OE/EIA-0272 The National

Interim Energy

Consumption Survey:

Exploring the Variability 

in Energy Consumption

July 1981

U.S. Department of Energy

Energy Information Administration

Assistant Administrator for Program Development

Office of the Consumption Data System

Industrial Data Systems Division
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The National DOE/E1Au c2 i3 

Interim Energy 

Consumption Survey:

Exploring the Variability 

in Energy Consumption

Julyi981

U.S. Department of Energy

Energy Information Administration

Assistant Administrator for Program Development

Office of the Consumption Data System

Industrial Data Systems Division

Washington, D.C. 20585
Prepared by: Robert Latta, Thomas H. Woteki, Lynda Carlson, 

Wendel Thompson, Kenneth Vagts

Released for printing August 18, 1981.
PREFACE

Authority for the National Interim Energy Consumption Survey (NIECS) is 

contained in Section 52 of the Federal Energy Administration Act of 1974, 

as amended, which charges the Energy Information Administration with 

creating and maintaining a National Energy Information System. The NIECS, 

a part this system, represents the first attempt at simultaneously 

collecting residential energy consumption data and household characteristics 

from a national, statistical sample. This NIECS publication is intended 

for use by representatives of Federal, State, and local governments as 

well as by representatives from the private sector. In addition, the 

Office of Management and Budget has plans to use the results in a report 

on the possible impact of natural gas deregulation.

This report is a description of some early efforts to model the variation 

in total energy consumption and consumption by end-use reported in the 

National Interim Energy Consumption Survey (NIECS). The analyses and 

estimates presented herein are very tentative; they are not presented as 

official estimates. Rather, it is our objective to point to some of the 

difficulties we have encountered in our analyses, to share some observations 

gleaned from the data, and to share ideas with other analysts who may be 

working on similar problems.

iii
EXECUTIVE SUMMARY

In this report, separate models for the electricity and natural gas 

consumption in single-family detached dwellings were developed. The 

following are some of the highlights of the two models.

 In both models, the number of bathrooms in the dwelling was 

a major factor in the space-heating component. The number 

of bathrooms is probably an indication of the size of the 

house as well as the life-style of the occupants.

 In the natural gas model, the type of main space-heating 

equipment has a big effect on the intercept term. In 

particular, the intercept term is highest for dwellings 

that use natural gas for main space-heating via radiators 

or water pipes. The next highest is central forced-air 

equipment.

 By assuming a hypothetical household's main space-heating fuel 

is electricity we can obtain the modeled space-heating component 

from the electricity consumption model. Alternatively, by assuming 

the main space-heating fuel is natural gas, we can obtain the 

modeled space-heating component from the natural gas consumption 

model. By looking at a range of hypothetical households, it can 

be seen that the modeled space-heating component from the natural 

gas model tends to be approximately twice the modeled space-heating 

component of the electricity model.

 In the electricity consumption model, the interaction term between 

income level and the potential number of rooms that can be air 

conditioned is significant. In particular, higher income groups 

not only are more likely to have air conditioning, but also use 

the equipment they do have more than lower income groups.

 In the electricity consumption models, it was possible to use 

separate terms for most of the major electrical appliances. 

In the natural gas model, this was not possible. The 

variability in the space-and water-heating components is 

probably masking the effect of the natural gas appliances.

 The heating degree-days and cooling degree-days data used in the 

model were both computed using 65 degrees Fahrenheit as a base. 

A preliminary analysis using other bases indicated £hat a lower 

base for heating degree-days and a higher base for cooling 

degree-days would be preferable.

IV
CONTENTS

Introduction ................................................................. 1

Section 1. The NIECS: Sampling Plan and Data ................................. 3

The Sampling Plan........................................................... 3

Mail Questionnaire.......................................................... 3

Response Rates.............................................................. 3

Energy Consumption Data and Missing Data.................................... 4

Use of a Subset of the Data................................................. 4

Variable Names and Definitions.............................................. 5

Section 2. A Theoretical Model for Household Energy........................... 7

Theory for a Single Household .............................................. 7

Extension to the NIECS Sample............................................... 8

The Modeling Strategy....................................................... 9

Fitting Methodology......................................................... 10

Summary..................................................................... 10

Section 3. Graphical Summaries of Consumption Data............................ 11

Section 4. Regression Results................................................. 23

Variables Used in the Models................................................ 23

Fitting by Iterative, Weighted Least Squares................................ 27

Consumption Models.......................................................... 30

Section 5. Discussion ........................................................ 39

Strategy vs. Tactics........................................................ 42

Demographic Characteristics................................................. 42

Measures of Size and Insulation and Heating Components...................... 43

Appliances.................................................................. 44

The Heating Component and Heating Equipment................................. 44

The Cooling Component of Electricity........................................ 45

Residuals................................................................... 46

Concluding Remarks.......................................................... 46

Appendixes ................................................................... 53

Appendix A. Sampling Plan for the NIECS..................................... 54

Appendix B. Energy Consumption Data, Missing Data, and

Degree-Day Data.......................................................... 55

Appendix C. NIECS Public Use File Variables Used in Final

Consumption Model........................................................... 59

Appendix D. Wandering Boxplots.............................................. 63

References.................................................................... 64

ILLUSTRATIONS

Figure 1. Natural Gas Consumption by Heating Degree-Days for 

Households that Use Natural Gas for the Main Space-Heating 

Fuel........................................................................ 12

Figure 2. Natural Gas Consumption by Heating Degree-Days for 

Households that Do Not Use Natural Gas for the Main SpaceHeating Fuel................................................................ 13
Page No.

Figure 3. Electricity Consumption by Heating Degree-Days for 

Households that Use Electricity for the Main Space-Heating 

Fuel....................................................................... 14

Figure 4. Electricity Consumption by Heating Degree-Days for 

Households that Do Not Use Electricity for Air Conditioning 

or for the Main Space-Heating Fuel......................................... 15

Figure 5. Electricity Consumption by Cooling Degree-Days for 

Households That Do not Use Electricity For the Main SpaceHeating Fuel But Do Not Use Electricity for Air Conditioning............... 16

Figure 6. Wandering Box Plot of Natural Gas Consumption by 

Heating Degree-Days for Households that Use Natural Gas for 

the Main Space-Heating Fuel................................................ 17

Figure 7. Wandering Box Plot of Electricity Consumption by 

Heating Degree-Days for Households that Use Electricity for 

the Main Space-Heating Fuel................................................ 18

Figure 8. Outlier Detection for Natural Gas Model: Predicted

Consumption by Residual.................................................... 28

Figure 9. Outlier Detection for Electricity Model: Predicted

Consumption by Residual.................................................... 29

Figure 10. Residual for Natural Gas Model by Heating Degree-Days 

for Households that Use Natural Gas for the Main Space-Heating 

Fuel....................................................................... 48

Figure 11. Residual for Electricity Model by Heating Degree-Days 

for Households that Use Electricity for the Main Space-Heating 

Fuel....................................................................... 49

Figure 12. Wandering Box Plot of Residual for Natural Gas Model 

by Heating Degree-Days for Households that Use Natural Gas for 

the Main Space-Heating Fuel................................................ 50

Figure 13. Residual for Electricity Model by Residual for Natural

Gas Model.................................................................. 51

TABLES

Table 1. Analysis of Variance Table for Natural Gas Model

(Using NCNGYRB as the Dependent Variable).................................. 31

Table 2. Weighted Least Square Solution for Natural Gas Model................ 32

Table 3. Households That Were Determined to be Outliers for

Natural Gas Consumption Models............................................. 33

Table 4. Analysis of Variance Table for Electricity Model

(Using NCELYRB as the Dependent Variable).................................. 34

Table 5. Weighted Least Square Solution for Electricity Model................ 35

Table 6. Households That Were Determined to be Outliers for

Electricity Consumption Model.............................................. 36

Table 7. Modeled Natural Gas Consumption for Hypothetical Household.......... 40

Table 8. Modeled Electricity Consumption for Hypothetical Households......... 41

VI
Page No.

Table Bl. Energy Consumption Records and Missing Data for Survey Households

Using Electricity and Utility Gas........................................... 56

Table B2. Ratio Adjustments................................................... 58

Table Cl. Household Variables Selected for Analysis of

Natural Gas Consumption and Electricity Consumption......................... 60

Table C2. Transformed Household Variables Selected for Analysis of Natural

Gas Consumption and Electricity Consumption................................. 61

VII

INTRODUCTION

By December of 1979, fieldwork for EIA's first survey of energy consumption 

in the residential sector, the National Interim Energy Consumption Survey 

(NIECS), was largely concluded. Since then, a variety of reports 

[References 1,2,3,4] have been produced, which tabulate and summarize the 

data and survey operations. Concurrently, a variety of detailed 

methodological and subject matter analyses were begun concerning six 

interrelated sets of problems:

 Variation in energy consumption; How does energy consumption

vary by region? By income group? By square footage? By household 

characteristics? By main space-heating fuel?

 Total energy consumption for the household; How should a

household's housing unit consumption be linked with its vehicle 

consumption to determine total energy consumption by household?

 Energy consumption by end-use; How much natural gas is used for 

space-heating? How much electricity is used for air conditioning? 

How much of either is used for water-heating? What can we say 

about end-use consumption of fuel oil?

 Energy performance ratios; Can energy consumption be normalized 

to eliminate variation in physical factors (such as climate) and 

can such normalization form the basis for comparing consumption 

at different points in time? For example, does normalization by 

degree-days in the ratio Btu/degree-day substantially eliminate 

the variation in consumption associated with temporal and geographic 

variations in climate? At what level of aggregation or over what 

partition of the household sector should this normalization be 

performed? Can these ratios be used as indicators of the energy 

quality of the housing stock?

 Small area estimates: Can the data from a relatively small

national sample be used to infer the energy consumption of "small" 

areas such as States? How should this be done?

 Imputing missing data: Every survey has missing data problems to 

one degree or another. What is the best way to handle them here? 

[References 5 and 6]. Can microaggregated consumption data assist 

in consumption imputations? Can consumption data be used to 

impute housing unit characteristics?
This progress report describes some early analyses of the first problem 

mentioned, the variability in energy consumption reported in the NIECS. 

It concentrates on regression models for describing the variability in 

natural gas and electricity consumption for households living in singlefamily detached houses. Section 1 provides a description of the NIECS 

sample data and the subsets of it that were used in our analyses. Several 

appendixes supplement this discussion. Section 2 presents a theoretical 

model for describing a household's energy consumption. Section 3 presents 

some graphical summaries of the data which serve to explain the specific 

models that were fit to the data and leads to some speculation about what 

contributes to their lack of fit. Section 4 describes the empirical 

models fit to the data, and the method of fitting, and relates them to 

the discussion in Section 2. Section 5 summarizes the results of the 

preceding sections and contains some speculation on interpretation of the 

model coefficients obtained in Section 4 and some potential uses of the 

model.
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Section 1. The NIECS: Sampling Plan and Data

The NIECS survey was designed as a probability sample of households using 

personal interviews to obtain energy-related characteristics of the housing 

unit, characteristics of appliances, information on the conservation 

activities and demographic characteristics of the household members, and 

data on energy consumption and expenditures. The latter data were obtained 

from the utilities serving the sampled households; permission to obtain 

these data was solicited during the interviews.

The availability of accurate consumption and expenditures data is a 

feature unique to the NIECS among Federal Surveys of the household sector. 

This section briefly describes the NIECS sampling plan and the subsets of 

the data used for preliminary analysis. The Appendixes provide greater 

detail.

The Sampling Plan

The NIECS was based on a multi-stage area probability sample. The 

selection technique was roughly equivalent to dividing the United States 

into small geographic segments each consisting of a cluster of about 10 

households and making a systematic random selection of such clusters for 

the survey. Probability methods were used at each stage of sample 

selection. Interviewers had no choice in the selection of households for 

the survey.

Altogether, 4,849 housing units were selected for the national sample. 

Of these, 342 were determined to be vacant or seasonal at the time of the 

first interviewer contact, leaving 4,507 occupied housing units (households) 

in the sample for the survey.

Mail Questionnaire

A number of households were unavailable for a personal interview so a 

mail questionnaire was used to solicit a subset of the data from the 

interview questionnaire including the request for permission to seek 

utility data. The responses to the mail questionnaire were used primarily 

to investigate potential nonresponse biases in the consumption data and 

to impute household and housing unit characteristics.

Response Rates

Personal interviews were completed at 3,842 households (85.2 percent) of 

the 4,507 occupied housing units, and mailed questionnaires were completed 

by an additional 239 households (5.3 percent). The overall response 

rate, including both personal household interviews and mailed questionnaires 

was 90.5 percent.
Energy Consumption Data and Missing Data

The energy consumption data for a sampled household was obtained from 

the utilities and fuel suppliers serving the household, provided the 

household consented and the suppliers cooperated. When consent was 

obtained, a supplier was requested to provide 12 consecutive monthly 

billing records, or other periodic billing data, spanning the nominal 

survey year April 1978 to March 1979. The success of these procedures 

is summarized in Table Bl (Appendix B): data were received from suppliers 

for 85.6 percent of the households using electricity and 75.2 percent of 

the households using natural gas. Disaggregation of these percentages 

and references to the procedures used to impute the missing data are 

also given in the Appendix.

The energy data used here are annual figures derived from the utility 

billing data. In cases when 11 or more months of data were obtained for 

a household, the annual figure is essentially the total reported consumption 

prorated to a nominal 365-day survey year. The adjustment procedure is 

described in Reference 5 and an updated report in Reference 6 (See also 

Appendix B, "Degree-Day Data").

Both the heating degree-day data, base 65 degrees Fahrenheit, and the 

cooling degree-day data, base 65 degrees Fahrenheit, used here are included 

in the NIECS public use file. These data represent 40-year averages 

computed on a per household basis and are adjusted for departures from a 

46-year average (1930-1975) on a regional basis. The adjustment procedures 

are also described in Appendix B.

Use of a Subset of the Data

The analysis of natural gas consumption discussed in later sections is 

based on data from only those single-family detached households that 

participated in the personal interviews, and consumed some natural gas 

and whose annualized natural gas consumption estimate was based on at 

least 11 months of reliable utility data. The households used in the 

analysis of electricity consumption were chosen in an analogous manner. 

Restricting the analysis to single-family detached dwellings emphasizes 

the importance of this type of dwelling in the NIECS data and simplifies 

the task of describing variability. Extending the results of this analysis 

to other housing types will be the subject of a later report.

Basing the analyses on only those households with at least 11 months of 

energy data was done to avoid confusion between systematic variation in 

the data, from variation introduced by the methods used to impute missing 

data. We have no reason to suspect systematic defects in our imputation 

methods [References 5 and 6]; nevertheless, we choose initially to explore 

the variation in energy consumption using only households with unimputed 

energy data. Later, we will extend our analyses to the entire data set.
Variable Names and Definitions

The names and definitions of the variables used here are documented in 

Tables Cl and C2 (Appendix C). The variables fall into two classes, 

those which are available directly from the NIECS users data (Table C) 

and those which are derivations or transformations of the former (Table 

C2). The names of the variables in the first category correspond to the 

names used for the public users data. The definitions of derived variables 

are presented in the text as appropriate.

Section 2. A Theoretical Model for Household Energy Consumption

Theory for a Single Household

In a continuing empirical study of energy consumption in occupied homes 

in Twin Rivers, New Jersey, (References 7-11) the amount of heating fuel 

(%) needed on a daily basis to maintain a house at a desired fixed 

temperature has been described by

(Equation 1) Ht = B(Pr - Tai ) + + E

where i is an index for days, Tai is the average outside temperature, Pr 

is a reference temperature, B is an overall performance index for the 

house which characterizes its response to cold weather, and E-^ is a 

stochastic error term with expected value zero. The quantity (Pr ~Ta i) 

is equal to (P r - Ta^) when the difference is positive, and is equal to 

zero otherwise. We assume nothing more about E for now.

According to the theory underlying the model, the reference temperature 

Pr carries information about factors under the control of residents, such 

as thermostat setting and the added heat load from the use of appliances 

(electric and gas), and some information about the thermal properties of 

the house (Reference 8). A lowered thermostat setting or increased use 

of appliances should result in a lowered value of Pr . The overall 

interpretation of P r is that it indicates the warmest outdoor temperature 

at which the heating system must supply heat to the house, or the effective 

temperature it must maintain. Although not independent of the physical 

properties of the house, it is dominated by the actions of the residents.

The value of B, in this theory, is independent of the outside temperature 

and internal and solar heat gains, and indexes the house's average rate 

of heat loss and heating system efficiency, factors determined primarily 

by the design, construction, and maintenance of the house (Reference 8). 

Adding insulation or weatherstripping or overhauling the heating system 

should decrease the value of B.

The empirical analyses carried out in the Twin Rivers program generally 

support these interpretations of T r and B (References 8-11). Differences 

in B-values among houses were observed to correspond in a way consistent 

with theory to differences in design and construction characteristics, 

such as number of bedrooms, presence of double-pane windows and compass 

orientation of the house, while reductions in B were observed to coincide 

with improvements in insulation (References 8-10). Also confirming the 

theory, variations in P r were associated with changes in the behavior of 

occupants: in one-owner homes, the value of Pr changed considerably 

less than it did in homes that changed owners (Reference 8). Additionally, 

the value of Pr was lower among those with more bedrooms, possibly because 

the smaller houses tend to be occupied by people without children and are 

therefore more frequently unoccupied, resulting in lower average-interior 

temperatures (Reference 9).
Extension to the NIECS Sample

The possibility of using these single-home observations in an analysis of 

the NIECS data is appealing. In order to do this, some modifications to 

the above model must be introduced.

First, HI in Equation 1 represents heating fuel consumption, exclusive of 

other fuel uses, such as cooking and water-heating. Let us introduce the 

term A0 which we define to be the average amount of energy used for other 

purposes so that Equation 1 becomes:

(Equation 2) H + AQ - AQ + B (Pr - Tai ) + + E ± .

Let FI = % + A0J F£ represents total consumption of a specified fuel. 

Approximate (Pr - Tai ) + by DD^^ = (65 - Tai ) +, the number of heating degreedays, base 65 degrees Fahrenheit, for the i fc " day. Summing over the days 

in a year, Equation 2 then becomes:

(Equation 3) F=ZFi = Z(AQ + B(Pr -Tai ) + ) + ZE±

= A + B DDi + EE.J

= A + B (DD) + E

where DD is the heating degree-day total for the year. Let us introduce 

a subscript to denote households.

Then, Equation 3 becomes

(Equation 4) Fh = Ah + Bh (DDh ) +Eh

where: F^ is the total consumption of fuel F 

by the htn household in a given year.

An summarizes the household's base load consumption, the 

amount of fuel needed for cooking, water-heating, etc.

6^ is a coefficient which summarizes the energy 

characteristics of the dwelling unit.

s tne annual degree-day figure for the household, 

and En is a random error term, the structure 

of which we leave unspecified in this report.
The Modeling Strategy

According to Equation 4 and the above theory, A^ depends heavily on the 

behavior of the households or the characteristics of their appliances, 

and much less so on the physical properties of the dwelling unit. A^ 

remains constant over time. On the other hand, B^ is seen as depending 

on the thermal characteristics of the dwelling unit and is constant over 

time.

In practice, neither of the above statements is likely to be strictly 

true; one can expect a good deal of interaction between behavioral factors 

and physical factors affecting energy consumption, and both coefficients 

will change over time as the composition of the household and features of 

the dwelling unit change. Nevertheless, Equation 4 suggests the strategy 

for describing the variability in energy consumption which has been 

adopted for this report: the coefficients A^ and B^ are set up as simple 

functions of items in the NIECS data, and a methodology for fitting the 

model is developed. Thus we consider models of the form of Equation 4 

with

K 

Ah = Z \ Xhk + A0

k=l

a linear combination of K coefficients A^ weighted by the value of an 

item X^ f rom tne NIECS data. Similarly, we express

Bh " Z B! Yhl 

1=1

Note that the coefficients A^ and B^ are constant across households.

Pursuant to our strategy, we emphasize characteristics X^ of the household 

in the development of the coefficients A^ and characteristics, Y^i, of 

the housing unit in the development of B n.

We can introduce terms to model the fuel consumption due to air conditioning 

in a similar manner. Let G^ be the portion of F n used for air conditioning. 

Model Gft by

M

Gh = ( Z Cm Zhm ) CCh 

m=l

where CC^ is the cooling degree-days for household h. The variables Z^m 

are characteristics of the housing unit or household. The Z^m are defined 

to be zero if the household does not have air conditioning. The coefficients 

Cm are constant across households.
Fitting Methodology

Substituting the expression for A^ and B^ in Equation 4 and adding in 

we get

(Equation 5)

K L

Fh = A0 + E Ak Yhk + ( I B! Yhl ) DDh 

k=l L=l

M

+ ( S Cm Zhra ) CCh + Eh 

m=l

which, when fully expanded, is a model linear in the parameters Ak , Bj_, 

and C m. This suggests the use of ordinary least squares methodology to 

fit the parameters. A variation of this approach which discounts outlier 

observations is the subject of Section 4.

Summary

The Twin Rivers experiments and the preceeding discussion provide a 

theoretical underpinning amid a body of empirical evidence for the approach 

taken here. However, there are vast differences between the NIECS data 

and the Twin Rivers experiments, and significant omissions in our 

preliminary statistical analysis, which must be taken into account before 

the results of our analysis can be accepted as a definitive, or even 

adequate, description of the variability in household energy consumption. 

This report is a first effort to provide that description.

10
Section 3. Graphical Summaries of Consumption Data

In this section, we present seven plots that illustrate trends in 

residential consumption of natural gas and electricity as a function of 

degree-days. The plots anticipate the modeling strategy adopted in 

Section 4 and outlined in Section 2. They also illustrate the great 

amount of variability of energy consumption among households living in 

single-family detached dwellings. The following is a list of the seven 

plots:

 Figure 1 is a plot of total natural gas consumption versus heating 

degree-days for households that use natural gas as the main 

heating fuel. The figure shows total gas consumption, with 

heating and nonheating uses combined.

 Figure 2 is a plot of natural gas consumption versus heating

degree-days for households that consume some natural gas, but do 

not use natural gas as the main space-heating fuel.

 Figure 3 is a plot of total electricity consumption versus heating 

degree-days for households that use electricity as the main spaceheating fuel.

 Figure 4 is a plot of total electricity consumption versus heating 

degree-days for households that do not use electricity for air 

conditioning or as the main space-heating fuel.

 Figure 5 is a plot of total electricity consumption versus cooling 

degree-days for households that use electricity for air conditioning, 

but not as the main space-heating fuel.

 Figure 6 supplements Figure 1 and Figure 7 supplements Figure 

3. The construction and meaning of these plots is discussed 

below.

In Viewing Figures 1 and 3, it is obvious that consumption of the main heating 

fuel is positively correlated with degree-days. In comparing the figures, 

it is obvious that households using natural gas for heating tend to use 

one-and-a-half to two times as many Btu's as houses using electricity for 

the same purpose. The natural gas houses tend to center around a line 

between 150 x 10 6 Btu and 200 x 10 6 Btu whereas the electrically heated 

houses center around a line between 75 x 10" Btu and 100 x 10 . However, 

this difference varies substantially over the range of degree-days 

considered. We will return to this point when we consider Figures 6 and 

7 and the relationship between consumption and degree-days evidenced in 

the present figures. (These differences do not imply that residential 

space-heating is an inefficient use of natural gas. A powerplant would 

consume several Btu's of natural gas in generating and delivering one 

Btu of electricity to a residence.)

11
FIGURE 1. NATURAL GAS COMSUMPTION BY HEATING DEGREE-DAYS FOR HOUSEHOLDS THAT USE NATURAL GAS FOR THE MAIN SPACE-HEATING FUEL.

NATURAL GAS COMSUMPTION 

(IN MILLION BTU'S)

500 ^

450 

400 

350 - 

300 

250 

200 

150

100 

50 H

1 

1-

 

h 

 

 

h

1- A

B

B

C

1- C

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A

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A

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A 

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A AA 

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AAB A A 

A BACAAB 

ABC B AD 

BABAB B 

AACD AAC 

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CC CDAFH

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DCFB 

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8000

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B B 

A C

A D

E

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A C

B

A

I i

9000 10000 11000

HEATING DEGREE-DAYS

LEGEND: A = i OBSERVATION. B = 2 OBSERVATIONS. ETC.
FIGURE 2. NATURAL GAS CONSUMPTION BY HEATING DEGREE-DAYS FOR HOUSEHOLDS THAT DO NOT USE NATURAL GAS FOR THE MAIN SPACE-HEATING FUEL.

NATURAL GAS CONCUMPTION 

(IN MILLION BTU'S)

500

450

400

350

300

250 -f

200

150

100

50

0 -t

A 

A

AA

B A 

A 

A

0 1000 2000 3000

LEGEND; A = i OBSERVATION* B = 2 OBSERVATIONS. ETC.

A A A

A A 

ABA 

AB BD A F A 

BE B 

A H A B 

AB

4000 5000 6000 

HEATING DEGREE-DAYS

AA A 

AAAAAA

7000 8000 9000 10000 11000
FIGURE 3. ELECTRICITY CONSUMPTION BY HEATING DEGREE-DAYS FOR HOUSEHOLDS THAT USE ELECTRICITY FOR THE MAIN SPACE-HEATING FUEL.

ELECTRICITY CONSUMPTION 

(IN MILLION BTU'S)

250

225

200

175 •

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125

100

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6000 7000 8000 9000 10000 11000

LEGEND: A = i OBSERVATION. B = 2 OBSERVATIONS* ETC.

HEATING DEGREE-DAYS
FIGURE 4. ELECTRICITY CONSUMPTION BY HEATING DEGREE-DAYS FOR HOUSEHOLDS THAT DO NOT USE ELECTRICITY FOR AIR CONDITIONING OR FOR 

THE MAIN SPACE HEATING FUEL.

ELECTRICITY CONSUMPTION 

<IN MILLION BTU'S)

250

225

200

175

150 -

125

100 •

75

50 •

25

•

•

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0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

LEGEND: A = i OBSERVATION. B = 2 OBSERVATIONS. ETC,

HEATING DEGREE-DAYS
FIGURE 5. ELECTRICITY CONSUMPTION BY COOLING DEGREE-DAYS FOR HOUSEHOLDS THAT DO NOT USE ELECTRICITY FOR THE MAIN SPACE-HEATING 

FUEL BUT DO USE ELECTRICITY FOR AIR CONDITIONING.

ELECTRICITY CONSUMPTION 

(IN MILLION BTU'S)

250

225

200

175 -

150 -

125 H

100

75 •

50 •

25 •

0 H

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400 800 1200 1600 2000 2400 2800 3200 3600 4000

COOLING DEGREE-DAYS

LEGEND} A = 1 OBSERVATION, B = 2 OBSERVATIONS* ETC.
FIGURE A. WANDERING BOX PLOT OF NATURAL. GAS CONSUMPTION BY HEATING DEGREE-DAYS FOR HOUSEHOLDS THAT USE NATURAL GAS FOR THE 

MAIN SPACE-HEATING FUEL.

NATURAL GAS COMSUMPTION 

(IN MILLION BTU'S)

500

450

400

350

300

250

200 4

150 -f

100

50 -f

0

0

0

03

02

02

0

02

03

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X

02

02

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1000

LEGEND*. X = EXTREME OUTLIER

0 = BORDERLINE OUTLIER 

* = MEDIAN.

3000 4000 5000 6000 

HEATING DEGREE-DAYS

___ _ i _ _ ____ _ _ _ „. _ „ 4. _- _ ___ _ _.__ _ _ 4. _ _ _. _ _ „ _ ,_ _ J- — _ _ _^._. _ _ _ 4. _ _ _.

7000 8000 9000 10000 11000
FIGURE 7. WANDERING BOX PLOT OF ELECTRICITY CONSUMPTION BY HEATING DEGREE-DAYS FOR HOUSEHOLDS THAT USE ELECTRICITY FOR THE 

MAIN SPACE-HEATING FUEL.

ELECTRICITY CONSUMPTION 

(IN MILLION BTU'S) 

250 +

25

00

175

150

125

100

75 -f

50

0 +

LEGEND: x = EXTREME OUTLIER

0 = BORDERLINE OUTLIER 

* = MEDIAN.

3000

___ _ J_____ _ _ _ _ _ _ _ _L _ _ _ _ _. _

4000 5000

„ _ _ _ I _ _ _ _., _

7000 8000 10000 11000

HEATING DEGREE-DAYS
Figures 2 and 4 provide a dramatic contrast to Figures 1 and 3 and 

emphasize the relationship between heating and degree-days observed in 

the latter. In addition, the large difference in consumption between the 

two energy types is gone. Natural gas consumption in Figure 2 tends to 

center around 25 x 10^ Btu (although the small number of observations and 

large variability tend to obscure this) and so does electricity consumption 

in Figure 4.

Figure 5 is a plot of electricity consumption versus cooling degree-days 

among households that use electricity for air conditioning and other uses 

but not for heating. The figure is stunning for its lack of any discernible 

association between the two variables. On the face of it, the plot 

seems to indicate that the demand for cooling does not vary with climatic 

conditions. In our opinion, however, it more than likely expresses the 

need to correct for other variables in modeling the demand for cooling and 

the deficiencies of cooling degree-days, base 65 degrees Fahrenheit, as a 

measure of the warmth of a day or a region, or as an indicator of peoples' 

demand for cooling. Figures 6 and 7 are intended to supplement Figures 

1 and 3 and reveal more of the relationship between energy consumption 

and heating degree-days. Construction of these figures is described in 

detail in Appendix D. A brief summary is: the data are divided into 

groups according to the distribution of the abscissa; within groups, the 

median and first and third quartiles of the ordinate are calculated. 

Then the statistics for the ordinate are plotted by groups and centered 

over the group medians along the abscissa. Outlying points are noted to 

give a sense of the variability of the data, and group statistics are 

linked by line segments to give a sense of the structure in the data.

In viewing Figure 6, a tendency is observed for gas consumption to rise 

smoothly from the lower end of the degree-day scale to the 6,500 to 

7,500 degree-day range. The rate of rise is about 100 x 10^ Btu per 

5,800 degree-days or about 17 cubic feet per degree-day where 1 cubic 

foot is valued at 1,020 Btu's. Over this entire range, the outlying 

values occur only on the upper end of the consumption scale. Within 

groups, outlying values as large as two and three times the group median 

are not uncommon.

Starting in the range 7,000-7,500 degree-days, the association between 

gas consumption and degree-days seems to change markedly. At this point, 

the group medians level off, tending to remain constant at around 175 x 

10^ Btu even at 10,200 degree-days. Unfortunately, we have no data in 

the range from 8,000 to 9,700 degree-days and it is therefore difficult 

to write with certainty of a change in trend.

19
There are several hypotheses explaining the drop in the upper end of the 

energy-consumption-per-degree—days curve observed in Figures 1 and 6:

i. Sampling variability: the households located at 9,800 and 10,200 

may be lower than "expected" relative to the other households 

simply because of random sampling variability. In this case, 

the presumed change in trend is probably a feature of the sampled 

households but not of the population of all households.

ii. Systematic differences: the change in trend may go beyond sampling 

variability so that the population of households at the upper 

end of the degree-day range is indeed different than the balance 

of the population. In this case, the change in trend is indicative 

of a real difference which might be due to:

—Better home insulation or construction than the general population.

—Acclimation to colder climate; households in northern climates 

may have adjusted better to cooler interior temperatures than 

their southern counterparts.

—More conscientious energy conservation: Households in northern 

climates may be more conservative in their use of energy 

resources. Higher natural gas prices in the Northern climates 

may contribute to this.

—Greater reliance on secondary heating systems: Households in 

northern climates may make greater use of secondary heating 

systems, such as fireplaces or portable heaters, than their 

southern neighbors. These secondary uses are not accounted for 

in Figures 1 and 6 unless the secondary and main fuels are both 

natural gas.

iii. Problems with the heating degree-day measure: heating degree-days 

are a convenient summary of the coldness of a day. However, they 

may not be a satisfactory measure of the demand for heat in colder 

climates. Alternatively, the degree-day base used here, 65 degrees 

Fahrenheit may not be the best choice. A lower degree-day base 

would tend to squeeze the plots, a higher base expand them; 

depending on how much the plots are changed, they could become 

more linear.

Turning to Figure 7, we observe a rather different relationship for 

electricity consumption versus heating degree-days. The Figure starts 

off with a sharp drop from a center of about 87.5 x 10° Btu down to one 

of about 25 x 10^ Btu and a rise back to its starting point all in the 

range from 300 to 1,200 degree-days. We believe this rapid variation is 

due either to systematic differences independent of the use of electricity 

for space-heating and cooling, or simply random variation.

20
After this initial burst of variation, the data in Figures 3 and 7 tend 

to settle down, rising slowly but steadily from about 75 x 10^ Btu at the 

2,800 degree-day mark to about 125 x 10 6 Btu at 7,800 degree-days, a rate 

of 50 x 10^ Btu over a 5,000 degree-day range. In equivalent cubic feet 

of gas, this rate is 9.8 cubic feet per degree-day.

In summary, there are hypotheses which can account for the structure of 

Figures 1 and 6 and Figures 2 and 7. If the leveling off in Figure 6 is 

indicative of systematic differences, then it may be possible to account 

for them in the subsequent analysis. We return to this point in Sections 

4 and 5.

The rather distinct differences between Figures 1 and 6 and 2 and 7 

indicate that the heating uses of electricity and natural gas are very 

different phenomena which should be treated in separate models. This is 

the approach we have taken.

21

Section 4. Regression Results

The principle aim of this project is to develop linear models to explain 

the variability in household electricity and natural gas consumption. 

The models being developed are based on the theory outlined in Section 

2 using selected household variables (see Table 3), transformations of 

these variables, and interaction terms. Natural gas consumption was 

modeled separately from electricity consumption as suggested by the graphs 

in Section 3. A single model was used within each fuel type.

Variables Used in the Models

From the large number of variables in the N1ECS data, only a few dozen 

were considered for use in modeling. Of these, several were discarded 

because of known or suspected problems with the data. This section 

discusses the candidate variables and why some were used and others 

weren't. The variables are organized into groups: demographic characteristics, 

measures of size and insulation, measures of potential air conditioning 

usage, indicators of fuels used for various purposes, degree-day variables, 

and appliance indicators.

• Demographic Characteristics: The specific variables used were:

number of individuals in the household (NHSLDMEM), age of respondent 

(NAGE01), and household income (KINCOME).

• Measures of size and insulation: Descriptive housing

unit variables relating to the size of the house and limited 

measures of insulation formed the second group.

Respondents were asked the size of their home and about the 

presence and amount of insulation. Unfortunately, nonresponse to 

these items was so large that we considered the data to be unusable 

for this analysis. In subsequent surveys, we plan to measure the 

square footage of the heated and unheated sections of individual 

housing units.

Surrogate variables were used to estimate the size of the housing 

unit. These variables were the number of rooms (NROOMS), number 

of doors and windows (NDRSAWS), number of bathrooms (NBATHRMS) 

and the total number of rooms, doors, and windows (NTOTAL). NROOMS 

can be obtained directly from the public use file. NDRSAWS, NBATHRMS 

and NTOTAL are transformations of variables listed in Table Cl 

(Appendix C); equations for these transformed variables are found 

in Table C2.

In computing NBATHRMS, the variables NCOMBATH and NHAFBATH are used. 

For some houses that do have complete plumbing, one or both of the 

last two variables are missing. For these households we assumed 

that NCOMBATH and NHAFBATH are actually zero.

23
We could only reliably obtain indirect measures of the insulation 

properties of the sampled houses. One measure is the number of 

storm doors and windows, NSDRSAWS. This term measures not only 

the effect of using storm doors and windows but also the propensity 

of houses with storm doors and windows to be better-insulated in 

other ways. For example, we expect a positive correlation between 

the number of storm windows and the amount of insulation. The 

other indirect measure is KYHSBREC. This variable codes the age of 

the house on an ordinal scale. The oldest houses are code 1 and 

the newest houses are code 7.

We are currently investigating the possibility that variables 

describing energy conservation activities will provide an 

additional indirect measure of insulation.

Measures of Potential Air Conditioning Usage: the next group of 

variables gives the number of rooms that can be air conditioned 

by various types of equipment. The resulting variables are 

NRMELCAC, NRMELRAC, and NRMGASAC. These variables represent the 

number of rooms that can be air conditioned by electric central 

units, electric room units, and gas central units, respectively. 

The logic used to compute these variables is described in 

Table C2 (Appendix C). One of the variables used in the logic 

is NROOMAC. This variable is missing for some of the households 

that stated that they had central air conditioning. For these 

households, we set NROOMAC equal to NROOMS.

Fuels by End-Use: The fourth group contains variables that 

describe the fuel used for water and space-heating. The 

variables are HELWHT, HGASWHT, HELMHT, HGASWHT, HSBNMELH, 

HSBNMGSH, HELHTPUM and KMHTEQRC. These variables are all 

transformations of variables that are listed in Table Cl.

The air conditioning terms in the models always involve 

cooling degree-days as well as the number of rooms air 

conditioned by different types of equipment. The variable 

KINCOME is also interacted with the above variables to 

represent the lifestyle of the households. The terms used 

for modeling the consumption of electricity to air conditioning 

are NCOOLDD x NRMELCAC, NCOOLDD x NRMELRAC, NCOOLDD x NRMELCAC x 

KINCOME and NCOOLDD x NRMELRAC x KINCOME.

Fewer people use natural gas as fuel for air conditioning 

purposes. As a result, only the single term, NCOOLDD x NRMGASAC 

was significant in the natural gas consumption model.

Degree-Day Variables: The fifth group gives the heating and 

cooling degree-days. The variables used were NHEATDD and NCOOLDD; 

both are based at 65 degrees Fahrenheit. These are the degreedays derived from 46-year averages as described in Appendix C. 

A new public use file will be issued shortly providing the 

approximate degree-days experienced by the households for several 

bases.

24
A preliminary analysis indicates that models using heating 

degree-days based at 60 degrees Fahrenheit and cooling 

degree-days based at 70 degrees Fahrenheit result in a 

slightly higher R^ than models with degree-days based at 65 

degrees Fahrenheit. This preliminary analysis did not 

investigate all possible bases. Due to the incompleteness 

of the analysis, we decided to use the base 65 degrees 

Fahrenheit degree-days that were obtained from the 46-year 

averages for this report.

Appliance Indicator: The last group of variables describes the 

major appliances that are contained in the household. The 

variables are NELCKDV, NELFR1G, HELDISHW, HELCLSDY, HSPFDFRZ, 

HAUTOWASH and NGASNDX. All of these except NELCKDV and NELFR1G 

are listed in Table Cl (Appendix C). These two additional 

variables are defined and described in Table C2.

In defining NELFRIG, three extra variables are defined first. 

These variables are HELFRIG1, HELFRIG2, and HELFRIG3. The 

details of these three extra variables are found in Table C2. 

The last variable (HELFRIG3) is an indicator variable that 

denotes if the third refrigerator in the household is fueled 

by electricity. The public use files does not list the fuel 

for the third refrigerator. Hence, if the first two refrigerators 

were electric, we assumed that the third one was also electric. 

Fortunately, all of the households in the sample that had three 

refrigerators also had orily electric refrigerators for the first 

two that were listed.

All of the variables listed above except NGASNDX correspond to 

major electrical appliances. All of these appliances are commonly 

found in households. Hence, the model can attach an electric 

consumption figure to each of these appliances separately. 

Unfortunately, the corresponding gas appliances are rare and the 

noise in the gas consumption model obscures their contributions. 

Hence, the gas appliances cannot be treated individually using 

our data set. Instead, we are using the variable NGASNDX, an 

index for gas appliances. It is a combination of the effects 

for all of the gas appliances contained in the household, exclusive 

of water- and space-heating appliances.

• Interaction Terms: Various multiplicative combinations, or

interactions, of the items mentioned above were also tried in the 

models. Interaction terms are suggested explicitly in Equation 5, 

Section 2, where housing unit characteristics are interacted with 

degree-days.

The interaction terms can be broken up into three groups, waterheating, space-heating, and air conditioning terms. Within each 

group, the terms can be divided into two subgroups, one for the 

electric consumption model and one for the natural gas consumption 

model.

25
Several interaction terms were tried when modeling the 

electricity consumption due to water-heating. The two 

terms that we found significant were HELWHT x NHSLDMEM 

and HELWHT x HELDISHW. For natural gas consumption, 

we only used the term HGASWHT x NHSLDMEM. The coeffi 

cient for the term HGASWHT x HELDISHW was positive, but 

it was only marginally significant.

These terms seem reasonable in that each additional 

household member is likely to increase the usage of hot 

water and some electric dishwashers tend to use a large 

amount of hot water. Also, some models require that the 

hot water heater be set at a higher temperature than if 

they were not present.

Turning to space-heating interactions, we note that the 

space-heating component of total usage is potentially 

much more complex than the water-heating component. In 

particular, the amount of fuel consumed for space-heating 

involves not only the fuel used, but also the heating 

degree-days, size of house, type of equipment, indirect 

insulation measures and indirect measures of the lifestyle 

of the household.

For natural gas consumption, there is no space-heating 

component unless the main or secondary heating fuel is 

natural gas. Hence, all of the other factors involved 

with space-heating need to be interacted with HGASMHT or 

HSBNMGSH. The type of equipment use for main heating is 

represented by the term KMHTEQRC, which might be thought 

of as system overhead, or start-up energy requirements. 

The size of the house comes in through the terms, HGASMHT x 

NHEATDD x NBATHRMS, HGASMHT x NHEATDD x NROOMS, and HGASMHT 

x NHEATDD x NDRSAWS. Note that the variables measuring the 

size of the house are always interacted with HGASMHT x 

NHEATDD. The lifestyle of the household is represented by 

the term HGASMHT x NHEATDD x NAGE01.

Finally, the terms HGASMHT x NHEATDD x KYHSBREC and HGASMHT 

x NHEATDD x NSDRSAWS indirectly represent the insulation 

properties of the dwelling. The component for secondary 

gas space-heating is not as easily broken up as the component 

for main gas space-heating. As a result, the only term used 

for modeling the secondary gas space-heating is the dummy 

variable HSBNMGSH.

The interaction terms used in the analysis of electricity 

were HELMHT x NHEATDD x NAGE01, HELMHT x NHEATDD x NBATHRMS, 

HELMHT x NHEATDD x NDRSAWS, HELMHT x NHEATDD x NSDRSAWS, and 

HELMHT x NHEATDD x HELHTPM.

26
Fewer terms were significant in the analysis of electricity 

than were significant in the analysis of gas consumption; 

fewer people heat with electricity than heat with gas. All 

of the terms listed except the last correspond to terms used 

in the gas analysis. The exceptional term represents to some 

degree the effect of using an electric heat pump.

Fitting by Iterative, Weighted Least Squares

Equations of the form described in Section 2 were fit to the data using 

iterative, weighted least squares and an outlier rejection procedure. 

The general linear model procedure of the SAS statistical package was 

used throughout. This section describes the techniques used to model 

the data.

Iteration: In the first step of each analysis, parameters were fit to 

the data using ordinary least squares. For each succeeding step up to 

a total of seven, new parameters were fit using a weighted least squares 

procedure with the weights equal to the reciprocal of the estimated 

consumption from the previous step. The weights reflect the observation 

that there is a larger variance in energy usage among households with 

high usage than among those with low usage. (See Figures 8 and 9.)

At the third iteration, we began systematically eliminating outliers before 

refitting the models. The process of elimination and refitting was continued 

until further outliers were removed, or until the seventh iteration was 

reached, as mentioned above.

The plots of residuals versus predicted consumption, Figures 8 and 9, revealed 

two outlier problems. One was the presence of outlying values, values far from 

the main body of residuals; and the other was the asymmetry of the residuals. 

Our method of dealing with the first problem was to eliminate values outside 

an interval determined by the standard error of the regression. Our method 

for dealing with skewness was an asymmetric interval based on a square root 

transformation of actual and predicted consumption after fitting the model. 

Methods for dealing with skewness based on transforming the dependent variables, 

energy consumption, and using it in the regression were rejected due to a 

desire to preserve the linear structure of the model. Using the logarithm of 

the energy consumption in fitting the model would result in a multiplicative 

model.

Let SRESID be the difference between the square root of the energy consumption 

and the square root of the predicted energy consumption. The values of SRESID 

were more normally distributed than the values of the residuals. A standard 

deviation was calculated based on SRESID using the equation:

Standard Deviation = [ Z (SRESID - SRESID) 2 /(N-K) J 1 / 2

27
FIGURE 8. OUTLIER DETECTION FOR NATURAL GAS MODEL} PREDICTED CONSUMPTION BY RESIDUAL.

PREDICTED CONSUMPTION 

(IN MILLION BTU'S)

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FIGURE 9. OUTLIER DETECTION FOR ELECTRICITY MODEL: PREDICTED CONSUMPTION BY RESIDUAL.

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(IN MILLION BTU'S)

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A.ACDCPSSYZZRLVMJFKFHECDBAA A A.. A A

.AABDMNXZZZZORJMHDGACBAAAAA .A. A

AA DKUZZZZUUNCIJGDBA BBA ,A A A

..AGITTZXTPGHFCAAA B .A.

. .DKOPZJKFBC BB ... A

o + ,:.....

-120 -90 -60 -30 0 30 60 90 120

RESIDUAL (IN MILLION BTU'S) LEGEND: A = i OBSERVATION. B = 2 OBSERVATIONS. ETC.

LIMITS FOR OUTLIERS SYMBOL USED IS •.• 

ZERO AXIS SYMBOL USED IS •!•
where N is the number of observations, K is the number of parameters estimated 

in the linear model and SRESID is the mean value of SRESID. Any household whose 

value of SRESID was more than three such standard deviations from zero was 

rejected as an outlier. When outliers were deleted, the value of the 

standard deviations was decreased at the next iteration. Hence, additional 

households were deleted after each step.

In Figures 8 and 9, the curves represented by the dots show the final outlier 

detection regions. The curves are not symmetrical about zero and the distance 

from the zero vertical axis increases as YHAT increases.

Consumption Models

The estimated natural gas consumption model that was obtained in the final 

step is summarized in Tables 1 and 2. In construction of the model, 28 house 

holds were deleted as being outliers and were not used. The ID numbers, 

NSQIDDOE, of these outliers are listed in Table 3.

Five of the deleted households listed electricity as their main heating 

fuel, but they consumed large amounts of natural gas. This suggests that 

the main heating fuel is actually natural gas and not electricity. For 

most of the outliers, there is no obvious reason why the model does not 

fit. One exception is a single-person-household in a large house. This 

suggests that some of the rooms in the house may have been left unheated 

during the winter. Another exception is a household that used natural gas 

to heat a swimming pool. This fact came from a remark placed on the 

questionnaire by the interviewer. The REGS survey will ask all households 

if they heat swimming pools.

If the outliers are not removed, the intercept term in the natural gas 

consumption model is greatly increased. On the other hand, the effect 

on the other terms is only moderate.

The estimated electricity consumption model that was obtained in the 

final step is summarized in Tables 4 and 5. In constructing the models, 

51 households were detected as outliers and were not used in constructing 

the model. The ID numbers (NSQIDDOE) of these households are listed in 

Table 6.

Four households are listed in Tables 3 and 6. Three of these appears to 

have the main heating fuel incorrectly listed. The other one consumed 

abnormally large amounts of both natural gas and electricity.

If the outliers had not been deleted when we constructed the electricity 

consumption model, the results would only be slightly different.

30
TABLE 1. ANALYSIS OF VARIANCE TABLE FOR NATURAL GAS MODEL (USING NCNGYRB AS THE DEPENDENT VARIABLE).

I 

SOURCE

MODEL 

ERROR 

CORRECTED TOTAL

DEGREES OF 

FREEDOM

13

1243

1256

WEIGHTED 

SUM OF SQUARES

44995013.38210071

14832524.60716271

59827537.98926342

MEAN SQUARE 

3461154.87554621 

11932.84360995

F-VALUE 

290.05

ATTAINED LEVEL 

OF SIGNIFICANCE

0.0001

WEIGHTED 

R-SQUARE

.752079
TABLE 2. WEIGHTED LEAST SQUARE SOLUTION FOR NATURAL GAS MODEL.

U!r-o

PARAMETER

INTERCEPT

NGASNDX

NHSLDMEM*HGASUHT

HSBNMGSH

KMHTEQRC

RADIATORS OR HOT WATER PIPES <1>

CENTRAL FORCED AIR <2>

OTHER <3)

NO GAS MAIN HEATING (4) 

NHEATDD*HGASMHT*NBATHRMS 

NHEATD0*HGASMHT*NAGE01 

NHEATDD*HGASMHT*KYHSBREC 

NHEATDD*HGASMHT*NROOMS 

NHEATDD*HGASMHT*NDRSAWS 

NHEATDD*HGASMHT*NSDRSAWS 

NCOOLDD*NRMGASAC

ESTIMATE

7885.86117328 *

478.57038686

8183.12797801

39380.14733876

35976.62454035 * 

21177.30479874 * 

7946.83589671 * 

0.00000000 * 

4.35890180 

0.05823754

-1.12679365 

1.14812215 

0.36930515

-0.19222837 

3.97906768

T-STATISTIC FOR 

HO: PARAMETERS

2.97

3.28

12.97

5.26

6.10 

5.03 

2.14

**

7.91 

5.01

-8.12 

6.45 

7.11

-4.62 

4.55

ATTAINED 2-SIDED 

LEVEL OF SIGNIFICANCE

0.0030

0.0011

0.0001

0.0001

0.0001 

0.0001 

0.0323

**

0.0001 

0.0001 

0.0001 

0.0001 

0.0001 

0.0001 

0.0001

STD ERROR OF 

ESTIMATE

2653.97724959

145.88367773

631.08680052

7488.38074856

5899.72507242 

4206.54981219 

3709.19030002

**

0.55073749 

0.01163191 

0.13882925 

0.17801440 

0.05192832 

0.04156752 

0.87531020

* THE SOLUTION IS NOT UNIQUE BECAUSE THE DESIGN MATRIX IS SINGULAR.

** NO TEST IS GIVEN BECAUSE THE ESTIMATE WAS ARBITRARILY SET EQUAL TO ZERO.
Table 3. Households that were Determined to be Outliers for Natural Gas Consumption Models

NSQIDDOE

1,065

1,206

1,208

1,631

1,885

1,908

2,275

2,299

2,302

2,315

o 2,357

2,377

2,416

2,594

2,611

2,721

2,827

2,895

2,933

3,262

3,405

3,414

3,681

3,972

4,187

4,473

4,692

4,693

NCNGYRB

541,313

460,915

129,336

68,158

64,888

238,242

502,923

250,941

191,954

140,315

253,221

121,396

348,149

24,830

228,293

178,054

371,738

6,890

104,077

305,750

481,234

395,757

279,671

48,398

404,907

130,936

109,437

105,766

Residual Remarks

226,768

235,734

104,742

-143,958

-110,471

204,255

379,765

146,080

124,853

106,119 Listed electricity as main heating fuel.

144,288

101,515 Listed electricity as main heating fuel.

190,599

-115,094

137,951

149,304 Listed electricity as main heating fuel.

217,693

-63,698

81,423 Listed electricity as main heating fuel

184,224

307,609

197,073

164,465

-118,288

226,933 Heats a swimming pool with natural gas.

96,173 Listed electricity as main heating fuel.

-164,902

-140,375 Single retired person in a large house.
TABLE 4. ANALYSIS OF VARIANCE TABLE FOR ELECTRICITY MODEL (USING NCELYRB AS THE DEPENDENT VARIABLE).

DEGREES OF WEIGHTED ATTAINED LEVEL WEIGHTED

SOURCE FREEDOM SUM OF SQUARES MEAN SQUARE F VALUE OF SIGNIFICANCE R-SQUARE

MODEL 22 25057741.26255367 1138988.23920699 318.01 0.0001 .771422

ERROR 2073 7424794.29083030 3581.66632457

CORRECTED TOTAL 2095 32482535.55338398
TABLE 5. WEIGHTED LEAST SQUARE SOLUTION FOR ELECTRICITY MODEL,

U) 

Ln

PARAMETER ESTIMATE

INTERCEPT 1838.90033348

NELCKDV 1542.91063357

KINCOME 249.49782225

NAGE01 -46.19145874

NHSLDMEM 1800.26754569

NHSLDMEM*HELUHT 3567.83543487

HELWHT*HELDISHW 5010.04258170

NELFRIG 3176.97311550

HELDISHU 3246.81149591

HELCLSDY 3827.05159181

HSPFDFRZ 4456.46196110

HAUTOWSH 2441.14974480

NTOTAL 10B.33553652

HSBNMELH 3282.23184877

NHEATDD*HELMHT*HELHTPUM -2.56940122

NHEATDD*HELMHT*NAGE01 0.04376684

NHEATDD*HELMHT*NBATHRMS 2.16693210

NHEATDD*HELMHT*NSDRSAWS -0,11337950

NHEATDD*HELMHT*NDRSAWS 0.31150668

NCOOLDD*NRMELRAC 0.69793901

NCOOLDD*NRMELRAC*KINCOME 0.07027372

NCQOLDD*NRMELCAC*KINCOME 0.12566062

NCOOLDD*NRMELCAC 0.41258501

T-STATISTIC FOR 

HOJ PARAMETERS

1.32

6.06

2.47

-3.01 

10.21 

16.11

4.08

5.45

5.14

7.31

9.69

4.22

3.57

4.23

-2.72 

4.27 

5.19

-3.04 

6.37 

4.04 

2.63 

5.81 

2.36

ATTAINED 2-SIDED 

LEVEL OF SIGNIFICANCE

0.1874

0.0001

0.0135

0.0026

0.0001

0.0001

0.0001

0.0001

0.0001

0.0001

0.0001

0,0001

0.0004

0.0001

0.0066

0.0001

0.0001

0.0024

0.0001

0.0001

0.0087

0.0001

0.0184

STD ERROR OF 

ESTIMATE

1394.

254.

100.

15.

176.

221.

1227.

582.

631.

523.

460.

577.

30.

776.

0.

0.

0.

0.

0.

0.

0.

0.

0.

29804463

42416974

89977992

32376895

30579562

41854047

15715352

64498142

57851582

81387074

08932694

80748929

34494681

69185130

94493510

01025377

41768602

03727163

04890592

17282322

02675765

02162087

17482890
Table 6. Households that were Determined to be Outliers for Electricity Consumption Model.

NSQIDDOE

1,063

1,065

1,268

1,435

1,559

1,583

1,700

1,770

1,774

1,796

1,810

1,913

1,954

2,273

2,377

2,417

2,482

2,493

2,513

2,520

2,522

2,560

2,685

2,695

2,697

2,721

2,933

NCELYRB

82,707

98,518

2,835

115,414

85,358

7,510

10,680

138,428

19,486

13,713

103,141

3,583

1,692

90,418

50,569

28,596

146,876

109,525

84,659

82,291

50,569

37,157

126,688

74,419

119,672

34,042

34,857

Residual Remarks

47,082

51,170 Natural gas consumption also high.

-31,040

69,746

-60,716

-56,678

-26,382

104,481

-51,069

-34,123

61,656

-20,202

-15,978

47,084

-49,744 Probably heats with natural gas.

-47,940 Probably heats with natural gas.

76,718

59,047

45,949

58,491

-89,558

-42,787

90,256

53,162

74,126

-71,395 Probably heats with natural gas.

-103,679 Probably heats with natural gas.
Table 6. Households that were Determined to be Outliers for Electricity Consumption Model (Continued).

NSQIDDOE

3,029

3,040

3,042

3,209

3,390

3,404

3,585

3,717

3,728

3,731

3,758

; 3,780

3,794

3,800

3,809

3,887

3,899

3,968

4,064

4,134

4,159

4,603

4,713

4,823

NCELYRB

22,304

72,113

56,687

34,680

826

103,640

4,593

35,294

17,807

75,770

7,435

28,190

90,500

52,224

12,362

48,805

109,935

67,998

119,440

86,549

10,492

39,961

12,512

246,909

Residual Remarks

-42,735

-64,952

-64,083

-43,597

-105,043

49,911

-22,713

-50,226

-48,319

43,985

-34,627

-50,786

61,269

33,897

-31,461

35,279

76,779

42,327

58,603

44,729

-26,514

-55,691

-29,070

127,238

Section 5. Discussion.

This section contains a discussion on the results of the analysis summarized 

in Tables 1, 2, 4, and 5. Highlights include interesting features of 

the models, what the models suggest about the relative contribution of 

different factors to household energy consumption, and some of the pitfalls 

encountered in interpreting individual coefficients. The discussion is 

organized according to the variable groupings used in Section 4.

The t statistics listed in Tables 2 and 5 indicate the significance of the 

marginal contributions of the associated term in the model. Thus, the t 

statistic associated with the term NGASNDX in Table 2 indicates whether 

the addition of this term is significant given that all of the other terms 

in the model are already present.

The order of appearance of the terms in a model is not significant. That 

is, there is no relationship between a term's position in its list and its 

relative contribution to the multiple R-square for the model. The current 

models were arrived at by a trial-and-error approach with attention to what 

terms proved significant when other terms were already in the model.

We caution the reader again that the estimates presented here are preliminary 

and derived from only part of the NIECS data. In addition, there are the 

usual problems of interpreting the coefficients of a regression model, and 

they are discussed elsewhere in this report. For now, the results are 

presented as a description of the variation in energy consumption among 

households.

Tables 7 and 8 summarize, respectively, the modeled natural gas, and the 

modeled electricity consumption for a hypothetical household's water-heating, 

space-heating, and air conditioning.

The modeled results for the two hypothetical households should be taken as 

a package and not as a sum of well-defined individual contributions. Some 

of the independent variables are highly correlated. Hence, the effect of a 

variable, including those not used in the model, could easily be represented 

in the model by the contribution of another variable.

39
Table 7. Modeled Natural Gas Consumption for Hypothetical Household___

Independent Hypothetical Contribution to 

Variable_____________________Value_______________Model______

Intercept - 7,886

NGASNDX 17 8,136

NHSLDMEM x HGASWHT 4x1 32,733

HSBNMGSH 0 0

KMHTEQRC 2 21,177

NHEATDD x HGASMHT x NBATHRMS 5,700 x 1 x 2 49,691

NHEATDD x HGASMHT x NAGE01 5,700 x 1 x 40 13,278

NHEATDD x HGASMHT x KYHSBREC 5,700 x 1 x 5 -32,114

NHEATDD x HGASMHT x NROOMS 5,700x1x7 45,810

NHEATDD x HGASMHT x NDRSAWS 5,700 x 1 x 18 37,891

NHEATDD x HGASMHT x NSDRSAWS 5,700 x 1 x 12 -13,148

NCOOLDD x NRMGASAC 1,200 x 7 33,424 

Total____________________________________________204,764

40
Table 8. Modeled Electricity Consumption for Hypothetical Household

Independent 

Variable

Intercept 

NELCKDV 

KINCOME 

NAGE01 

NHSLDMEM 

NHSLDMEM x HELWHT 

HELDISHW x HELWHT 

NELFRIG 

HELDISHW 

HELCLSDY 

HSPFDFRZ 

HAUTOWASH 

NTOTAL

HSBNMELH

NHEATDD x HELMHT x HELHTPUM

NHEATDD x HELMHT x NAGE01

NHEATDD x HELMHT x NBATHRMS

NHEATDD x HELMHT x NSDRSAWS

NHEATDD x HELMHT x NDRSAWS

NCOOLDD x NRMELRAC

NCOOLDD x NRMELRAC x KINCOME

NCOOLDD x NRMRLCAC x KINCOME

NCOOLDD x NRMELCAC

Total

Hypothetical 

Value

2 

8 

40 

4 

4x1 

1x1 

2 

1 

1 

1 

1 

25

0

5,700 x 1 x 1

5,700 x 1 x 40

5,700 x 1 x 2

5,700 x 1 x 12

5,700 x 1 x 18

1,200 x 0

1,200 x 0 x 8

1,200 x 7 x 8

1,200 x 7

Contribution to 

Model

1,839 

3,086 

1,996 

- 1,848 

7,201 

14,271 

5,010 

6,354 

3,247 

3,827 

4,456 

2,441 

2,708

0

-14,646

9,979

24,703

- 7,755

31,961

0

0

8,444

3,466

110,740

41
Strategy vs. Tactics

As outlined in Section 4, our strategy was to develop an overall intercept 

equivalent to a linear combination of household and appliance data and a 

coefficient of degree-days equivalent to a linear combination of housing unit 

characteristics. In practice, our strategy was modified to accommodate the 

data, dropping housing unit characteristics into the intercept, for example. 

One effect of not strictly following the strategy outlined above is that the 

electricity and natural gas models are not simply comparable. There is no 

term for term correspondence between the models. This is another factor 

which contributes to the difficulty of comparing the effects of different 

factors on the use of the two energy forms.

Demographic Characteristics

The variables NAGE01 and NHSLDMEM appear in both models, but in different 

forms, and the variable KINCOME appears only in the electricity model.

The age variable^ enters with a negative coefficient in the electricity 

model and with a positive coefficient interacted with degree-days in the 

natural gas model. The positive coefficient in the gas model suggests 

increased demand for heating with increasing age of the respondent. On 

the other hand, the negative coefficient in the other model suggests a 

decreased demand for electricity, other than that associated with the 

heating (degree-days) components. The two indications are not inconsistent: 

households comprising older people may operate at lower levels of activity, 

thereby requiring less electricity on the average, while demanding higher 

interior temperatures than the average.

Both models indicate that the larger the household (NHSLDMEM), the greater 

the energy consumption. In addition, both suggest that the number of 

household members has a significant impact on the amount of fuel used for 

hot water-heating.

The income variable, KINCOME, enters with a positive coefficient in the 

electricity model. In the current gas model, the addition of this variable 

is not significant; it may be significant in other versions of the model.

-'•Note that NAGEOl is the age of the respondent, not necessarily that of 

the head of household.

42
Care needs to be taken in interpreting the income variable in any 

formulation of the model. The income data available in the NIECS 

are inherently only ordinal data. Respondents were asked what income 

range they were in, not their actual income. Thus, one cannot say from 

analyses such as these that if income changes by a stated amount, then 

electricity changes by a proportional amount. Rather, one can only say 

that if income increases, an increase in electricity consumption is 

indicated. This limitation is inherent in the data.

Measures of Size and Insulation and Heating Components

In both models, the measures of size and insulation data are concentrated 

in the heating component of the models, the interaction terms which include 

degree-days. The only exception to this is NTOTAL, which counts the total 

number of doors, windows, and rooms, and which stands alone in the 

electricity model.

All of the size of house coefficients are positive, suggesting that energy 

consumption increases with the size of the dwelling unit, as was expected. 

The fact that these terms appear as interactions with heating degree-days 

indicates this importance in determining the heating component of energy 

demand, and is consistent with the experiments and modeling strategy 

described in Section 4.

The importance of the number of bathrooms as a measure of size is interesting. 

In both models, it is the variable which, when interacted with degree-days, 

has the largest positive coefficient, in some cases, by orders of magnitude. 

Its importance likely derives from being a proxy for several other measures 

of the size of the housing unit or status of the household: square footage, 

income of the household, quality of housing and living habits of the 

household members.

The uncertainty of just what NBATHRMS may be a proxy for suggests the care 

that must be taken in interpreting this coefficient. For example, the 

conversion of storage space to a bathroom will not automatically result in 

adding 4,360 Btu per degree-day to the gas consumption of gas-heated homes. 

Nor should it even result in increased gas consumption, unless, perhaps, the 

addition signals other changes that result in higher energy consumption.

Note the differences between the values of NBATHRMS across the two models. 

The ratio of the coefficient in the gas model to that in the electricity 

model is on the order of 2 to 1. The analogous ratios for the other 

coefficients in the heating component are also large in the gas model, the 

ratios being on the order 1.5 to 1. These ratios recall the discussions of 

Figures 1 and 6, and 2 and 7 in Section 3.

The differences between NDRSAWS and NSDRSAWS within models suggests a 

relationship between energy consumption and size of dwelling, and the 

energy conserving effects of the presence of storm doors and windows.

43
Once again, the interpretation must be made with caution. The variable 

NSDRSAWS, the total number of storm doors and windows, likely reflects 

the fact that houses with storm windows tend to be better-insulated in 

other ways than those that do not have storm windows; installing storm 

windows on all windows in a house will not necessarily reduce energy 

consumption due to heating by the amount indicated in the models.

Households which heat with electricity and operate an electric heat pump 

may enjoy a very large reduction in their space-heating demand, at least 

as indicated by the coefficient associated with HELHTPUM interacted with 

NHEATDD. Out of the 2,095 households used in the electricity model, only 

approximately 40 have heat pumps, yet this factor was significant.

Appliances

Important differences in the consumption of electricity and gas are indicated 

by the composition of the intercepts. In the electricity models, individual 

appliances are accounted for, whereas in the gas model, the use of appliances 

is summarized in NGASNDX. On the other hand, important differences due to 

differences in heating equipment are indicated in the gas model.

Care should be taken in interpreting the coefficient of individual appliances 

in models like the electricity model. For example, the 4,456 MBtu that the 

model adds for having a separate food freezer may not all be consumed by the 

freezer. Households that have freezers may cook more or tend to have more 

electrical appliances generally than households that do have freezers. 

Therefore, multiplying the coefficient for separate food freezers by the number 

of freezers in residential use may give a biased estimate of the energy 

consumed by freezers.

The Heating Component and Heating Equipment

The natural gas model suggests there are large differences in consumption 

unrelated to degree-days but associated with differences in heating equip 

ment. The large values of these baseload or intercept terms may be a result 

of the curve in the overall natural gas consumption with respect to 

degree-days.

It should be noted that because of the way the model was fit only certain 

linear combinations of the intercept term and the four coefficients for 

KMHTEQRC can be estimated. In particular, the intercept plus any of the 

four coefficients can be estimated, and the differences between pairs of 

equipment coefficients can be estimated.

Thus, we estimate that households which use natural gas, but not as their 

main heat source, (Category 4 of KMHTEQRC) have an annual baseload of 

INTERCEPT + 0 = 7,886 MBtu. Continuing by estimating differences, we see 

that Category 3 of KMHTEQRC (which includes all types of gas heating 

systems except forced-air, Category 2, and hot water-radiator systems, 

Category 1) increases a household's annual baseload by approximately
7,950 MBtu annually compared to a household which uses gas but not as its 

main heating fuel (Category 4). Similarly, forced-air systems have a baseload consumption which is 21,177 - 7,947 = 13,230 MBtu greater than other 

systems, and hot water systems have a baseload 35,977 - 21,177 = 14,800 

MBtu greater than forced-air systems.

The model suggests that baseload consumption can be very substantial in 

relation to the heating component. For example, suppose a household has 

2 bathrooms, the age of the head of household is 40, the house was built 

during 1960 (KYHSBREC=6), and the house has 6 rooms, and a dozen doors 

and windows, 6 of which are insulated. Then

(4.36 NBATHRMS + 0.06 NAGE01 1.13 KYHSBREC + 1.15 NROOMS 

+0.37 NDRSAWS - 0.19 NSDRSAWS) x NHEATDD

=(4.362 4- 0.0640 1.13 + 1.156 + 0.3712 - 0.196) x NHEATDD 

=(14.5 MBtu/degree-day) x NHEATDD 

=14.2 cu. ft./degree-day x NHEATDD

If the house is in a 5,000 heating degree-day zone, then the heating 

component is estimated to be approximately 71,100 cubic feet or 

72.5 x 10" Btu annually. For a household with a hot-water system, the 

baseload is (7.886 + 35,976) MBtu = 43.9 x 106 Btu which is 61 percent of 

the heating component, (43.9/72.5) = 61 percent or 38 percent of the total 

heating load which is (43.9 + 72.5) = 116.4 x 106 Btu.

Originally, we interacted the equipment variable, KMHTEQRC, with 

degree-days on the grounds that the overhead associated with various 

systems should vary with the severity of winters. For example, households 

located in a 4,000 to 5,000 degree-day region were expected to have lower 

system baseloads than households in an 8,000 to 9,000 degree-day regions 

because winters degree-day are less severe. However, the interaction 

term did not show any significant differences between the various types 

of heating equipment.

The Cooling Component of Electricity

In discussing Figure 5, we noted an apparent lack of association between 

electricity consumption and cooling degree-days among households that do 

not use electricity for heating. However, in the electricity model inter 

action, terms which include the number of rooms air conditioned, income, 

and cooling degree-days, appear. This suggests that a component of 

variation in electricity consumption due to cooling can be observed when 

other characteristics are accounted for, such as a household's appliance 

inventory.

45
Residuals

Figures 10 and 11 show the residuals from the gas and electricity models, 

respectively, plotted against degree-days. Figure 12 presents another 

look at the data in Figure 10. Figure 13 is a plot of the residuals from 

the electricity model against the residuals from the gas model for those 

households which use both fuels.

Figures 10 and 12 repeat the patterns displayed in Figures 1 and 6: the 

residuals from the gas model rise gently from just below zero to slightly 

above it at about 6,100 degree-days, at which point they once again fall 

below zero. This is most easily seen in Figure 12.

It is apparent from these figures that the gas model does not account for 

the hypothesized change in trend observed in Figure 6 and discussed in 

Section 3. Since the present model includes proxy measures of size and 

insulation, the indication is that these variables are not sufficiently 

powerful to account for the differences between households in the coldest 

regions and the rest of the sample, assuming that the differences are due 

to differences in insulation. Therefore, real, unmeasured differences in 

insulation cannot be ruled out as the explanation. Neither can the other 

hypotheses (acclimation, use of secondary heating sources, conservation 

behaviors) advanced in Section 3 be ruled out.

Figure 11 shows the residuals from the electricity model versus degree-days. 

The plot indicates a reasonably good fit to electricity consumption across 

the range of degree-days. The residuals are centered at zero over the 

whole range, and the variability in the residuals is uniform.

Figure 13, the electricity residuals versus gas residuals, is a commentary 

on the "wasters are wasters" while "savers are savers" hypothesis. Under 

this hypothesis, households which are below-average in the consumption of 

one fuel should be below-average in the consumption of the other and those 

who are above-average consumers of one should be above-average consumers of 

the other. Under this hypothesis, we would expect the residuals in Figure 13 

to exhibit a positive correlation. In fact, the diagram and correlation 

coefficient of .04 reveal a negligible association.

Concluding Remarks

In this paper, we have presented some preliminary investigations of the 

variability in energy use among single-family households. Several important 

indications appeared which we believe should be accounted for in further 

analysis:

• The differences between electricity and gas consumption; 

Because of the large differences between the heating 

components for these fuels, one should be wary of 

combining the data into a single, "total fuel 

consumption" model.

46
• The deviation of houses in the coldest regions from 

the regression average. More work needs to be done 

to uncover the systematic differences, if any, between 

the households in the coldest region from the rest of 

the population.

• The large differences in baseload requirements among 

different types of heating systems.

• The importance of the number of bathrooms as a predictor 

of energy consumption.

In subsequent analyses, we will extend the models to the full data set, 

estimate the sampling errors of regression coefficients, and attempt to 

estimate average heating and baseload components by characteristics of 

households.

47
FIGURE 10. RESIDUAL FOR NATURAL GAS MODEL BY HEATING DEGREE-DAYS FOR HOUSEHOLDS THAT USE NATURAL GAS FOR THE HAIN SPACE- 

, HEATING FUEL.

RESIDUAL

(IN MILLION BTU'S)

oo

400 -

300 H

200 •

100 •

0 •

100 •

•

•

•

A

n

A

D

BA

BL

B A CH

B A A I

B C

B B

A

200 +

300 1000 1700

A

A

A

A

A

A

B A

A AA A A A

A

BAB A

B D A C

A D AB B B A

AGCBGA BA

C 0 EG J EBA B FAC

D L BBC L EBA CAD C B

V CDD Z D B A BAB A

A Y BE M AA ABC

H AB KB A AA

A G B

A

A

2400 3100 3800 4500

A .

A

A

AC

A B

BDA

AC

DABB

AHDA

BED

AJBB

BJD

BGDB

DAA

D A

A

A

——— +_. 

5200

A

A

A A

A AA

AB AA B

AA AA

AAA AB

A CB B

ABCAB B

ABDBAAAD

BCDACABF

AEEACAAI

F CCCA H

CCCCCBAF

BADCCAFH

BACBBBFG

AAFBBA B

BA BABCB

A A

A

A

- ——— + —— - 

5900

A

A

A

A B

B

A A

AA

C AEB

C C CC

AD BAG

DB ICLB

AFA HDMA

AG JBUB

EB KATA

AFA JBJD

GBJF

C G CB

AAA AB A

B A

A BA

A A

A

A

A A

A

B

B

B A A

F A AA

D A

G A

K A C

D A CE

F B AB

C C

D B

A BA

A

A

6600 7300 8000

A

A

A

C

A

A C

A C

A F

C

A C

F

B

A A

I i t _ ___

8700 9400 10100

HEATING DEGREE-DAYS LEGEND: A = i OBSERVATION^ B = 2 OBSERVATION* ETC.
FIGURE 11. RESIDUAL FOR ELECTRICITY MODEL BY HEATING DEGREE-DAYS FOR HOUSEHOLDS THAT USE ELECTRICITY FOR THE MAIN SPACEHEATING FUEL.

RESIDUAL

(IN MILLION BTU'S)

125

100

75

50

25 H

0

-25 •

-50 •

-75 •

100

125 •

•

h

h

A

A A

A

A

B A A A

B A A D B A B

B ABA BAA B B

B C A AA A C

A AAA ABBBBA A

ADA A A B D BA D

BBAB CCBABB C

BBA BABBAD

ABBA AAAAB A

D A B BAA

A A A A A A

B A A

A A A

A

B

A

A

0 1000 2000 3000 4000

A

A

A

B A A

A

AAA A

CA A A

C C A

ABA B B

ABB AAA A

AA B AA B C A

A E BB A

A A B E AAA A

AA B BD A A A

A A BB A

A A DA A

A A B A A

A A AA B A

A A A A

A A A

A

B AB

A

A

5000 6000 7000 8000 9000 10000

HEATING DEGREE-DAYS LEGEND: A = i OBSERVATION* B = 2 OBSERVATIONS^ ETC.
FIGURE 12. WANDERING BOX PLOT OF RESIDUAL FOR NATURAL GAS MODEL. BY HEATING DEGREE-DAYS FOR HOUSEHOLDS THAT USE NATURAL GAS FOR 

THE MAIN SPACE-HEATING FUEL.

RESIDUAL

(IN MILLION BTU'S) 

400 -f

300 ••

200

100 +

-100

•200

02

03

X

0

0

0

0

05

X

X

0

0

02

0 02

04

X

X

_ _..._ _ _. _..... _ 4- _ — — -.. — ~- 4- — ~ _ —. _ —.4. _ _. _ _ _. _ 4. _ _

300 1000 1700 2400

_ _ _ I _ _ _ _ _ _. 4. _ _. .

3100 3800

_ __ _ 4, „ _ _ _. _ _ 4. __ _,

4500 5200 5900 7300

0

0

_ _„ _ ,_ 4. _ „ ,- _ ~ — 4. — _. _. _ __ — 4. — — — — TM — X ... — ~

8000 8700 9400 10100

HEATING DEGREE-DAYS LEGEND; x = EXTREME OUTLIER

0 = BORDERLINE OUTLIER 

* = MEDIAN.
FIGURE 13. RESIDUAL FOR ELECTRICITY MODEL BY RESIDUAL FOR NATURAL GAS MODEL.

ELECTRICITY RESIDUAL 

<IN MILLION BTU'S)

75

50 +

25

0

-25

-50 +

-75

-100

-125 +

„ _ 1 _ _ _

-300

A A

A A A A A

AAB B A 

A C A A A 

A AA AA BABB A A A 

A A AA AC AABC CB BB A AA 

A A ABAC BBDBB C A A A A 

A AB CACABHAHAGEDFFB BBAACC B AA

A BBA EABDCJLJDEGLJEF EBBA A BA BA 

A ABACDFGKHGMSNSZIMLFHEAHBEDB ECAA AB B 

A D BAGriFGILJZYUZZUXGPTLFFNFDDFACA A B A A 

AA ABACEBECHLNSSZZZZUZOXOJGGJGEECBABBACAA B AA

ACAAA DDFGLOLNLKNJHMMBCDFBEBAACAA A A A BAA 

A A AAACBEABCDEABEFBCCEBAB BA A AA AA A 

BD AA BCBBCAA AA A A A 

A B A AB A AAA A 

A A A A A A

B A A A A 

A 

A

A

A

A 

A

A 

A

A 

A A

A 

A

„„„ J-~-

-150

-t0

_ i „ _

225

__ l __

375 -225 -75 75 150 

NATURAL GAS RESIDUAL (IN MILLION BTU'S)

300 450

LEGEND: A = i OBSERVATION B = 2 OBSERVATIONS. ETC.

APPENDIXES

53
Appendix A 

SAMPLING PLAN FOR THE NIECS

Households used in the NIECS were selected from the universe of households 

according to a plan whereby each household had roughly the same probability 

of being selected.

Definitions of the universe of households used for the survey were generally 

the same as those used for U.S. Census Bureau surveys except that households 

in Alaska and Hawaii and those located on military installations were not 

included.

A number of steps were carried out in the selection. Briefly they were:

• The approximately 3,000 counties and independent cities 

in the United States (exclusive of Alaska and Hawaii) 

were grouped into 1,140 primary sampling units (PSU's).

• The 1,140 PSU's were next divided into 103 groups or 

strata; each stratum consisted of PSU's as much alike 

as possible in terms of geographic region, community 

type, and socio-economic characteristics.

• One PSU was selected for each of the 103 strata; these 

selected PSU's were the primary areas for the survey.

• Within selected PSU's, a number of subsampling steps were 

used to select specific clusters of housing units for the 

survey. These subsampling steps made use of 1970 Census 

data for small units such as block groups and enumeration 

districts, supplementary data to identify areas with sub 

stantial new residential construction since 1970, and field 

visits to make rough counts of housing units as well as 

detailed housing unit listings.

• These subsampling steps resulted in the selection of 456 

ultimate sampling units (USU's). Each USU is a cluster 

of households, averaging approximately 10 per cluster.

After the households were selected and interviewed, they were assigned 

weights that reflected the nonresponse rate in their cluster and the 

approximate probability that they were selected. The weights were not 

used in the analysis presented in this publication.

54
Appendix B

ENERGY CONSUMPTION DATA, MISSING DATA, 

AND DEGREE-DAY DATA

A preliminary public use version of the NIECS data is available in 

machine-readable form from the National Technical Information Service 

(Reference 8).

There are two important features of the public use file. One is the manner 

in which the energy consumption data is reported, and the other is that 

degree-day information is included.

Table Bl summarizes the type of energy consumption data obtained from the 

utilities. The table also summarizes the situation by varying degrees of 

missing data. The category "11 or more months" corresponds to the com 

bination of "complete" and "nearly complete" mentioned in Reference 5. The 

category "less than 5 months" corresponds to "missing" in the reference.

The reason why data are missing vary with the extent to which they are 

missing. In the case of completely missing data, the reasons range from 

outright noncooperation from households or utilities, to failure to find a 

household in a utility's records. For the other missing data situations, 

the most frequent cause is changing ownership of households: if ownership 

or occupancy of a housing unit changed hands during the period March 1978 

to April 1979, we were able to obtain data for the time period when the 

house was occupied by the person signing the authorization.

Another reason for missing data is inefficient record-keeping by utilities. 

Some utilities do not keep 12 months of billing data on-line, or readily 

accessible, at any given time.

55
Table Bl. Energy Consumption Records and Missing Data for Survey Households 

Using Electricity and Utility Gas

Total Households 

Using Fuel

Data Received 

From Fuel Supplier

11 Months or More

5-10 Months

Less Than 5 Months

Household Pays Directly 

To Supplier — No Data 

Available

Household Not Identi 

fied In Company Records

Company Refused to 

Participate

Company Unknown Or 

Not Located

Authorization Form • 

Not Signed

Fuel Used Included In 

Rent Or Paid In Other 

Way

Electricity 

Number of 

households

4080

3509

3023

340

146

334

128

0

0

206

237

Utility Gas

Number of 

Percent households Percent

100.0 2577

86.0 1947

74.1 1754

8.3 124

3.6 69

8.2 270

3.1 110

— S

0

5.1 155

5.8 360

100.0

75.5

68.0

4.8

2.7

10.5

4.3

0.2

-

6.0

14.0

Source: NIECS: Report On Methodology, Part 1. Household and Utility Compan;

Surveys, Response Analysis Corporation, Princeton, New Jersey; February 1981, 

Section 5.

56
The heating degree-day data and cooling degree-day data are annual figures, 

adjusted for the 1978 to 1979 weather, and rounded to the nearest 100 

degree-days. The annual degree-days, prior to adjustment, were the long 

term averages published by the National Oceanic and Atmospheric Administration 

(NOAA). Adjustments were made to these long term averages on a regional basis 

(9 Census Regions). For heating degree-days, the adjustment was based on 

the 1978 to 1979 heating season. For cooling degree-days, the adjustment 

was based on the 1978 cooling season. The procedure used to obtain the 

adjustment factors is as follows:

The country was partitioned into 344 divisions as defined by NOAA, where each 

division is a geographic area within which climatic conditions are relatively 

homogeneous. The divisions generally follow county boundaries, the principal 

exceptions occurring in certain coastal and mountain areas. The division within 

which a household resides was then determined, and average annual heating 

and cooling degree-day figures were computed by averaging over all NOAA weather 

stations within the division and over the years from 1930 to 1975. The 

mathematical form for a household's unadjusted average then is:

HDDh = £ HDDik /46 

k

where:

HDDft is the 46-year average heating degree-day figure 

for household^

i denotes the NOAA division in which the household resides 

k denotes the years from 1930 to 1975, inclusive, and

HDD-j^ is the number of heating degree-days reported in the 

i ch division for the kt" year.

The cooling degree-day average, CDD^ is defined analogously. Note that if 

two households, h and 1, are in the same NOAA division, then HDD^ = HDD^; 

the same would be true for cooling degree-days. Thus, the variability in 

the degree-day within a NOAA division is zero.

The average values HDD^ were then adjusted on a regional basis for departures 

from the 46-year norm using the ratios in Table Bl. The ratios were derived 

as follows:

Qr = HDDsr /HDDar 

where r is the r^fe census region

HDDsr is the average heating degree-day

figure for the survey year, April 1978 

to March 1979, averaged over all NOAA 

Divisions in the r tn .

and HDDar is the 40-year average ove~ all NOAA

divisions in the r^ n region.

57
Table B2. Ratio Adjustments

Census Region

New England

Middle Atlantic

East North Central

West North Central

South Atlantic

East South Central

West South Central

Mountain

Pacific

78-79 HDD 

Adjustment Factor

1.020

1.044

1.112

1.151

1.044

1.103

1.174

1.103

1.049

1978 CDD 

Adjustment Factor

.893

.896

.945

1.026

.992

1.000

1.036

.984

1.195

58
Appendix C

NIECS PUBLIC USE FILE VARIABLES USED IN 

FINAL CONSUMPTION MODEL

Table Cl defines the household variables selected for the final analysis 

of natural gas consumption and the final analysis of electricity consumption. 

The variable names and values are documented in the NIECS public use file. 

Table C2 defines the variables that are transformations of variables listed 

in Table Cl.

Table Cl. Household Variables Selected for Analysis of Natural Gas 

Consumption and Electricity Consumption

Variable Name Variable Description

NCNGYRB

NCELYRB

NHEATDD

NCOOLDD

NAGE01

KINCOME

NHSLDMEM

KYHSBREC

NROOMS

NCOMBATH

NHAFBATH

NGASNDX

HELDISHW

HAUTOWSH

HELCLSDY

HELOVEN

HELRANGE

HSPFDFRZ

NREFRIG

KREFRIG1

KREFRIG2

NDOORS1

NSDOORS

NSWINSGD

NUMWINDS

NSTRMWIN

KMHEATEQ

KFLMHEAT

KFLSHEAT

HELHTPUM

KWHEATFL

HROOMAC

HCENTAC

KFLCNAC

NROOMAC

Annual Consumption of Natural Gas in Thousands of Btu's

Annual Consumption of Electricity in Thousands of Btu's

Number of Heating Degree-Days Based on 40-year Average

Number of Cooling Degree-Days based on 40-year Average

Age of Respondent

Code for Household Income Level

Number of Household Members

Code for Year House Built

Number of Rooms in House

Number of Complete Bathrooms

Number of Half Bathrooms

Gas Appliance Index

Indicator Variable for Electric Dish Washer

Indicator Variable for Automatic Washing Machine

Indicator Variable for Electric Clothes Dryer

Indicator Variable for Electric Oven

Indicator Variable for Electric Range

Indicator Variable for Separate Food Freezer

Number of Refrigerators

Code for First Refrigerator Fuel

Code for Second Refrigerator Fuel

Number of Outside Doors and Sliding Glass Doors

Number of Storm Doors

Number of Storm Sliding Glass Doors

Number of Windows

Number of Storm Windows

Code for Main Heating Equipment

Code for Main Heating System Fuel

Code for Secondary Heating System Fuel

Indicator Variable for Electric Heat Pump

Code for Water-Heating Fuel

Indicator Variable for Electric Room Air Conditioners

Indicator Variable for Central Air Conditioning

Code for Central Air Conditioning Fuel

Number of Rooms Air Conditioned

59
Table C2. Transformed Household Variables Selected for Analysis of Natural Gas Consumption 

and Electricity Consumption.

ON

O

Variable

NSDRSAWS

NDRSAWS

NTOTAL

NBATHRMS

NRMELCAC

NRMELRAC

NRMGASAC

Definition

NSDOORS + NSWINSGD + NSTRMW1N

NDOORS1 + NUMWINDS

NROOMS + NDOORS1 + NUMWINDS

NCOMBATH +1/2

0 

0 

NROOMAC-HROOMAC

0 

1 

NROOMAC

0 

0 

NROOMAC-HROOMAC

(NHAFBATH)

if HCENTAC = 

if HCENTAC = 

if HCENTAC =

if HROOMAC = 

if HROOMAC = 

if HROOMAC =

if HCENTAC = 

if HCENTAC = 

if HCENTAC =

0 

1 and KFLCNAC = 1 

1 and KFLCNAC = 2

0 

1 and HCENTAC = 1 

1 and HCENTAC = 0

0 

1 and KFLCNAC = 2 

1 and KFLCNAC = 1

Description

Number of storm doors 

and windows.

Number of doors and 

windows .

Overall measure of the 

size of the house.

Number of bathrooms.

Number of rooms potentially 

air conditioned by electric 

central units.

Number of rooms potentially 

air conditioned by electric 

room units.

Number of rooms potentially 

air conditioned by natural 

gas central units.
Table C2. Transformed Household Variables Selected for Analysis of Natural Gas Consumption 

and Electricity Consumption (Continued).

Variable

HELWHT

HGASWHT

HELMHT

HGASMHT

HSBNMELH

Definition

1 

0

1

0

1 

0

1 

0

1

if KWHEATFL 

otherwise

if KWHEATFL 

otherwise

if KFLMHEAT 

otherwise

if KFLMHEAT 

otherwise

if KFLSHEAT

= 5

= 1

= 5

= 1

= 5 and KFLMHEAT jt 5

Description

Indicator variable for 

electric water heater.

Indicator variable for 

natural gas water heat.

Indicator variable for 

electric main heating.

Indicator variable for 

natural gas main heating.

Indicator variable for

HSBNMGSH

HELHTPUM

KMHTEQRC

0 otherwise

1 if KFLSHEAT 

0

1 if KMHEATEQ 

0 otherwise

1 if KFLMHEAT

2 if KFLMHEAT

3 if KFLMHEAT

4 if KFLMHEAT

1 and KFLMHEAT

1 and KMHEATEQ 

1 and KMHEATEQ 

1 and KMHEATEQ

1 or 2

3

1,2, and 3

electric secondary but 

not main space-heating.

Indicator variable for 

natural gas secondary but 

not main space-heating.

Indicator variable for 

electric heat pump.

Class variable for gas 

main heating equipment.

1 - System where heat is

distributed by water

2 - Central forced-air

3 - Other (usually space 

heater)

4 - Nongas main heating
Table C2. Transformed Household Variables Selected for Analysis of Natural Gas Consumption 

and Electricity Consumption (Continued).

Variable

Description

NELCKDV

HELFRIG1

HELFRIG2

HELFRIG3

HELOVEN + HELRANGE

1 if KREFRFL1 = 1

0 otherwise

1 if KREFRFL2 = 1

0 otherwise

1 if NREFRIG = 3, KREFRFL1 = 1

0 otherwise

Number of major electric cooking 

appliances.

Indicator variable for electric 

refrigerator.

Indicator variable for electric 

refrigerator.

Indicator variable for electric 

refrigerator.

NELFRIG HELFRIG 1 + HELFRIG 2 + HELFRIG 3 Number of electric refrigerators.
Appendix D.

WANDERING BOXPLOTS

Figures 6, 7, and 12 are variations of the graphical technique known as 

wandering boxplots or wandering schematics, discussed by John Tukey in 

his book, "Exploratory Data Analysis". To construct our version,

• Compute the 3rd, 6th, 12th, 25th, and 50th

percentiles of the abscissa, and their symmetric 

counterparts the 97th, 94th, 88th, and 75th 

percentiles.

• Divide the data into groups according to the values 

of the abscissa using the computed percentiles as 

dividing points.

• Within each group, calculate the quantiles and the 

median of the ordinate. These points are the ends 

and center, respectively, of the boxes.

• Calculate the midspread for each group, midspread = 

upper quantile - lower quantile.

• Flag all value between one and one-half and two 

midspreads of the upper quantile with an 'o 1 , 

and all values beyond two midspreads of the 

upper quantile with an '*'. Perform the similar 

operation with respect to the lower quantile.

• Within each group, plot the box and the flagged 

values of the ordinate centered over the median 

of the abscissa for the group.

*U.S. GOVERNMENT PRINTING OFFICE i 1981 0-341-068/1152

63
REFERENCES

1. Residential Energy Consumption Survey: Characteristics of the Housing 

Stock and Households, 1978, Report No. DOE/EIA-0207/2, February 1980.

2. Residential Energy Consumption Survey; Conservation, Report No. 

DOE/EIA-0207/3, February 1980.

3. Residential Energy Consumption Survey: Consumption and Expenditures,

April 1978 Through March 1979, Report No. DOE/EIA-0207/1, December 1979.

4. Single Family Households; Fuel Inventories and Expenditures; National 

Interim Energy Consumption Survey, Report No. DOE/EIA-0207/1, 

December 1979.

5. Woteki, T. H. "Imputing Residential Energy Consumption Data for the

National Interim Energy Consumption Survey: A Progress Report", February 

1980, Office of the Consumption Data System, Energy Information 

Administration, U.S. Department of Energy.

6. "NIECS Imputations and Adjustments for Missing Data" Memorandum from

Reuben Cohen to Lynda Carlson, August 1980. Response Analysis Corporation, 

Princeton, New Jersey.

7. Energy and Buildings, 1, April 1978.

8. Shrader, T. F., "A Two Parameter Model for Assessing the Determinants of 

Residential Space-Heating", Princeton University Center for Environmental 

Studies, Report No. 69, June 1978, Princeton, New Jersey.

9. Mayer, L. S. and Benjamin, Y., "Modeling Residential Natural Gas Demand 

as a Function of the Coldness of the Month", Energy and Buildings, 

1, April 1978.

10. Woteki, T. H. "The Princeton Omnibus Experiment: Some Effects of Retrofits

on Space-Heating Requirements, "Princeton University Center for Environmental 

Studies, Report No. 43, December 1976, Princeton, New Jersey.

11. Fels, M. F. and Woteki, T. H. "Studies of Energy Consumption; An Exploratory 

Analysis of a Utility's Monthly Billing Data", Energy, 5, 1979.

64
Other Reports Produced by the Office of the Consumption Data System

Residential Energy Consumption Survey; Conservation, February 1980, 

DOE/EIA-0207/3, GPO Stock No. 061-003-00087-8, $6.00.

Single-Family Households: Fuel Inventories and Expenditures: National 

Interim Energy Consumption Survey, December 1979, DOE/E1A-0207/1, GPO 

Stock No. 061-003-00075-4, $1.75.

Residential Energy Consumption Survey; Characteristics of the Housing 

Stock and Households, 1978, February 1980, DOE/EIA-0207/2, GPO Stock No. 

061-003-00093-2, $4.25.

Residential Energy Consumption Survey; Consumption and Expenditures, 

April 1978 through March 1979, July 1980, DOE/EIA-0207/5, GPO Stock No. 

061-003-00131-9, $6.50.

Residential Energy Consumption Survey: Consumption Patterns of Household 

Vehicles, June to August 1979, June 1980, DOE/EIA-0207/4, GPO Stock No. 

061-003-00156-4, $3.75.

Nonresidential Buildings Energy Consumption Survey; Building Characteristics, 

March 1981, DOE/EIA-0246, GPO Stock No. 061-003-00171-8, $5.50.

Residential Energy Consumption Survey: 1979-1980 Consumption and 

Expenditures, Part I; National Data (including Conservation), April 

1981, DOE/EIA-0262/1, GPO Stock No. 061-003-00191-2, $5.00.

Residential Energy Consumption Survey: 1978-1980 Consumption and 

Expenditures, Part II: Regional Data, May 1981, DOE/EIA-0262/2, GPO 

Stock No. 061-003-00189-1, $5.00.

Copies of the above reports are available from:

Superintendent of Documents 

U.S. Government Printing Office 

Washington, D.C. 20402

National Interim Energy Consumption Survey: Household Interview File, 

DOE/DF-81/001 (Magnetic Tape), $125.00 available from the National 

Technical Information Service - Computer Products Division, 5285 Port 

Royal Road, Springfield, Virginia, Accession No. PB-81-108714, $125.00.
U.S. Department of Energy 

Energy Information Administration 

National Energy Information Center, El- 20 

Forrestal Building 

Washington, D.C. 20585

FIRST-CLASS MAIL 

POSTAGE & FEES PAID 

U.S. DEPT. OF ENERGY

PERMIT NO. G 20

FIRST CLASS MAIL

OFFICIAL BUSINESS

PENALTY FOR PRIVATE USE, $300