26 lists the significant deterioration rate
differences between test sites. These patterns are quite consistent with
the differences noted in Table 20 for total observed bag value deterioration
rates, except that no significant differences between the low altitude, non-
California test sites and Los Angeles were found.
50
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Table 25
SDS SIGNIFICANT DETERIORATION FACTORS IN IDLE MODE BAG VALUES
BY TEST SITE (MODEL YEARS 1972-1974)
Test Site
Deterioration Factors Significantly
Different from Zero
Pollutant
Deterioration
Factor
(Gm/Mi per Mile)
Significance
Level
Low Altitude,
Non-Calif. Cities
None
—
—
Denver
HC
CO
0.1002 -04
0.2740 -03
.99
.975
Los Angeles
NOXC
-.6376 -06
.75
51
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Table 26
SDS IDLE MODE SIGNIFICANT DETERIORATION DIFFERENCES:
TEST SITE EFFECTS (MODEL YEARS 1972-1974)
Significant Differences
Between Deterioration Factors
Test Site
Test
Pollutant
Deterioration Difference
Significance
Level
Low Altitude, Non-Calif,
vs.
Denver
HCLow ^ HCDenver
C0Low < C0Denver
.95
Low Altitude, Non-Calif,
vs.
Los Angeles
No significant differences
—
Denver
vs.
Los Angeles
Denver > HCLA
C0Denver ^ C0LA
.95
.90
52
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Section 5
PROBLEMS AND RECOMMENDATIONS
This section reviews the problems of predicting emissions with
available EFP data including the engineering and statistical significance
of the predictions and the danger of extrapolating beyond age and/or mileage
ranges. Some of the problems are general to any prediction process; others
are specific to the EFP design and format. In all cases the final use or
application of the deterioration estimates influences the relative importance
of these problems and dictates the appropriate remedies. The problems
discussed below apply to both direct emission estimates and emission estimates
derived by means of a modal emissions model.
5.1 USING EFP DATA TO DETERMINE HISTORICAL EMISSION TRENDS
This study has shown that it is possible to characterize samples
from vehicle populations in terms of overall emission trends with mileage and
age. Furthermore, these emission trends, on a population basis, can be
assumed to be linear with mileage. It is reasonable therefore to use the
EFP data to answer questions of the type "What is the overall emission
deterioration of the entire vehicle population over the EFP test years?" or
"How did 1971 model vehicles, as a group, deteriorate over the EFP test years?"
The answers to these questions do not involve predicting emission levels, or
extrapolating to years or mileages outside the tested ranges, but merely require
analysis of historical trends. Neither do these questions require knowledge
of how the emissions of individual vehicles have changed or are expected to
change.
The EFP data itself does not contain deterioration information for
individual vehicles. The reason that the data can be used to indicate overall
emission trends can be seen by considering the EFP vehicles as random samples
from, say, three subsets of vehicles -- (1) those with very low mileage,
(2) those with moderate mileage, and (3) those with high mileage. The
samples from each subset can be used to estimate the mean or average
emission level for that subset. Assume now that the estimated mean of
S3
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subset (2) is greater than the estimated mean of subset (1). We can
conclude that if the only difference in the character of the two subsets is
accumulated mileage, then the difference in the means must be a result
of mileage accumulation. Even though no emission measurements at the low
mileages have been made for those vehicles from subset (2), we assume
that the results for the low mileage vehicles in subset (1) are indicative
of what those measurements would have been. Similarly, we can compare
the estimated mean of subset (3) with those of subsets (1) and (2).
In reality the EFP consists of samples from many "subsets" of vehicles
spanning the range of accumulated mileages. Linear regression analysis
is used to estimate the most consistent trend over all the subsets.
What are the problems with this procedure? First, it is not
possible to assume that the only difference among the subsets is accumulated
mileage. Vehicle age, for example, is also expected to be different. This
problem may be insignificant for vehicles from one model year. Even in
samples taken from several model years, it appears that either mileage or
age can be used as the basis for emission deterioration analysis;
simultaneous consideration of both parameters is not necessary (see Section 3.4).
A more significant problem arises when one wishes to determine the
emission trends from a very restricted class of vehicles, for example, 1971
Chevrolets with 250-300 CID engines. The number of vehicles in the EFP
representing this class would be too small to yield adequate sample sizes
in the mileage accumulation "subsets." The result would be a very low level
of confidence in the estimate of each subset mean and, therefore, in the overall
emission trend estimates. Furthermore, without being able to adequately analyze
deterioration results for small groups of vehicles, it is impossible to predict
or extrapolate the emissions for particular mixtures of these groups.
Another consideration, although not specifically a problem, is the
engineering significance of the deterioration estimates. For data sets
where the statistical significance level is low, the deterioration
factor must be accepted to be zero. This situation results when the
data indeed indicates that the slope of the regression is very close to
zero or when the data set is small and the variance is large. This latter
case can result in non-zero slope estimates, but the estimates are too
uncertain to be accepted. For some data sets, on the other hand, especially
when the sample size is large, a statistically significant result may have
questionable engineering importance, With enough data, even a slight
54
-------
deviation from a zero slope will be detected in the regression analysis.
In all cases it is necessary to consider the magnitude of the deterioration
estimate in terms of its impact, in an engineering sense, on emission levels.
This point can be illustrated by considering the NOX deterioration
results from two data sets. From the FY 71 EFP, the regression on 1971 Model
Year vehicles is:
NOX (gm/mi) = 4.914 (gm/mi) + 0.05388 (gm/mi) per 10,000 miles
This regression shows a deterioration factor of approximately 1% per
10,000 miles. In addition to being insignificant in an engineering sense,
this estimate based on 74 observations is statistically insignificant
(slope F-ratio = 0.05). Next, consider the overall regression on all
vehicles in the three EFPs:
NOX (gm/mi) « 4.409 (gm/mi) -0.02870 (gm/mi) per 10,000 miles
This regression shows an even smaller deterioration factor, approximately
3/4%; but because the estimate is based on 1667 observations, the results
are listed as statistically significant (slope F-ratio ¦ 2.91).
5.2 USING EFP DETERIORATION ESTIMATES TO PREDICT OVERALL
EMISSION LEVELS
Predicting emission levels over future mileage or age ranges
requires consideration of the expected error in extrapolating historical
emission trends to future time, If one is concerned with the general quality
of air at some future date, it is tempting to substitute the appropriate
ages and mileages in the regression analysis equations. Prediction errors,
however, can distort the estimates in several ways.
The first problem is the uncertainty with which the historical
emission trend has been determined. It is a straightforward procedure
to determine the confidence bounds on the regression or on the mean of the
observations at a specified accumulated mileage range. As the specified
mileage or age is taken to be farther and farther from the mean mileage
55
-------
or age associated with the historical data, the uncertainty in the emission
level estimates, as expressed by the confidence bounds, becomes larger and
larger. To illustrate this concept, consider the regression of HC emissions
with mileage for 1971 Model Year vehicles (three EFPs). At the mean
accumulated mileage value for the historical data set (27,350 miles),
the regression estimate is 3.86 gm/mi. The 95% confidence interval on the
mean of observations at this mileage is at a minimum and equal to +.23 gm/mi,
or about +5.9% of the estimate. As the specified mileage is increased to
50,000 or 100,000 miles, the confidence bound about the regression estimate,
i.e. the uncertainty, grows. Table 27 shows that at 100,000 miles
the 95% confidence interval is +19.6% of the regression estimate. For CO
emissions the results are essentially the same, but for NOX emissions
the confidence interval is greater than $30% of the estimate at 100,000
miles.
Similar results are obtained for emissions estimated using a^e
regressions,
The second problem is a most important one and arises in the estima-
tion of the vehicle mix at some future time. The number of vehicles of specific
types and model years must be estimated, including vehicles (and estimates of
their associated emission levels) which do not exist now but will be on the road
in the future. Each of these estimates involving population dynamics will contain
uncertainties which further compound the prediction errors.
Even if a reasonable estimate of the vehicle mix can be made,
it is still necessary to estimate the accumulated mileage levels which will
exist for each of the vehicle groups, This problem of course does not
exist if age is used as the emission deterioration independent variable,
All vehicles of a specific model year will be at age «(test year « model
year), The model year mix must be estimated, however, just as with the
mileage regression estimates.
A final problem exists in that future emission deterioration
rates may change over future intervals, Even though deterioration with
mileage appears to be linear for the model years and EFPs considered in
this study, there is no way to guarantee that these rates will not change
or that the deterioration rates of newer vehicles with different emissions
control equipment will deteriorate linearly.
-------
Table 27
PREDICTION ERROR FOR 1971 MODEL YEAR EMISSIONS
HC
CO
NOX
FTP Data - EFP FY 71-73
Low-Altitude, Non-California Cities
Estimate from
Mileage Regression -95 Confidence on 7 at x*
x* 7 * a + bx* Interval Relative
27,350 = x 3.86 gm/mi ± .23 gm/mi ±5.9%
50,000 4.55 + .45 ± 9.9
75,000 5.30 + .79 +14.9
100,000 6.06 +1.19 +19.6
27,350 a x 52.65 gm/mi + 3.5 gm/mi + 6.6%
50,000 64.28 ± 6.5 +10.1
75,000 77.13 +12.2 +15.8
100,000 89.97 ±18.1 ±20.1
27,350 = x 4.61 gm/mi + .26 gm/mi + 5.6%
50,000 4.53 + .50 +11.0
75,00° 4.45 * 9g t21>3
100,000 4.36 +1.42 +32.6
57
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5.3 USING EFP DETERIORATION ESTIMATES TO PREDICT EMISSION
LEVELS OF INDIVIDUAL VEHICLES
For any analysis which requires an estimate of emission changes
for individual vehicles, the EFP data in its current format is not
applicable. This limitation prevents addressing questions of the form
"What percentage of 1971 vehicles are deteriorating at a rate twice as high
as the average?" or "What extremes of deterioration are experienced in
catalyst equipped vehicles?" or "How do the deterioration rates of
vehicles which had emission levels below the Federal Standards at 10,000
miles compare to the deterioration rates of vehicles which exceeded the
Standards in at least one pollutant" or "What is the correlation between
HC, CO, and NOx deterioration rates?"
These and other questions can be answered only by first
generating deterioration estimates for individual vehicles. The vehicles
must be tested over a period of time at least twice, preferably three or
four times. The deterioration rates for a group of vehicles then can be
presented as a frequency distribution of deterioration values. With
appropriate analysis, the mean rate for the group can be determined along
with other statistics necessary to address questions of the type listed
above. The disadvantage of this procedure of course is the increased
cost of testing and recalling the vehicles.
5.4 RECOMMENDATIONS FOR FUTURE STUDIES
The primary concern for future studies should be the identification
of the expected or the required goals of using the EFP data in establishing
deterioration rates. As discussed above, if only historical trends are of
interest, the current EFP design can be used. Additional attention is necessary,
however, in specifying the types and numbers of vehicles which should be tested
in specific groups so as to produce statistically significant results where
required.
If, however, a prediction capability is desired, either in terms
of specific vehicle groups or in terms of the entire vehicle population,
further studies are recommended;
58
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1. Consideration of historical, current, and postulated
vehicle mixes in terms of model years, engine types,
emission control equipment, and expected accumulated
mileage levels per year.
2. Consideration of the number of vehicles from a specific
group which are required to be tested over a period of
time to yield emission predictions of specified precision,
and consideration of how these should be stratified with
respect to the current and future populations.
3. Consideration of the form of the emission deterioration
curves for newer vehicles.
4. Comparison of emission level predictions derived from
the FY 71-73 EFP data as contained in this study with
actual emission levels measured at this time (1976).
If, in fact, it is desired to determine the factors which
contribute to emission deterioration or to design and evaluate
inspection/maintenance procedures in order to reduce deterioration,
additional tests or a redesign of the EFP test format is required.
Emission deterioration rates must be determined for individual vehicles
and the maintenance of these vehicles must be closely controlled.
Limited data from such a test program exists and has been reported
(Reference 8). It is necessary to trade off the costs of similar
testing with the expected gains in information.
An additional advantage in measuring emissions deterioration
for individual vehicles is that it becomes possible to analyze the correla-
tion between the deteriorations of the three emittants. Just as there
exists a correlation between emission levels at any one time, it is
suspected that the rates of change in these levels over a period of time
are also correlated. It may be possible to develop a theory of composite
deterioration by applying Principal Component Analysis and Factor Analysis
procedures to the existing data reported in Reference 8. If the results
are promising, additional testing and studies should be planned.
S9
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REFERENCES
1. Paul Kunselman, H.T. McAdams, C,J. Domke, and Marcia Williams,
Automobile Exhaust Emmission Modal Analysis Model, Environmental
Protection Agency Report. No. EPA-460/3-74-005 (January 1974).
2. H.T. McAdams, Automobile Exhaust Emission Modal Analysis Model
Extension and Refinement, Environmental Protection Agency Report No.
EPA-460/3-74-024 (October 1974).
3. Automobile Exhaust Emission Surveillance--A Summary, Environmental
Protection Agency Report No. APTD-1544 (March 1973).
4. Marcia E. Williams, John T. White, Lois A. Platte, Charles J. Domke,
Automobile Exhaust Emission Surveillance—Analysis of the FY 72 Program,
Environmental Protection Agency Report No. EPA-460/2-74-001 (February
1974).
5. Jeffrey Bernard, Paul Donovan, H.T. McAdams, Automobile Exhaust
Emission Surveillance—Analysis of the FY 73 Program, Environmental
Protection Agency Report No. EPA-460/3-75-007 (July1975).
6. Norman Draper and Harry Smith, Applied Regression Analysis, John
Wiley and Sons, Inc. (1966).
7. K. Diem and C. Lenther, Editors,. Scientific Tables, GEIGY Pharma-
ceuticals Division of CIBA-GEIGY Corp. (1970).
8. J.A. Gunderson and L. Resnick, Degradation Effects on Motor Vehicle
Exhaust Emission, Society of Automotive Engineers Congress and
Exposition Report No. 760366 (1976).
60
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APPENDIX I
T-TEST FOR THE EQUALITY OF TWO SLOPES
(Adapted from Reference 7)
Given two regression:
Yj = a.j + bjXj n^ ¦ no of data points
Y2 = a2 + b2x2 n2 » no of data points
Test the hypothesis that ¦ b2< under the conditions that the residual
variances are unknown and unequal.
bi — ba.
The test statistic is given as
and is compared to at variable with degress of freedom, where
** " s*,
s?c, ¦yar (*i)*6v0
S)lz = var (X2) ' (nz~0
(fyx), = estimate of = residual mean square (1)
estimate of * residual mean square (2)
J
= n,-2.
2^2 s «V-Z-
K *
(Syx),'$*x +
1-1
-------
APPENDIX II
LINEAR REGRESSION RESULTS FOR FTP DATA
The tables in this appendix list the results of linear regression
analysis on FTP data from the FY 71^73 Emission Factor Programs, Regress
sion results are given for both the basic data sets and corrected data
sets with 10% outliers removed. The intercept and slope data is
presented in scientific notation with the power of ten listed after the
four-place characteristic. Calculated F-ratios for testing the significance
of the slope (deterioration factor) are also included.
II-l
-------
Table II-1
REGRESSION RESULTS BY MODEL YEAR
EFP FY 71-73
Low-Altitude, Non-California Cities
MODEL
YEAR
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.7800
+01
0.2306
-04
2.13
BASIC
CO
0.8497
+02
0.3590
-03
8.59
Pre-1968
(N=329)
NOXC
0.3365
+01
0.1096
-05
0.07
HC
0.7334
+01
0.1486
-04
2.79
CORRECTED
CO
0.8761
+02
0.2754
-03
5.91
(N»301)
NOXC
0.3484
+01
-.1990
-05
0.26
HC
0.4247
+01
0.2884
-04
4.25
BASIC
CO
0.5303
+02
0.3717
-03
7.79
1970
(N=266)
NOXC
0.4824
+01
-.5786
-05
0.85
HC
0.3790
+01
0.2267
o
1
13.21
CORRECTED
CO
0.4636
+02
0.4332
-03
17.47
(N=242)
NOXC
0.4843
+01
-.8343
-05
2.41
HC
0.3347
+01
0.3508
-04
12.87
BASIC
CO
0.4405
+02
0.4821
-03
11.62
1971
(N=308)
NOXC
0.4674
+01
1
04
o
-05
0.20
HC
0.3038.
+01
0.3018
-04
30.32
CORRECTED
CO
0.3860
+02
0.5137
-03
23.88
(N=285)
NOXC
0.4703
+01
-.3384
-05
0.25
II-2
-------
TABLE II-l
(continued)
MODEL
YEAR
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.3366 +01
0.3003
-04
3.35
BASIC
CO
0.4171 +02
0.5710
-03
10.35
1972
(FY 72 § 73)
(N=260)
NOXC
0.4375 +01
0.1181
-04
2.01
CORRECTED
HC
CO
0.3074 +01
0.4003 +02
0.2536
0.4710
-04
-03
15.56
12.22
(N»246)
NOXC
0.4515 +01
0.9674
-06
0.02
HC
0.4098 +01
-.1347
-05
0.01
BASIC
CO
0.5571 +02
-.1277
-03
0.24
1973
(FY 73)
(N»140).
NOXC
0.3215 +01
0.1399
-0.4
1.27
HC
0.3692 +01
0.3876
-05
0.16
CORRECTED
CO
0.4862 +02
-.1935
-04
0.01
(N=129)
NOXC
0.3162 +01
0.9978
-05
1.28
11*3
-------
Table 11-2
REGRESSION RESULTS BY FISCAL YEAR
Model Year 1971
Low-Altitude, Non-California Cities
EFP
FY
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.2956 +01
0.3004
-04
2.25
BASIC
CO
0.4562 +02
0.4597
-04
0.01
1971
(N=80)
NOXC
0.5074 +01
-.5312
-05
0.05
HC
0.2907 +01
0.1539
-04
1.10
CORRECTED
CO
0.4039 +02
0.1675
-03
0.26
(N«74)
NOXC
0.4914 +01
0.5388
-05
0.05
HC
0.4241 +01
0.6382
-05
0.07
BASIC
CO
0.6184 +02
-.5377
-04
0.02
1972
(N=120)
NOXC
0.3961 +01
0.1049
-04
0.49
HC
0.3574 +01
0.1377
-04
1.23
CORRECTED
CO
0.5614 +02
-.1092
-04
0.00
(N=112)
NOXC
0.4038 +01
0.1286
-04
0.71
HC
0.3997 +01
0.2291
-04
1.51
BASIC
CO
0.3771 +02
0.6471
-03
8.50
1973
(N=108)
NOXC
0.4736 +01
-.1654
-05
0.02
HC
0.3396 +01
0.2280
-04
5.77
CORRECTED
CO
0.2631 +02
0.8169
-03
25.07
(N=97)
NOXC
0.4778 +01
-.3604
-05
0.10
II-4
-------
Table II-3
REGRESSION RESULTS BY FISCAL YEAR
All Model Years
Low-Altitude,. Non-California Cities
EFP
FY
DATA POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
1971
BASIC
(N*412)
HC
CO
NOXC
0.2S46 +01
0.3928 +02
0.5283 +01
0.8737 -04
0.8683 -03
-.2052 -04
62.41
79.56
24.11
CORRECTED
(N=377)
HC
CO
NOXC
0.2701 +01
0.3732 +02
0.5285 +01
0.6542 -04
0.7634 -03
-.2066 -04
127.99
101.61
27.47
1972
BASIC
(N-680)'
HC
CO
NOXC
0.3023 +01
0.4214 +02
0.4563 +01
0.6935 -04
0.7033 -03
-.1002 -Q4
91.15
124.40
15.39
CORRECTED
(N*630)
HC
CO
NOXC
0.2645 +01
0.3846 +02
0.4666 +01
0.5899 -04
0.6868 -03
-.1183 -04
296.88
187.04
23.90
1973
BASIC
(N«720)
HC
CO
NOXC
0.3616 +01
0.4606 +02
0.3841 +01
0.5429 -04
0.6660 -03
0.1425 -04
51.03
102.40
21.82
CORRECTED
(N»658)
HC
CO
NOXC
0.3598. +01
0.4278 +02
0.3712 +01
0.3585 -04
0.5909 -03
0.1542 -04
97.46
136.55
32.79
II-S
-------
Table II-4
REGRESSION RESULTS FOR ALL MODEL YEARS
FOR EFP FY 71-73
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.3190 +01
0.6657 -04
196.28
BASIC
CO
0.4341 +02
0.7170 -03
301.17
(N=1812)
NOXC
0.4414 +01
-.2304 -05
1.58
CORRECTED
(N=1667)
HC
CO
NOXC
0.3006 +01
0.3988 +02
0.4409 +01
0.5243 -04
0.6678 -03
-.2870 -05
499.71
424.88
2.91
II-6
-------
Table II-5
REGRESSION RESULTS BY TEST SITE
EFP FY 71-73
CITY
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.3347
+01
0.3508
-04
12.87
LOW
BASIC
CO
0.4405
+02
0.4821
-03
11.62
ALTITUDE,
(N*308)
NOXC
0.4674
+01
-.3170
LO
o
I
0.20
NON-
HC
0.3038
+01
0.3018
-04
30.32
CALIF.
CORRECTED
CO
0.3860
+02
0.5137
-03
23.88
(N*285)
NOXC
0.4703
+01
-.3384
-05
0.25
HC
0.6074
+01
0.5763
-05
0.12
BASIC
CO
0.1014
+03
-.9555
-04
0.09
DENVER
(N«77)
NOXC
0.3010
+01
-.2751
-Q5
0.06
HC
0.5634
+01
0.1427
©
1
1.11
CORRECTED
CO
0.9775
+02
-.8694
I
o
0.10
(N»70)
NOXC
0.2901
+01
-.2144
-05
0.06
HC
0.3497
+01
0.2146
-04
2.83
BASIC
CO
0.6079
+02
0.5459
-04
0.05
LOS
(N=78)
NOXC
0.3927
+01
-.1092
i
o
2.38
ANGELES
HC
0.3188,
+01
0.1958
-04
5.58
CORRECTED
CO
0.5069
+02
0.2180
1
o
u*
1.74
(N*69)
NOXC
0.4101
+01
-.1411
0
1
4.48
II-7
-------
Table II-6
REGRESSION RESULTS BY CID
EFP FY 71-73
Low-Altitude," Non-California Cities
CID
RANGE
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.2079
+01
0.7691
-04
10.54
BASIC
CO
0.4298
+02
0.4238
o
1
0.03
0-249
(N=90)
NOXC
0.4485
+01
-.2209
-04
1.79
HC
0.2518
+01
0.4312
-04
8.73
CORRECTED
CO
0.3931
+02
0.1305
-03
0.43
(N=85)
NOXC
0.4905
+01
-.4295
-04
7.37
HC
0.3924
+01
0.1896
-04
1.93
BASIC
CO
0.3800
+02
0.6793
-03
19.91
250-360
(N=134)
NOXC
0.4837
+01
-.7817
-05
0.93
HC
0.3293
+01
0.2533
-04
12.78
CORRECTED
CO
0.3553
+02
0.6518
-03
25.56
(N=121)
NOXC
0.4717
+01
-.4506
-05
0.33
HC
0.3643
+01
0.2751
-04
2.70
BASIC
CO
0.6784
+02
0.1305
-03
0.13
361-500
(N=84)
NOXC
0.5187
+01
0.1234
-05
0.01
HC
0.3614.
+01
0.1510
-04
2.04
CORRECTED
CO
0.6368
+02
0.5027
-04
0.03
(N=77)
NOXC
0.5284
+01
-.5367
-06
0.00
II-8
-------
Table II-7
REGRESSION RESULTS BY ACCUMULATED MILEAGE RANGE
EFP FY 71-73
Low-Altitude, Non-California Cities
MILEAGE
ACCUMULATION
RANGE
iles per year) DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.3732
+01
0.2522
-04
0.84
BASIC
CO
0.5078
+02
0.3552
-03
0.66
0-9,999
(N=105)
NOXC
0.5034
+01
-.3620
-04
2.98
HC
0.3039
+01
0.3768
-04
5.75
CORRECTED
CO
0.5036
+02
0.9265
-04
0.08
(N»97)
NOXC
0.4910
+01
-.2751
-04
1.66
HC
0.2024
+01
0.8083
-04
12.80
BASIC
CO
0.2735
+02
0.8667
-03
17.47
10,000-
(N*104)
NOXC
0.4589
+01
0.1109
-04
0.53
13,999
HC
0.2403
+01
0.5100
-04
23.52
CORRECTED
CO
0.2924
+02
0.7030
-03
15.35
(N=97)
NOXC
0.4483
+01
0.1754
-04
1.34
HC
0.3519
+01
0.2411
-04
3.24
BASIC
CO
0.4698
+02
0.4348
-03
2.84
14,000-
(N=99)
NOXC
0.4925
+01
-.1204
-04
1.44
100,000
HC
0.3258
+01
0.2051
-04
5.07
CORRECTED
CO
0.3741
+02
0.5820
-03
9.85
(N»93)
NOXC
0.5067
+01
-.1340
-04
1.75
11-9
-------
Table II-8.
AGE AND MILEAGE REGRESSION RESULTS
EFP FY 71-73
Low-Altitude, Non-California Cities
INDEPENDENT
VARIABLE
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.3347
+01
0.3508
-04
12.87
BASIC
CO
0.4405
+02
0.4821
-03
11.62
MILEAGE
(N=308)
NOXC
0.4674
+01
-.3170
-05
0.20
HC
0.3038
+01
0.3018
o
1
30.32
CORRECTED
CO
0.3860
+02
0.5137
-03
23.88
(N=285)
NOXC
0.4703
+01
-.3384
-05
0.25
HC
0.3069
+01
0.4474
-01
15.12
BASIC
CO
0.4421
+02
0.4716
+00
7.87
AGE
(N=308)
NOXC
0.4794
+01
-.7463
-02
0.80
HC
0.3085
+01
0.2851
1
o
18.43
CORRECTED
CO
0.4282
+02
0.3568
+00
7.80
(N=286)
NOXC
0.4854
+01
-.8365
-------
APPENDIX III
LINEAR REGRESSION RESULTS FOR SDS BAG VALUE DATA
AND FOR SELECTED MODAL EMISSION MODEL PARAMETERS
The tables in this appendix list the results of linear regression
analysis on SDS data from the FY 71 and FY 73 Emission Factor Programs.
Regression results are given for both the basic data sets and corrected
data sets with 10% outliers removed. The intercept and slope data
is presented in scientific notation with the power of ten listed after
the four-place characteristic. Calculated F-ratios for testing the
significance of the slopes (deterioration factors) are also included.
The first four tables are observed bag value emissions vs. mileage
regressions. The next three tables are mileage regressions on the a2,
and a^ coefficients from the modal emissions model for Model Year 72-74
vehicles (low-altitude, non-California test sites). The last table gives
mileage regressions for observed idle mode bag values.
III-i
-------
Table III-l
BAG VALUE REGRESSION RESULTS FOR PRE-1968 VEHICLES
CITY
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.4825
+01
0.2452
o
1
2.94
LOW
BASIC
CO
0.6051
+.02
0.5628
-04
0.51
ALTITUDE,
(N=385)
NOXC
0.5043
+01
-.5229
-05
1.03
NON-
HC
0.5089
+01
0.2831
J
o
tn
0.24
CALIF.
CORRECTED
CO
0.5940
+02
0.1028
-04
0.02
(N=351)
NOXC
0.5212
+01
-.7901
-05
2.91
HC
0.7095
+01
0.1383
-04
0.44
BASIC
CO
0.1285
+03
0.9289
-06
0.00
DENVER
(N=97)
NOXC
0.1800
+01
0.7648
-05
1.01
HC
0.7586
+01
-.7270
-06
0.00
CORRECTED
CO
0.1201
+03
0.9025
-04
0.14
(N=91)
NOXC
0.1782
+01
0.6088
-05
1.01
HC
0.2967
+01
0.5060
-04
2.55
BASIC
CO
0.3296
+02
0.3878
-03
5.22
LOS
(N=106)
NOXC
0.5882
+01
-.2547
-04
8.93
ANGELES
HC
0.3427
+01 '
0.2841
-04
3.86
CORRECTED
CO
0.3085
+02
0.3829
-03
7.77
(N=95)
NOXC
0.5945
+01
-.2461
o
i
9.21
ni*2
-------
Table III-2
BAG VALUE REGRESSION RESULTS FOR MODEL YEARS 1968 § 1969
CITY
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.2776
+01
0.3028.
-04
2.77
LOW
BASIC
CO
0.2955
+02
0.3112
-03
2.67
ALTITUDE,
(N*141)
NOXC
0.6934
+01
-.1203
-04
0.89
NON-
HC
0.2702
+01
0.1621
-04
4.72
CALIF.
CORRECTED
CO
0.2532
+02
0.2632
-03
5.04
(N=130)
NOXC
0.6954
+01
-.9421
-05
0.57
HC
0.5384
+01
0.2962
-05
0.02
BASIC
CO
0.9573
+02
0.2307
-03
0.18
DENVER
(N«35)
NOXC
0.2526
+01
0.4509
-05
0.08
HC
0.4969
+01
0.1538
-04
0.61
CORRECTED
CO
0.9938
+02
0.2604
-03
0.21
(N= 32)
NOXC
0.1890
+01
0.1888
-04
1.60
HC
0.2069
+01
0.3124
-04
4.44
BASIC
CO
0.1705
+02
0.4619
-03
3.98
LOS
(N*32)
NOXC
0.8646
+01
-.5734
-04
2.74
ANGELES
HC
0.1981
+01 '
0.3026
-04
5.26
CORRECTED
CO
0.2021
+02
0.3118
-03
2.35
(N-30)
NOXC
0.8718
+01
-.5515
i
o
2.39
in-3
-------
Table III-3
BAG VALUE REGRESSION RESULTS FOR MODEL YEARS 1970 § 1971
CITY
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.2262
+01
0.2657
-04
8.88
LOW
BASIC
CO
0.3846
+02
-.1484
-03
0.77
ALTITUDE,
(N=150)
NOXC
0.6448
+01
0.1104
-04
0.54
NON-
HC
0.2177
+01
0.1974
-04
9.54
CALIF.
CORRECTED
CO
0.2721
+02
0.1679
-03
2.13
(N=137)
NOXC
0.6914
+01
-.5011
-05
0.11
HC
0.4905
+01
0.2338
-04
0.34
BASIC
CO
0.1309
+03
-.7526
-03
1.28
DENVER
(N=37)
NOXC
0.3115
+01
-.2963
-05
0.03
HC
0.5325
+01
-.2386
-04
1.08
CORRECTED
CO
0.1246
+03
-.8214
-03
3.22
(N=32)
NOXC
0.3094
+01
-.7741
-05
0.32
HC
0.2205
+01
0.3717
-04
1.60
BASIC
CO
0.2206
+02
0.2182
-03
1.08
LOS
(N=37)
NOXC
0.4868
+01
0.7000
-04
5.29
ANGELES
HC
0.1920.
+01
0.3772
-04
7.06
CORRECTED
CO
0.2456
+02
0.8014
-04
0.17
(N=34)
NOXC
0.5156
+01
0.7016
-04
6.34
111-4
-------
Table III-4
BAG VALUE REGRESSION RESULTS FOR MODEL YEARS 1972 - 1974
CITY
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.3180
+01
0.4161
-05
0.17
LOW
BASIC
CO
0.5052
+02
-.1908
-03
1.76
ALTITUDE,
(N=300)
NOXC
0.4213
+01
0.4362
-04
21.96
NON-
HC
0.2928
+01
0.1381
-05
0.09
CALIF.
CORRECTED
CO
0.4755
+02
-.2411
-03
4.97
(N=280)
NOXC
0.4142
+01
0.4119
-04
25.70
HC
0.4042
+01
0.4839
-04
6.36
BASIC
CO
0.1134
+03
0.9526
-03
1.89
DENVER
(N=75)
NOXC
0.1950
+01
0.3970
-04
8.68
HC
0.3854
+01
0.4890
-04
7.77
CORRECTED
CO
0.1076
+03
0.1020
-02
2.54
(N*69)
NOXC
0.1944
+01
0.3875
-04
10.80
HC
0.3046
+01
-.3449
-05
0.02
BASIC
CO
0.2572
+02
0.2513
-03
2.81
LOS
(N=75)
NOXC
0.3489
+01
0.4441
-04
7.20
ANGELES
HC
0.2655.
+01
-.1787
-05
0.02
CORRECTED
CO
0.2747
+02
0.1149
-03
0.68
(N»69)
NOXC
0.3290
+01
0.5057
-04
11.73
III-5
-------
Table III-S
REGRESSION RESULTS FOR MODAL EMISSION MODEL COEFFICIENT A1
CITY
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.3149
-01
0.9707
-07
0.31
LOW
BASIC
CO
0.6007
+00
-.2220
-05
1.25
ALTITUDE,
(N=300)
NOXC
0.1425
1
o
-.5678
-07
0.24
NON-
HC
0.2628
-01
0.1859
-06
3.28
CALIF.
CORRECTED
CO
0.5920
+00
-.2983
-05
3.15
(N=281)
NOXC
0.1427
-01
-.1358
-07
0.02
HC
0.2905
-01
0.7953
-06
8.07
BASIC
CO
0.8646
+00
0.2150
-04
7.54
DENVER
(N=75)
NOXC
0.7282
-02
-.2634
-06
3.54
HC
0.2254
-01
0.9960
-06
14.13
CORRECTED
CO
0.7308
+00
0.2393
-04
11.51
(N=66)
NOXC
0.6679
-02
-.3079
-06
6.36
HC
0.3501
-01
-.3233
-06
1.06
BASIC
CO
0.1671
+00
0.3000
-05
0.94
LOS
(N-75)
NOXC
0.5309
-02
-.2294
-06
1.32
ANGELES
HC
0.2656
-01
-.1266
-06
0.24
CORRECTED
CO
0.1160
+00
0.3688
-05
1.71
(N=70)
NOXC
0.3114
-02
-.2306
-06
1.92
m-6
-------
Table III-6
REGRESSION RESULTS FOR MODAL EMISSION MODEL COEFFICIENT A2
CITY
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RAT10
HC
-.1445
-02
-.5080
-08
0.19
LOW
BASIC
CO
-.4502
-01
0.3263
-06
4.17
ALTITUDE,
(N=3Q0)
NOXC
-.9549
-03
0.1115
-07
1.35
NON-
HC
-.1112
-02
-.9885
-08
2.07
CALIF.
CORRECTED
CO
-.4092
-01
0.3213
-06
6.66
(N=275)
NOXC
-.1015
-02
0,9473
-08
1.47
HC
-.1404
-02
-.4717
-07
6.89
BASIC
CO
-.5604
-01
-.1798
-05
9.07
DENVER
(N=75)
NOXC
-.4412
-03
0.3400
-07
6.03
HC
-.1319
-02
-.3379
-07
4.09
CORRECTED
CO
-.6178
-01
-.1028
-05
3.41
(N=«66)
NOXC
-.3095
-03
0.2333
-07
2.82
HC
-.2170
-02
0.2689
-07
1.77
BASIC
CO
-.8897
-02
-.1513
-06
0.50
LOS
(N*75)
NOXC
-.3835
-03
0.1115
-07
0.41
ANGELES
HC
-.1556
-02
0.8131
-08
0.20
CORRECTED
CO
-.1101
-01
-.3487
-07
0.03
(N=69)
NOXC
0.1306
-03
-.4740
-08
0.10
III-7
-------
Table III-7
REGRESSION RESULTS FOR MODAL EMISSION MODEL COEFFICIENT A3
CITY
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0.1021
-02
0.1789
-08
0.01
LOW
BASIC
CO
0.2629
-01
-.3236
-07
0.01
ALTITUDE,
(N=300)
NOXC
0.1571
-03
-.3852
-07
3.49
NON-
HC
0.2330
-03
0.2617
-07
3.80
CALIF.
CORRECTED
CO
0.1204
-01
0.1918
-06
0.36
(N=268)
NOXC
-.4207
-03
-.2150
-07
1.72
HC
-.1206
-02
0.1465
-07
0.12
BASIC
CO
0.4494
-01
-.4502
-06
0.11
DENVER
(N-75)
NOXC
-.9798
1
o
0.3173
-0.7
1.22
HC
-.6080
-03
0.1566
-07
0.28
CORRECTED
CO
0.2237
-01
-.1576
-06
0.03
(N=67)
NOXC
1
1—»
N>
-03
0.3929
-07
2.73
HC
0.3065
-02
0.2406
-07
0.26
BASIC
CO
0.8763
-01
0.3015
-06
0.13
LOS
(N-75)
NOXC
0.3785
fO
o
¦
-.7023
-07
1.51
ANGELES
HC
0.1565.
-02
0.5672
-07
2.78
CORRECTED
CO
0.7234
-01
0.5770
-06
0.60
(N*69)
NOXC
-.5866
-03
-.4512
-07
0.86
III-8
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Table III-8
REGRESSION RESULTS FOR IDLE MODE BAG VALUES
EFP FY 73
MODEL YEARS 1972-1974
CITY
DATA
POLLUTANT
INTERCEPT
SLOPE
SLOPE
F-RATIO
HC
0,8391
+00
0,1521
-05
0.03
LOW
BASIC
CO
0.1274
+02
0.4092
r04
0.48
ALTITUDE,
(N = 300)
NOXC
0.2325
+00
-.8385
-06
0.04
NON-
HC
0.6940
+00
0.6561
-06
0.07
CALIF.
CORRECTED
CO
0.1108
+02
0.2505
-04
0.29
(N = 286)
NOXC
0.1531
+00
-.3274
-06
0.09
HC
0.7163
+00
0.6781
-05
1.39
BASIC
CO
0.1122
+02
0.2895
-03
3.63
DENVER
(N = 75)
NOXC
0.7643
-01
0.3251
-06
0.11
HC
0.4855
+00
0.1002
-04
8.20
CORRECTED
CO
0.7831
+01
0.2740
-03
6.53
(N = 65)
NOXC
0.6884
-01
-.1365
-06
0.07
HC
0.6276
+00
-.2769
-05
0.17
BASIC
CO
0.6332
+01
0,5689
-04
0.49
LOS
(N « 75)
NOXC
0.8787
-01 .
-.8795
-06
3.08
ANGELES
HC
0.4036
. +00
0.9529
-06
0.16
CORRECTED
CO
0.5870
+01
0.338Q
-04
0.28
(N - 68)
NOXC
0.7650
-01
-.6376
-06
2.60
III-9
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