Econometric Models for Major Residential Energy End-Uses

8/13/2019 Econometric Models for Major Residential Energy End-Uses

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Canadian Residential Energy End-use Data and Analysis Centre

CREEDAC

CREEDAC, Dalhousie University5269 Morris Street, Halifax, Nova Scotia, Canada B3J 1B6Tel: (902) 494 6183 Fax: (902) 494 3165 E-mail:[email protected]://www.dal.ca/daltech/creedac

Econometric Models for Major Residential Energy End-uses

(CREEDAC-1999-04-05)

Submitted to:Cristobal Miller

Policy Development and Analysis DivisionEfficiency and Alternative Energy Branch

Natural Resources Canada580 Booth Street

Ottawa, OntarioCanadaK1A 0E4

CREEDAC Project Team:Alan S. Fung

Merih AydinalpV. Ismet Ugursal

April 1999


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ECONOMETRIC MODEL FOR RESIDENTIAL ENERGY END-USES

PAGE 2 CREEDAC APRIL 1999

Table of Contents

TABLE OF CONTENTS ................................................................................................ 2

LIST OF TABLES.......................................................................................................... 3

LIST OF FIGURES ........................................................................................................ 5

EXECUTIVE SUMMARY ............................................................................................. 6

1. INTRODUCTION ...................................................................................................9

2. REGRESSION MODEL........................................................................................ 11

2.1 OVERVIEW ...................................................................................................... 112.2 GENERAL FORM OF THE MODEL EQUATIONS ........................................................ 122.3 DETERMINATION OF THE ELASTICITIES.................................................................. 142.4 MODEL EQUATIONS FOR DIFFERENT END-USES..................................................... 15

2.4.1 Household Appliance model Equation ......................................................... 152.4.2 Space Heating Model equation .................................................................... 162.4.3 DHW Heating Model equation .................................................................... 162.4.4 Combined Space and DHW Heating model equation ..................................17

3. DATA SET............................................................................................................18

3.1 OVERVIEW .......................................................................................................... 183.2 PHYSICAL AND DEMOGRAPHIC CHARACTERISTICS OF HOUSEHOLDS .......................183.3 HOUSEHOLD APPLIANCE CHARACTERISTICS......................................................... 19

3.4 WEATHER CHARACTERSITICS............................................................................... 203.5 HOUSEHOLD ENERGY CONSUMPTION DATA......................................................... 21

3.5.1 Disaggregation of Energy Consumption data............................................... 223.5.1.1. Disaggregation of Energy Consumption in Natural Gas Heated Houses . 233.5.1.2. Disaggregation of Energy Consumption in All-Electric Houses.............. 24

3.6 AVERAGE PROVINCIAL FUEL PRICE ..................................................................... 25

4. RESULTS AND DISCUSSION.............................................................................27

4.1 OVERVIEW .......................................................................................................... 274.2 HOUSEHOLD APPLIANCE ENERGY CONSUMPTION MODEL .................................... 294.3 SPACE HEATING ENERGY CONSUMPTION MODEL ................................................. 32

4.4 DHW HEATING ENERGY CONSUMPTION MODEL ................................................. 344.5 COMBINED SPACE AND DHW HEATING ENERGY CONSUMPTION MODEL .............. 37

5. CONCLUSION...................................................................................................... 64

6. REFERENCES AND BIBLIOGRAPHY ............................................................... 66


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List of Tables

Table 1: Household End-use Energy Consumption Elasticities calculated using 20%significance criterion....................................................................................................... 8

Table 2: List of model equations ................................................................................... 12

Table 3: List of model equations developed................................................................... 12

Table 4: Average Current and Lagged Provincial Fuel Prices ........................................ 26

Table 5: Data Statistics for Appliance Energy Consumption Model for Natural GasHeated Households........................................................................................................ 40

Table 6: Data Statistics for Appliance Energy Consumption Model for ElectricHeated Households........................................................................................................ 41

Table 7: Appliance Energy Consumption Model Summary for Fossil FueledHouseholds ................................................................................................................... 42

Table 8: Appliance Energy Consumption Model Summary for Electric HeatedHouseholds ................................................................................................................... 43

Table 9: Appliance Energy Consumption Model Elasticities Estimates for NaturalGas Fueled Households................................................................................................. 44

Table 10: Appliance Energy Consumption Model Elasticities Estimates for Electric

Heated Households........................................................................................................ 45

Table 11: Data Statistics for Natural Gas Space Heating Energy Consumption Modelin Natural Gas Heated Households ................................................................................ 46

Table 12: Data Statistics for Electric Space Heating Energy Consumption Model inElectric Heated Households........................................................................................... 47

Table 13: Natural Gas Space Heating Energy Consumption Model Summary forNatural Gas Fueled Households..................................................................................... 48

Table 14: Electric Space Heating Energy Consumption Model Summary for ElectricHeated Households........................................................................................................ 49

Table 15: Natural Gas Space Heating Energy Consumption Model ElasticitiesEstimates for Natural Gas Fueled Households ............................................................... 50

Table 16: Electric Heating Energy Consumption Model Elasticities Estimates forElectric Heated Households........................................................................................... 51


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Table 17: Data Statistics for Natural Gas DHW Heating Energy Consumption Modelin Natural Gas Heated Households ................................................................................ 52

Table 18: Data Statistics for Electric DHW Heating Energy Consumption Model inElectric Heated Households........................................................................................... 53

Table 19: Natural Gas DHW Heating Energy Consumption Model Summary forNatural Gas Fueled Households..................................................................................... 54

Table 20: Electric DHW Heating Energy Consumption Model Summary for ElectricHeated Households........................................................................................................ 55

Table 21: Natural Gas DHW Heating Energy Consumption Model ElasticitiesEstimates for Natural Gas Fueled Households ............................................................... 56

Table 22: Electric DHW Heating Energy Consumption Model Elasticities Estimatesfor Electric Heated Households ..................................................................................... 57

Table 23: Data Statistics for Natural Gas Space and DHW Heating EnergyConsumption Model in Natural Gas Heated Households ............................................... 58

Table 24: Data Statistics for Electric Space and DHW Heating Energy ConsumptionModel in Electric Heated Households............................................................................ 59

Table 25: Natural Gas Space and DHW Heating Energy Consumption ModelSummary for Natural Gas Fueled Households............................................................... 60

Table 26: Electric Space and DHW Heating Energy Consumption Model Summaryfor Electric Heated Households ..................................................................................... 61

Table 27: Natural Gas Space and DHW Heating Energy Consumption ModelElasticities Estimates for Natural Gas Fueled Households ............................................. 62

Table 28: Electric Space and DHW Heating Energy Consumption Model ElasticitiesEstimates for Electric Heated Households ..................................................................... 63


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List of Figures

Figure 1: Typical monthly natural gas consumption in natural gas heated households.... 23

Figure 2: Typical monthly electricity consumption in air-conditioned electric heatedhouses ........................................................................................................................... 24


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EXECUTIVE SUMMARY

A comprehensive econometric regression analysis was carried out on the three major

components of the residential end-use energy consumption, namely space heating energyconsumption, domestic hot water (DHW) heating energy consumption and appliance

energy consumption, to determine their long- and short-term price and income

elasticities.

The analysis was carried out on the 1993 Canadian housing stock. Three main data

sources were utilized in the analysis: (1) Survey of Household Energy Use (SHEU,

1993), (2) Energy billing records for a subset of SHEU data, and (3) Energy Statistics

Handbook (Statistics Canada, 1998), Electric Power Statistics (Statistics Canada, 1992),

and Canadian Economic Observer (Statistics Canada, 1998). SHEU provided most of the

demographic and physical housing characteristics while its subset of billing records

provided the total annual household fuel consumption data for both natural gas and

electricity. Both current and lagged average provincial fuel prices were obtained and/or

estimated using Statistics Canadas Energy Statistics Handbook, Electric Power

Statistics, and Canadian Economic Observer.

Log-linear variable price and variable income elasticity energy demand model, which

was first proposed by Betancourt (1981) and later used by Donnelly and Diesendorf

(1985) and Douthitt (1989), was adopted and modified to determine the price and income

elasticities of the major components of the residential end-use energy consumption in

natural gas and electric heated households. Model equations that incorporate

demographics, weather and equipment characteristics as explanatory variables were

developed, and price and income elasticities were derived from the model equations. The

price, income and expenditure elasticities thus derived are presented in Table 1.

Both the long- and the short-term own fuel price elasticities were found to have the

expected negative sign, implying that fuel price has a negative effect on energy

consumption (i.e. as fuel price increases, energy consumption decreases) for all types of


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end-use energy consumption and fuel types. The magnitude of the short-term price

elasticities were found to be significantly less than unity, indicating that the impact of

price increase on end-use energy consumption was quite inelastic. The magnitude of the

long-term price elasticities were found to be negative and above unity, indicating that in

the long-term consumers would respond to a one percent increase in fuel price by

reducing energy consumption by more than one percent.

Income elasticity on end-use energy consumption was found to be statistically

insignificant in most cases, and the ones that proved to be significant were very inelastic,

i.e. the absolute magnitudes of the elasticities were very close zero. Household energy

expenditure elasticities for all end-uses and fuel types proved to be positive indicating

that the energy consumption for all three major residential end-uses (appliance, space

heating and domestic hot water heating) behave like normal goods. All cross price effects

were proved to be statistically significant with negative sign, except that for electric

DHW heating which was insignificant. This indicated that consumers would have a

similar response on energy demand to substitute price change as to own price change.


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Table 1: Household End-use Energy Consumption Elasticities calculated using 20%

significance criterion

End-use Energy Consumption Elasticities All Natural Gas All Electric

Heated Household Heated Household

Appliance Energy Consumption

Short-run Price Elasticity -0.341 -0.594 Long-run Price Elasticity -1.746 -1.208

Income Elasticity 0.009 N/A

Expenditure Elasticity 1.115 0.830

Space Heating Energy Consumption

Short-run Price Elasticity -0.246 -0.467

Long-run Price Elasticity -0.904 -2.804

Income Elasticity -0.005 N/A


Cross Price Effect -0.793 -0.606

DHW Heating Energy Consumption


Long-run Price Elasticity -2.510 -1.213 Income Elasticity N/A 0.022


Cross Price Effect -0.366 N/A

Space + DHW Heating Energy Consumption



Income Elasticity N/A N/A


Cross Price Effect -0.701 -0.257

Note: N/A indicates the variables are statistically not significant at 20% level


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1. INTRODUCTION

In 1996 the end-use energy consumption in Canada was about 7630 PJ (NRCan, 1998),

making Canada one of the highest per capita energy consumers in the world. The carbondioxide emission associated with this energy consumption was about 416 Mt. Mostly

owing to its northerly location and the prevalence of single family housing, residential

energy consumption was about 1450 PJ, representing 19% of the total energy

consumption in Canada. The carbon dioxide emission associated with the residential

energy consumption was about 72 Mt.

With the Kyoto Protocol signed in December 1997, developed countries committed to

legally binding greenhouse gas (GHG) emission reductions of at least five percent by

2008 to 2012. Canada promised a six percent reduction below 1990 emission levels by

2010. Canada's commitment represents a reduction in greenhouse gas emissions of at

least 19 percent below what they would be without the agreement. To meet this

challenging commitment, Canada has to evaluate and exploit every feasible measure to

reduce the energy consumption and GHG emissions while maintaining its economic

growth.

Residential energy consumption in Canada is primarily for space heating (61%), followed

by domestic hot water heating (21%), appliances and lights (17%), and finally, cooling,

which is negligibly small (0.4%) (NRCan, 1998). End-use energy consumption in the

residential sector could be reduced by improving the building envelope characteristics

(better insulation, better windows and doors, tighter buildings), and by using higher

efficiency lighting, appliances, domestic hot water (DHW) heating and space heating,

ventilating and air-conditioning (HVAC) equipment. Reducing the end-use energy

consumption and switching to less carbon-intensive fuels for space and domestic hot

water heating would result in reduced carbon dioxide emissions from the residential

sector. However, the energy consumption pattern of consumers is a result of many

complex and interrelated socioeconomic and technical factors as well as consumers

energy conservation consciousness. Thus, an effective and efficient energy conservation


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policy requires accurate and comprehensive estimates of residential energy demand

parameters. These parameter estimates are among the most important inputs into

informed policy decisions. In turn, accurate estimation of energy demand parameters

requires realistic modeling of the consumers energy demand behavior, detailed data on

energy consumption, and careful treatment of any econometric problems created by the

model and the data used.

In this report, econometric residential end-use energy models are developed to identify

income and price elasticities of major residential energy end-uses.Using the models, the

impact of various socioeconomic and physical housing characteristics on the residential

energy consumption in Canada are also evaluated. In addition, some conclusions are

made regarding possible strategies for reducing energy consumption from the residential

sector.


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2. REGRESSION MODEL

2.1 OVERVIEW

The objective of this study is to develop price and income elasticities for energy demand

in the Canadian residential sector. The analytical approach is based primarily on the work

done by Betancourt (1981), Donnelly and Diesendorf (1985) and Douthitt (1989). Ideally,

the analysis should provide both price and income elasticities of energy demand for each

of the three major residential energy end-uses; namely, space heating, domestic hot water

heating, and appliance energy end-uses.

It is expected that each one of the three major residential energy end-uses poses a distinct

consumption profile for different fuel types and equipment characteristics. Consequently,

each different end-use is expected to have a distinct demand equation based on the fuel

type and equipment characteristic. Thus, three sets of model equations are developed

here: (i) appliance, (ii) space heating, (iii) DHW heating. Additionally, a fourth set of

model equations are developed for combined space and DHW heating since these two

end-uses generally utilize the same fuel.

The major fuel types considered in this study are natural gas, electricity and oil. Thus, a

set of four equations (one for each end use; i.e. appliance, space heating, DHW heating,

combined space and DHW heating) were to be developed for each of the three fuel types

as shown in Table 2.However, as it is explained in Section 3.5, the number of oil heated

households in the database is not sufficient to conduct a statistical analysis; therefore, oil

is not included in the analysis. On the other hand, two sets of equations would be needed

for households heated with electricity: (i) all-electric households in regions where naturalgas is available, and (ii) all-electric households in regions where natural gas is not

available. However, it is not possible to categorize the households in the database

according to this criterion because the exact locations of the houses are not known,

consequently, availability of natural gas is not known either. Therefore, a single set of

equations were developed for all of the electric heated households.


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To facilitate the evaluation of long-term price elasticity as suggested by Poyer and

Williams (1993), a set of model equations were developed by excluding the lagged fuel

price from the variable list used in the regressions. The long-term price elasticities can be

estimated by dividing the short-term estimates by unit minus the estimated coefficient of

the lagged variable.

In conclusion, a total of 16 model equations were developed as shown in Table 3.

Table 2: List of model equations

End-use Energy Electric Heated Natural Gas

Consumption Model Households Heated Households

Appliances

DHW HeatingSpace Heating

Combined Space & DHW Heating

Table 3: List of model equations developed

Electric Heated Natural Gas Heated

End-use Energy House holds House holds

Consumption Model Model I Model II Model I Model II

(No Lag) (with Lag) (No Lag) (with Lag)

Appliances

DHW Heating

Space Heating

Combined Space & DHW Heating

2.2 GENERAL FORM OF THE MODEL EQUATIONS

The general stochastic econometric variable elasticity demand model, first proposed by

Betancourt (1981) and later modified by Donnelly and Diesendorf (1985) to yield unitlessmeasures of elasticity, is given in Equation (1):

n5432mm a

n

a

k

a

j

aaXa

i0i XPPEYPaQ = (1)


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where Qi= Total end-use energy consumption (GJ or kWh)

a0,a1, . an= Variable coefficients

Y = Household income ($)

E = Total expenditure on fuel or energy ($)

Piand Pi,-1 = Average current and lagged chosen fuel prices ($/GJ)

Pj, Pk= Substitute fuel prices ($/GJ)

Xn= Other socioeconomic and engineering variables

Xm= Other socioeconomic and engineering variables

Vector for other variables Xn and Xm includes all other pertinent variables. These are

given below categorized in groups of related parameters (units given in parentheses):

1) Structural Variables:

Number of floors (-): STOREY

Total Heated floor area (m2): AREA

Basement area (m2): BASE

Number of windows (-): WIN

Number of doors (-): DOOR

Number of skylights (-): SKY

2) Weather and Temperature for space heating:

Average indoor temperature (C): TEMP

Average heating degree days (C-day): HDD

3) Human Capital Factors:

Household size (no. of people): HHS

Overall heating equipment efficiency (%): EFF

Total appliance energy consumption (GJ): APP

4) Domestic Hot Water Heating:

Number of aerators and low-flow shower heads (-): AERATOR

Average ground temperature (C): GT

Hot water tank size (liters): TANK

Presence of tank insulation (0 or 1): INSUL

5) Cooling:


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Central air-conditioning usage in the cooling season (% of time):

AC_USAGE

Average cooling degree days (C-day): CDD

6) Appliances:

Dishwasher load (no. of loads/year): DW

Clothes washer load (no. of loads/year): WA

Clothes dryer load (no. of loads/year): DRY

Cooking range/oven age (years): RANGE_A

Presence of cooktop (0 or 1): COOKTOP

Freezer age (years): FREEZER_A

Freezer size (ft3): FREEZER_S

First frost-free fridge age (years): FF1_A

First frost-free fridge size (ft3): FF1_S

First non frost-free fridge age (years): NFF1_A

First non frost-free fridge size (ft3): NFF1_S

Second frost-free fridge age (years): FF2_A

Second frost-free fridge size (ft3): FF2_S

Second non frost-free fridge age (years): NFF2_A

Second non frost-free fridge size (ft

3

): NFF2_SNumber of light bulbs (-): LIGHT

Presence of furnace fan (0 or 1): FFAN

2.3 DETERMINATION OF THE ELASTICITIES

Variable coefficients in the general model equation can be determined by multi-variate

linear regression conducted on the available data once Equation (1) is transformed by

taking the natural logarithm of both sides:

)Xln(a)Pln(a)Pln(a)Eln(a)Yln(a)Pln(XaA)Qln( nnk5j432imm0i ++++++= (2)

Once the variable coefficients are determined, the price and income (and other

parameters) elasticities on energy demand can be determined using the classical


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economic elasticity definition. The general and price elasticities derived from Equation

(1) can be expressed as:

Q

X

X

Q

X

X

Q

Q

EX

=

= (3)

mmP XaQ

P

P

Q

P

P

Q

QE =

=

= (3a)

Since the general elasticity, shown in equation (3), provides the measure of percent

change in Q for one percent change in X, it is a unitless measure of elasticity. On the

other hand, Equation (3a) does not provide such a unitless measure of elasticity as in

Equation (3), since it has the unit of parameter Xm. Thus, it is necessary to transform the

exponent variable, Xm, in Equation (3a) into a unitless variable. The method of

transforming the exponent variables by dividing them by their corresponding standard

deviations, as proposed by Donnelly and Diesendorf (1985), is used in this study.

2.4 MODEL EQUATIONS FOR DIFFERENT END-USES

To identify the variables to be included in the model equations and the final form of the

model equations, various model equations were tested. As a result of these tests, the

variables and the form of the equations were determined.

The resulting equations are presented below.

2.4.1 HOUSEHOLD APPLIANCE MODEL EQUATION

The model equation for appliance end-use energy consumption is given in Equation (4).

There is no substitute price in the equation because electricity is predominantly the only

fuel choice for appliances.


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n109

87654321,i1

a

n

aa

aaaa)HHSa()GTaHDDaPa(

i0i

XBASEAREA

STOREYTEMPEFFEYPaQ ++

=(4)

where variables Xnfor appliance energy consumption model are:

FFANaCOOKTOPaa

CDDaaA_2NFFa

A_1NFFaA_2FFaA_1FFa

A_FREEZERaaaaa

n

13n12n11n

10n9n8n

7n6n5n

4n3n2n1nn

eeLIGHT

USAGE_ACA_RANGES_2NFF

S_1NFFS_2FFS_1FF

S_FREEZERDRYWADWX =

(4a)

2.4.2 SPACE HEATING MODEL EQUATION

The model equation for space heating end-use energy consumption is given in Equation

(5). The appliance energy consumption variable, APP is a proxy for internal heat gain.

n121110

987654321,i1

a

n

aa

s

a

aaaaa)HHSa()GTaHDDaPa(

i0i

XAPPPBASE

AREASTOREYTEMPEFFEYPaQ ++

=(5)

where variables Xnfor space heating energy consumption model are:

3n2n1nn aaaan WINSKYDOORX = (5a)

2.4.3 DHW HEATING MODEL EQUATION

The model equation for space heating end-use energy consumption is given in Equation

(6):

n1110

987654321,i1

a

n

a

s

a

aaaaa)HHSa()GTaHDDaPa(

i0i

XPBASEAREASTOREYTEMPEFFEYPaQ

++=

(6)

where variables Xnfor DHW heating energy consumption model are:


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INSULaaaaaa

n5n4n3n2n1nn eWADWAERATORTANKX = (6a)

2.4.4 COMBINED SPACE AND DHW HEATING MODEL EQUATION

The model equation for combined space heating and DHW heating end-use energy

consumption is given in Equation (7)

n1211109

87654321,i1

a

n

aa

s

aa

aaaa)HHSa()GTaHDDaPa(

i0i

XAPPPBASEAREA

STOREYTEMPEFFEYPaQ ++=

(7)

where variables Xn for combined space and DHW heating energy consumption model

are:

INSULaa

aaaaaaa

n

8n7n

6n5n4n3n2n1nn

eWA

DWAERATORTANKWINSKYDOORX =(7a)

The equation contains only one substitute price and several building and DHW heating

equipment specific parameters. There is only one substitute price in the model equation

because most homeowners have only one alternative fuel choice.1

1Only 31 households out of a total of 320 electric heated households have natural gas

available in their areas. Thus, the only alternative fuel choice for these electric heatedhouseholds is fuel oil. Most of the natural gas heated households are located in regionswhere oil is not a major player in residential home heating market due to significantlylower price of natural gas compared to oil.


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3. DATA SET

3.1 OVERVIEW

To construct the necessary data set for the development of the econometric model, three

main sources of data were used in this study: (i) Survey of Household Energy Use

(SHEU, 1993), (ii) Energy billing records for a subset of SHEU data, and (iii) Energy

Statistics Handbook (Statistics Canada, 1998), Electric Power Statistics (Statistics

Canada, 1992), and Canadian Economic Observer (Statistics Canada, 1998).

SHEU (1993) contains comprehensive data physical and demographic data on 10,982

households across Canada. 8,767 of these 10,982 records are for low-rise single family

dwellings. These include single detached and attached dwellings. The energy billing data

for about 3,000 of the 8,767 single family dwellings are also available from a SHUE data

file. Since this study focuses on low-rise dwellings, physical, demographic and energy

billing data from these 3000 households were used here.

Both current and lagged average provincial fuel prices were obtained and/or estimated

using the Energy Statistics Handbook, Electric Power Statistics, and Canadian Economic

Observer published by Statistics Canada.

3.2 PHYSICAL AND DEMOGRAPHIC CHARACTERISTICS OFHOUSEHOLDS

The values for most of the variables used in the parameter vector Xnof the models given

in Equations (4) - (7) were obtained directly or indirectly from the SHEU data as given

below (the column numbers refer to the SHEU micro-data file):

1) Structural Variables:Number of floors/storeys: Column 181.

Total heated area: Column 189 (mean value of each category is use).

Basement area: Column 192 (mean value of each category is used).

Number of windows: Column 231, 232, 234, 235, 237, 238, 240, 241.

Number of doors: Column 210, 211, 213, 214, 216, 218.


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Number of skylights: Column 227, 228, 229.

2) Weather and Temperature:

Average indoor temperature: Column 178, 179, 180.

3) Human Capital Factors:

Household size: Column 8.

Household income: Column 355 (mean value of each category is used).

Overall heating equipment efficiency: Column 142: (mean value of each

category is used. 100%, 150%, and 250% are assigned for electric

resistance, air-source heat pump, and water/ground source heat pump

heated households, respectively.)

4) Domestic Hot Water Heating:

Number of aerators and low-flow shower heads: Column 327, 329.

Hot water tank size: Column 323.

Presence of DHW tank insulation: Column 324.

3.3 HOUSEHOLD APPLIANCE CHARACTERISTICS

In order to capture the effect of appliance stock holding, its characteristics and usage on

energy demand, data on major household appliances were included in the appliance

energy demand equation. The following data from SHEU were used:

1) Dishwasher:

Number of loads: Column 75 (value is multiplied by 52 to obtain number

of loads/year).

2) Clothes washer:

Number of loads: Column 100, 101 (values are multiplied by 26 and

added to obtain number of loads/year).

3) Clothes dryer:

Number of loads: Column 114, 115 (values are multiplied by 26 and

added to obtain number of loads/year).

4) Freezer:

Age of freezer: Column 79 (mean value of each category is used).


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Size of freezer: Column 83 (mean value of each category is used).

5) First Refrigerator:

Age of Refrigerator: Column 42 (mean value of each category is used).

Size of Refrigerator: Column 46 (mean value of each category is used).

Frost free or manual defrosted: Column 48.

6) Second Refrigerator:

Age of Refrigerator: Column 43 (mean value of each category is used).

Size of Refrigerator: Column 47 (mean value of each category is used).

Frost free or manual defrosted: Column 49.

7) Cooking equipment:

Electric range/oven age: Column 56 (mean value of each category is

used).

Presence of electric cooktop: Column 53.

8) Lighting:

Number of light bulbs: Column 331, 332, 334, 335, 345, 346, 347.

9) Furnace fan:

Presence of furnace fan: Column 138.

10)Central air conditioning:

Central air-conditioning usage: Column 300: assign 0, 25, 50, 75, and 100

percent usage to response 1 to 5, respectively.

3.4 WEATHER CHARACTERSITICS

Weather plays a major role on overall residential energy consumption. Ideally, both long-

term average and temporal heating degree-days (HDD) should be included in the model

development. Long-term average heating degree-days would be expected to have an

influence on price elasticity since consumers are likely to be energy conscious in colder

climates due to high energy expenditures. On the other hand, temporal heating degree-

days mainly influence the temporal space heating energy consumption because of its

direct influence on the amount of heat loss through the building envelope.


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It was decided not to include the temporal heating degree-days in this study because of

the time and cost associated in obtaining temporal degree-day information.

Cooling degree-days have an effect on air-conditioning energy consumption, therefore

long-term average cooling degree-days were used in the model.

3.5 HOUSEHOLD ENERGY CONSUMPTION DATA

To formulate the energy demand model equations, actual data on overall as well as

disaggregated end-use energy consumption for houses are needed. A subset of SHEU

database contains one year of energy consumption billing records from utility companies.

There are a total of 133, 972, and 1424 households with oil, natural gas, and electricitybilling records, respectively.

To ensure data quality, a number of data screenings were performed. The following

procedures were employed to screen the data:

No household was accepted if supplemental space heating is different from the main

space heating fuel. For example, if wood or propane was indicated as the

supplemental space heating fuel in a natural gas/electric/oil heated house, then thishousehold was rejected.

Only households that use the same fuel for both space and DHW heating were

accepted because the number of households in the database that use different fuels for

space and DHW heating is 18, which is not sufficient to conduct a statistical analysis.

Only households with complete twelve month fuel billing records were accepted. This

was essential for disaggregating the space heating energy consumption from DHW

heating energy consumption for fossil fuel heated houses, and for disaagregating the

space heating energy consumption from other end-uses in electrically heated houses.

After applying this screening process, only 22 oil, 249 natural gas, and 320 electric

heated households were left to be used in the analysis.


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The data set of 22 samples for oil heated houses is unacceptably low to carry out a

meaningful statistical analysis with a high number of explanatory variables. Moreover, an

inspection of these 22 household files revealed that all are from one province. This

renders the fuel price invariant in all of these 22 households, making the regression

process on oil heated households even more pointless. Thus, oil heated households are

not included in this work.

3.5.1 DISAGGREGATION OF ENERGY CONSUMPTION DATA

To formulate the energy demand model equations, it is necessary to disaggregate the

energy consumption data obtained from energy bills into three major components, i.e.

space heating, DHW heating and appliances energy consumption. To accomplish this, it

is commonly assumed that that there is no space heating requirement during the summer

months of July and August. Thus, the energy consumption in these two months can be

assumed to be for DHW heating and appliances (including lighting) only (see Figure 1).

Furthermore, it is assumed that the energy consumption for DHW heating and appliances

is independent of the time of the year (i.e. constant over the whole year). This second

assumption is clearly questionable since water supply temperature, daylight hours, indoor

temperature, etc. all have impact on DHW and appliance energy consumption. However,

in the absence of disaggregated data, the inaccuracy involved with this assumption is

tolerated.

The disaggregation of the energy consumption data was accomplished as described

below.


23/67



Typical Monthly Household Natural Gas Consumption

Profile

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

Month

Figure 1: Typical monthly natural gas consumption in natural gas heated households

3.5.1.1. Disaggregation of Energy Consumption in Natural Gas Heated Houses

Appliance energy consumption: The total annual appliance energy consumption is

available from the total annual electricity billing.

DHW heating energy consumption: The average monthly natural gas consumption for

DHW heating was estimated from the natural gas billings for July and August.

Space heating energy consumption: The annual space heating energy consumption is

estimated by subtracting the estimated DHW heating energy consumption from the total

annual natural gas billing record.


24/67



3.5.1.2. Disaggregation of Energy Consumption in All-Electric Houses

Appliance and DHW heating energy consumption: The average monthly electrical

consumption for appliances and DHW heating (combined) was estimated from the

electricity billings for July and August. In air-conditioned households, July and August

energy consumption includes electricity consumption for air-conditioning (see Figure 2).

Therefore, in air-conditioned houses, data from shoulder months of June and September

were used to represent the average monthly electrical consumption for appliances and

DHW heating.

Typical Monthly Household Electricity Consumption

Profile

0

500

1000

1500

2000

2500

3000

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

Month

E

lectricityConsumption(kWh)

Figure 2: Typical monthly electricity consumption in air-conditioned electric heatedhouses

To disaggregate the electrical energy consumption for DHW heating and appliances, the

following approach was used:

It was assumed that the average ratio of appliance energy consumption to that of DHW

heating energy load is constant in all houses. The average efficiency of natural gas heated

DHW heaters is 55%. The ratio of appliance energy consumption to DHW heating energy


25/67



load in natural gas heated houses was calculated using this average efficiency and the

estimated appliance and DHW heating consumption values as follows:

nconsumptio

DHWloadAPP

DHW55.0

mptionnergyConsuApplianceER =

(8)

This ratio was found to be 1.51. The average efficiency of electrically heated DHW

heaters is 83%. Thus, using the ratio calculated using Equation 8 and this average

efficiency, the ratio of electricity consumption of appliances to the electricity

consumption for DHW heating was calculated as follows:

25.1)51.1)(83.0(DHW

mptionnergyConsuApplianceE

nconsumptio

== (9)

Using this ratio, the total energy consumption for appliances and DHW heating was

disaggregated into its two components.

Space heating energy consumption: The annual space heating energy consumption is

estimated by subtracting the estimated appliance and DHW heating energy consumption

from the total annual electricity billing records.

3.6 AVERAGE PROVINCIAL FUEL PRICE

It was not possible to obtain the actual fuel price, tax, rate structure, and basic service

charge information for each household in the database since the exact location of the

households is not available; therefore, average provincial fuel prices were used in this

study.

Average provincial natural gas prices for residential uses were obtained directly from

Statistics Canadas Energy Statistics Handbook (1998). Since electricity prices are not

given in Energy Statistics Handbook, electricity price data were estimated using data

obtained from Electric Power Statistics (1992) multiplied by the consumers price index

from Canadian Economic Observer (1998). The average current and lagged provincial


26/67



fuel prices used in this study are presented in Table 4. The total household energy

expenditure for each household was calculated using the billing records and the average

provincial fuel prices.

Table 4: Average Current and Lagged Provincial Fuel Prices

Lagged Price Current Price

Province Electricity Natural gas Oil Electricity Natural gas Oil

(cents/kWh) (cents/m^3) (cents/liter) (cents/kWh) (cents/m^3) (cents/liter)

NFLD 4.70 N/A 39.70 4.71 N/A 39.60

PEI 11.70 N/A 35.50 11.69 N/A 36.00

NS 7.70 N/A 36.50 7.69 N/A 36.50

NB 5.60 N/A 38.20 5.79 N/A 38.70

QUE 4.80 28.07 37.70 4.87 28.12 37.00

ON 7.00 20.60 36.40 7.47 20.99 38.00

MAN 4.70 20.04 41.00 4.73 20.70 42.50

SAS 5.90 15.90 36.10 6.24 16.49 35.70AB 5.20 12.67 N/A 5.37 14.59 N/A

BC 4.60 19.06 40.40 4.78 19.75 41.40


27/67



4. RESULTS AND DISCUSSION

4.1 OVERVIEW

Eight end-use energy consumption models were developed and analyzed. These are:

- For households heated with natural gas:

. Space heating energy consumption,

. Appliance energy consumption,

. DHW heating energy consumption,

. Combined space heating and DHW heating energy consumption;

- For households heated with electricity:

. Space heating energy consumption,

. Appliance energy consumption,

. DHW heating energy consumption,

. Combined space heating and DHW heating energy consumption.

To facilitate the evaluation of long-term price elasticity suggested by Poyer and Williams

(1993), another eight sets of model regressions without lagged price (Pi,-1) variables were

also performed. These eight sets of model equations were denoted as Model I while the

set of model equations with lagged fuel prices are denoted as Model II.

All of the regression analyses were performed using Version 9 of SPSS (1998) computer

statistical software package. For each model equation analysis, two statistical analyses

were run using SPSS:

(i) "As Entered": The first scenario was run using the As Entered feature of SPSS

to determine the coefficients of all of the entered variables regardless of their

statistical significance. The results of this scenario are denoted as As Entered in

the summary tables 7, 8, 13, 14, 19, 20, 25, and 26.

(ii) "Backward Elimination": The second scenario was run using Backward

elimination" feature of SPSS to determine the coefficients of the variables with

the 20 percent significance level option. This relatively high significance level

option of 20 percent was used for the backward elimination method to ensure that


28/67



most of the important variables (such as the lagged price, substitute price, and

income) were included in the final model equations so that price and income

elasticities as well as cross-price effects on end-use energy consumption can be

identified. It was however found that most of these variables are statistically

significant at or below 5 percent significance level. The results of this second

scenario were denoted as Up to 20 Percent in the summary tables 7, 8, 13, 14,

19, 20, 25, and 26.

The statistics on the variables used in each one of the energy end-use model equation are

presented in Tables 5, 6, 11, 12, 17, 18, 23, and 24. The coefficients of the variables, the

t-statistics and the R2values are presented in Tables 7, 8, 13, 14, 19, 20, 25, and 26. The

estimated short-term and long-term price elasticities, income elasticities, and cross-price

effects are presented in Tables 9, 10, 15, 16, 21, 22, 27, and 28. To represent price

elasticities for households that face average, higher than average, and lower than average

initial fuel prices, price elasticities were estimated at (i) sample mean, (ii) sample mean

plus its standard deviation, and (iii) sample mean minus its standard deviation,

respectively.

At up to 20 percent significance level, the adjusted R2 values (i.e. goodness of fit) range

from 0.376 to 0.987. All R2 values are above 0.64 except that for natural gas DHW

heating, which has an adjusted R2 of 0.376. The adjusted R2values are surprisingly high

for combined space and DHW heating energy consumption models. The adjusted R2

values are 0.949 and 0.987 for natural gas and electric heated households, respectively.

These adjusted R2values are much higher than those reported by Douthitt (1989) for a

similar study of the Canadian housing stock. This could be attributed to the fact that

estimated, instead of actual, household space heating energy consumption data were used

in his analyses.

Some interesting observations can be made from comparisons of the data sets of natural

gas heated and electric heated households:


29/67



- Natural gas heated households, in general, consume more energy for all end-uses,

including electric appliances (higher energy consumption for both space and DHW

heating energy end-uses is to be expected since natural gas has lower overall fuel

utilization efficiency),

- On average, natural gas heated households have higher household income and bigger

home.

- Natural gas heated households experience colder climate (higher heating degree-days)

in winter and warmer climate (higher cooling degree-days) in summer.

- Indoor temperature setpoint in natural gas heated households is higher than those of

electric heated households.

- Natural gas heated households have a greater number of light bulbs.

4.2 HOUSEHOLD APPLIANCE ENERGY CONSUMPTION MODEL

Results from the appliance end-use energy consumption model are presented in Tables 5

to 10. The discussion of the results here is limited to the results for the "up to 20%"

significance level.

All economic factors used in the models proved to be statistically significant except the

lagged price in the electricity heated household model. Appliance energy consumption

proved to be positively related to household energy expenditure and income, and

negatively related to price and heating degree-days. Other appliance variables that proved

to be significant are dishwasher load, clothes dryer load, refrigerators, and air

conditioning usage. As expected, all of these variables, except the first non frost-free

refrigerator, are positively related to energy consumption. This could be attributed to the

fact that non frost-free refrigerators consume less energy than their frost-free counterparts

since they do not employ defrost-cycles.

As expected, both estimated short- and long-term price elasticities were negative. The

short- and long-term elasticities, evaluated at the sample mean, were found to be 0.341

and 1.746 for natural gas heated households, and 0 .594 and 1.208 for electric heated

households, respectively. Natural gas heated households respond to price changes less


30/67



than the electric heated households in the short-term. This trend is reversed in the long-

term price responses. Since electric heated households face higher fuel prices and have

higher household energy expenditures, in the short- term they are expected to respond to

price changes more than natural gas heated households. The elastic nature of the long-

term price elasticities indicate that consumers tend to become more energy conscious if

they are faced with long-term price increases. The higher long-term price elasticity for

the natural gas heated households may indicate that these households would consider

switching to natural gas fueled appliances (such as gas cooktop/oven/range and dryer) if

they faced long-term electricity price increases.

Household energy expenditure elasticities were found to be significant and positive,

indicting that appliance energy consumption behaves as a normal good. However, the

magnitude was greater for natural gas heated households (1.115 versus 0.83.)

Income elasticities were found to be significant only for natural gas heated households.

The income elasticity for this group of households was positive and very inelastic at

0.009.

The final econometric model equations for appliance end-use energy consumption for

both natural gas and electric heated households at 20 percent significance level are

presented in Equations 10 to 13.

Natural gas heated household without lagged fuel price:

na

n

2E81.91E93.11E73.3

1E68.9)HHS3E75.5()GT2E75.8HHD1E12.1(

ii

XBASESTOREYTEMP

EYP98.40Q

=

(10)


FFAN1E39.31E18.1CDD5E33.7

A_1NFF3E59.12E40.32E26.1a

n

eLIGHTUSAGE_AC

S_1NFFDRYDWX n

=

(10a)


31/67



Natural gas heated household with lagged fuel price:

n

1,i

a

n

2E68.81E64.1

E12.1)HHS3E54.3()HHD2E05.2P2E76.5(

ii

XBASESTOREY

EYP92.7Q

=(11)


2E91.7CDD5E33.5A_1NFF3E32.2

A_2FF3E45.12E70.22E00.1a

n

LIGHTUSAGE_ACS_1NFF

S_2FFDRYDWX n

=

(11a)

Electric heated household without lagged fuel price:

na

n

2E86.61E29.11E12.4

1E30.8)HHS3E27.9()GT2E28.4HHD2E73.4(

ii

XBASESTOREYEFF

EYP23.8Q

=

(12)


A_2NFF3E68.1

A_1NFF3E53.22E13.22E53.1a

n

S_2NFF

S_1NFFDRYDWX n

=

(12a)

Electric heated household with lagged fuel price:

na

n

2E86.61E29.11E12.4

1E30.8)HHS3E27.9()GT2E28.4HHD2E73.4(

ii

XBASESTOREYEFF

EYP23.8Q

=

(13)


A_2NFF3E68.1

A_1NFF3E53.22E13.22E53.1a

n

S_2NFF

S_1NFFDRYDWX n

=

(13a)

4.3 SPACE HEATING ENERGY CONSUMPTION MODEL

The results for the space heating end-use energy consumption model are presented in

Tables 11 to 16. Major economic factors, such as substitute and lagged prices, income,


32/67



and household energy expenditure, proved to be statistically significant. However,

substitute fuel price for electric heated households was not significant. This could

partially be explained by the fact that oil is not truly an alternative fuel for electricity due

to its higher capital requirement, marginally lower price (in most provinces), and

inconvenience. Space heating energy consumption is positively related to household

energy expenditure, house area, and heating degree-days, and negatively related to lagged

price, income, and total household appliance consumption. Other housing variables

proved to be significant are number of storeys, total heated area, total basement area,

number of doors, windows, and skylights. As to be expected, variables such as number of

doors, windows, and skylights, are positively related to space heating energy

consumption since these house features provide less thermal resistance against heat loss

than solid wall assemblies. Also as expected, both average ground temperature and total

appliance energy consumption variables proved to be negatively related to space heating

energy consumption. This can be explained by the fact that higher ground temperature

reduces heat loss through basement while higher total appliance energy consumption

increases the amount of internal heat gain in the house, lowering its overall space heating

requirement. Space heating equipment efficiency variables in both cases are found to be

not significant statistically.

As expected, both estimated short- and long-term price elasticities are negative. The

short- and long-term elasticities, evaluated at sample mean, were found to be 0.246 and

0.904 for natural gas heated households, and 0.467 and 2.804 for electric heated

households, respectively. Natural gas heated households respond to fuel price changes

less than electric heated households in both the short- and the long-term. Since electric

heated households face higher fuel prices and have higher household energy expenditure,

they were expected to respond to price changes more than natural gas heated households

in the short-term. The very elastic nature of the long-term price elasticities in electric

heated households indicate that consumers tend to become extremely energy conscious if

they are faced with long-term price increases; or, they may supplement their space

heating energy requirements with a less expensive fuel such as wood.


33/67



Household energy expenditure elasticities are found to be significant and positive,

indicting that appliance energy consumption behaves like normal goods. However, the

magnitude is larger for natural gas heated households (1.791 versus 1.755).

Income elasticities are found only to be significant for natural gas heated households. The

income elasticity for this group of households is positive and very inelastic at 0.005.

Cross-price effects for both natural gas and electricity space heating energy consumption

are statistically significant and negative. The cross-price effect coefficient values are

estimated to be 0.793 and 0.606 for natural gas and electricity, respectively. For every

percent increase in electricity price, there would be a 0.793 percent decrease in natural

gas space heating energy consumption. Similarly, for every percent increase in oil price,

there would be a 0.606 percent decrease in electricity space heating energy consumption.

The final econometric model equations for space heating end-use energy consumption for

both natural gas and electric heated households at 20 percent significance level are



na

n

1E4.91E2.8

s

2E2.32E5.9

2E3.8E8.1)HHS3E6.1()GT2E1.5HHD2E5.3(

ii

XAPPPBASEAREA

STOREYEYP15.0Q

=

(14)


2E5.3a

n WINXn = (14a)


n

1,i

a

n

1E2.91E9.7

s

2E1.32E0.92E2.8

E8.1)HHS3E0.2()HHD2E1.1P2E7.5(

ii

XAPPPBASEAREASTOREY

EYP069.0Q

+ =(15)


34/67




2E7.4a

n WINXn = (15a)


na

n

1E7.71E1.7

s

2E4.42E0.6

1E1.1E7.1)GT1E5.1HHD1E3.1(

ii

XAPPPAREASTOREY

TEMPEP0011.0Q

=

(16)


2E0.31E3.1a

n WINSKYXn = (16a)


n

1,i

a

n

1E9.71E1.6

s

2E2.6

1E0.1E8.1)GT2E5.2P2E0.4(

ii

XAPPPSTOREY

TEMPEP019.0Q

=(17)


2E7.92E0.3a

n SKYDOORXn = (17a)

4.4 DHW HEATING ENERGY CONSUMPTION MODEL

The results for DHW heating end-use energy consumption models are presented in

Tables 17 to 22. Major economic factors, such as substitute and lagged prices, income,

and household energy expenditure proved to be statistically significant. Similar to the

space heating energy consumption model, the substitute fuel price for electric heated

households is insignificant. DHW heating energy consumption is positively related to

household energy expenditure and household income, and negatively related to lagged

price. Other DHW related variables that proved to be significant are DHW tank size,

ground temperature, and number of dishwasher loads. As expected, the ground

temperature is negatively related to DHW heating energy consumption.


35/67



Again, both estimated short and long-term price elasticities proved to be negative. The

short- and long-term elasticities, evaluated at sample mean, are 0.534 and -2.510 for

natural gas heated households, and 0.548 and 1.213 for electric heated households,

respectively. Natural gas heated households respond to fuel price changes less than

electric heated households in the long-term, whereas for the short-term, for every percent

increase in DHW fuel price, there would be a about half of a percent decrease in energy

consumption for both natural gas and electric heated households. The very large

magnitude of long-term fuel price elasticity for natural gas heated households may

indicate that consumers are very sensitive to fuel price on DHW heating energy

consumption.

Household energy expenditure elasticities are significant and positive, indicting that

appliance energy consumption behaves like a normal good. However, the magnitude is

larger for natural gas heated households (1.197 versus 0.860.)

Income elasticities only significant for electric heated households. The income elasticity

for this group of households is positive and very inelastic at 0.022.

The cross-price effect for natural gas DHW heating energy consumption is statistically

significant and negative. The cross-price effect coefficient value is 0.366 for natural gas

heated DHW, which means that for every percent increase in electricity price (substituted

price for natural gas), there would be a 0.366 percent decrease in natural gas DHW

heating energy consumption.

The final econometric model equations for DHW heating end-use energy consumption

for both natural gas and electric heated households at 20 percent significance level are




36/67



na

n

1E66.4

s

1E83.4E18.1)GT2E78.6HHD2E02.7(

ii

XP

TEMPEP08.1Q

=

(18)


1E01.6a

n TANKXn = (18a)


n1,i a

n

1E66.3

s

1E82.4E20.1)P2E91.7(

ii XPTEMPEP23.0Q = (19)

where variables Xnfor DHW heating energy consumption model are:1E65.5a

n TANKXn = (19a)


na

n

1E06.1

1E60.8)HHS3E70.9()GT2E84.4HHD2E24.5(

ii

XSTOREY

EYP12.0Q

=

(20)


2E51.1a

n DWXn = (20a)


na

n

1E06.1

1E60.8)HHS3E70.9()GT2E84.4HHD2E24.5(

ii

XSTOREY

EYP12.0Q

=

(21)


2E51.1a

n DWXn = (21a)


37/67



4.5 COMBINED SPACE AND DHW HEATING ENERGYCONSUMPTION MODEL

The results for combined space and DHW heating end-use energy consumption models

are presented in Tables 23 to 28. Major economic factors, such as substitute and lagged

prices, and household energy expenditure, proved to be statistically significant. However,

income effects in both cases are not significant. For natural gas heated households, the

combined space and DHW heating energy consumption is positively related to household

energy expenditure, total heated area, heating degree-days, number of windows, DHW

tank size, and number of clothes washer loads are negatively related to lagged price,

substitute price, total household appliance consumption, and extra DHW tank insulation.

On the other hand, the combined space and DHW heating energy consumption is

positively related to household energy expenditure, indoor temperature, and number ofstoreys, and negatively related to lagged price, substitute price, number of doors, number

of windows, number of clothes washer loads, and total household appliance energy

consumption.

As expected, both estimated short- and long-term price elasticities are negative. The short

and long-term elasticities, evaluated at sample mean, were found to be 0.303 and 1.036

for natural gas heated households, and 0.419 and 1 .694 for electric heated households,

respectively. Natural gas heated households respond to fuel price changes less than

electric heated households in both short- and long-term. Similar to the space heating

energy consumption case, electric heated households face higher fuel prices and have

higher household energy expenditures; therefore, they are expected to respond to price

changes more than natural gas heated households in the short-term. The very elastic

nature of the long-term price elasticities in the electric heated households indicate that

consumers would tend to become extremely energy conscious if they are faced with long-

term price increases.

Household energy expenditure elasticities are significant and positive, indicting that

appliance energy consumption behaves like normal goods. The magnitude for natural gas

heated households is larger than that for electric heated households (1.733 versus 1.292).


38/67



Income elasticities are statistically insignificant for both natural gas and electric heated

households.

Cross-price effects for both natural gas and electricity combined space and DHW heating

energy consumption are statistically significant and negative. The cross-price effect

coefficients are 0.701 and 0.257 for natural gas and electricity, respectively. This

indicates that for every percent increase in electricity price, there would be a 0.701

percent decrease in natural gas consumption. Similarly, for every percent increase in oil

price, there would be a 0.257 percent decrease in electricity consumption.

The adjusted R2 values for combined space and DHW energy consumption are quite

highat 0.987 and 0.949 for natural gas and electricity, respectively.

The final econometric model equations for combined space heating end-use energy

consumption for both natural gas and electric heated households at 20 percent

significance level are presented in Equations 22 to 25.


na

n

1E41.81E42.7

s

2E93.2

2E87.31E03.1

E73.1)HHS3E13.1()GT2E44.7HHD2E02.6(

ii

XAPPPAREA

STOREYTEMP

EYP25.0Q

=

(22)

where variables Xnfor space and DHW heating energy consumption model are:

2E38.51E07.1a

n TANKSKYXn = (22a)


n

1,i

a

n

1E30.81E01.7

s

2E06.32E23.3

1E04.1E73.1)HHD2E04.1P2E48.5(

ii

XAPPPAREASTOREY

TEMPEP1.0Q

+ =(23)


39/67




INSUL2E03.33E01.7

2E13.62E61.11E08.1a

n

eWA

TANKWINSKYX n

=

(23a)


na

n

E96.21E85.4

s

2E26.32E20.4

2E59.7E29.1)HHS4E82.8()GT2E84.9HHD2E33.8(

ii

XAPPPAREASTOREY

TEMPEYP6.0Q

=

(24)


2E65.12E88.1a

n DWAERATORXn = (24a)


n

1,i

a

n

1E98.21E57.2

s

2E33.3

2E64.4E29.1)GT2E08.2HHD3E11.9P2E05.3(

ii

XAPPPSTOREY

TEMPEP078.0Q

=(25)


3E68.32E50.12E40.1a

n WAWINDOORXn = (25a)


40/67

ECONOMETRIC MODEL FOR RESIDENTIAL ENE RG Y EN D-USES


Table 5: Data Statistics for Appliance Energy Consumption Model for Natural Gas Heated Households

Variables Name Count Max Min Average Median StDev 25 Percentile 75 Percentile

App E Con (kWh) Q 271 39688.0 3901.0 10207.4 8956.0 5145.3 6716.0 11645.5

Energy Exp. ($) EXP 271 2864.6 699.3 1282.4 1199.8 398.3 1008.2 1461.0

Income ($) IN 230 100000.0 6000.0 47467.4 45000.0 25198.9 27500.0 70000.0

HHSize HHS 271 8.0 1.0 3.1 3.0 1.3 2.0 4.0

Old price ($/GJ) P-1 271 32.5 12.8 16.2 15.6 5.0 13.1 16.4Price ($/GJ) P 271 32.5 13.1 16.7 16.1 5.0 13.1 17.3

HDD (C-day) HDD 271 6562.0 3007.0 5513.4 5889.0 734.1 5345.0 5920.0

GdTemp (C) GT 271 12.3 4.8 6.4 6.1 1.8 4.8 6.6

SHEff (%) EFF 271 77.5 57.5 63.3 64.0 6.6 57.5 64.0

Temp (C) TEMP 271 23.3 15.0 19.8 20.0 1.5 19.0 21.0

No. of Storey STOREY 271 3.0 1.0 1.3 1.0 0.4 1.0 1.5

Hted Area (m^2) AREA 271 278.7 46.5 124.0 116.1 45.4 116.1 118.4

BsmtSize (m^2) BASE 271 223.0 1.3 96.3 97.5 32.5 77.4 111.5

DW-Total DW 271 780.0 0.0 174.6 156.0 189.0 0.0 312.0

Wash-Total WA 271 780.0 0.0 308.9 260.0 192.3 156.0 455.0

Dryer-Total DRY 271 780.0 0.0 268.1 208.0 190.5 130.0 364.0

Age-free FREEZER-A 271 28.0 0.0 12.4 13.0 9.1 4.0 18.0

Size-free (ft^3) FREEZER-S 271 25.0 0.0 13.4 16.0 6.9 11.0 16.0

FF-1-Age FF1-A 271 23.0 0.0 8.2 9.0 6.4 2.0 13.0

FF-1-Size (ft^3) FF1-S 271 22.0 0.0 14.8 15.0 6.0 15.0 19.0

NFF-1-Age NFF1-A 271 23.0 0.0 1.9 0.0 5.7 0.0 0.0NFF-1-Size (ft^3) NFF1-S 271 19.0 0.0 1.6 0.0 4.8 0.0 0.0

FF-2-Age FF2-A 271 23.0 0.0 2.0 0.0 5.6 0.0 0.0

FF-2-Size (ft^3) FF2-S 271 22.0 0.0 1.9 0.0 5.2 0.0 0.0

NFF-2-Age NFF2-A 271 23.0 0.0 3.9 0.0 7.8 0.0 0.0

NFF-2-Size (ft^3) NFF2-S 271 19.0 0.0 2.7 0.0 5.4 0.0 0.0

Range Age RANGE-A 271 23.0 0.0 10.4 9.0 6.7 5.0 13.0

Cooktop (0/1) COOKTOP 271 1.0 0.0 0.0 0.0 0.2 0.0 0.0

CDD (C) CDD 271 238.0 19.0 140.8 155.0 57.2 94.0 189.0

AC usage (%) AC-USAGE 271 100.0 0.0 17.4 0.0 25.8 0.0 25.0

Light LIGHT 271 132.0 10.0 40.1 37.0 19.0 27.5 49.0

Ffan (0/1) FFAN 271 1.0 0.0 1.0 1.0 0.1 1.0 1.0


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Table 6: Data Statistics for Appliance Energy Consumption Model for Electric Heated Households

Variable Name Count Max Min Average Median StDev 25 Percentile 75 Percentile

App E Con (kWh) Q 320 19423.7 1599.7 6783.6 6403.3 2699.0 4809.1 8291.5

Energy Exp. ($) EXP 320 3246.8 490.6 1535.9 1487.2 447.4 1244.0 1806.1

Income ($) IN 263 100000.0 6000.0 40667.3 37500.0 24397.7 22500.0 55000.0

HHSize HHS 320 9.0 1.0 3.0 3.0 1.3 2.0 4.0

Old price ($/GJ) P-1 320 32.5 12.8 15.1 15.6 1.8 15.6 15.6

Price ($/GJ) P 320 32.5 13.1 15.5 16.1 1.9 16.1 16.1

HDD (C-day) HDD 320 7930.0 3007.0 5077.2 4771.0 904.4 4709.0 4884.0

GdTemp (C) GT 320 11.3 2.7 7.3 7.7 1.4 7.6 7.7

SHEff (%) EFF 305 250.0 100.0 101.1 100.0 10.3 100.0 100.0

Temp (C) TEMP 320 25.0 15.0 19.1 19.7 2.1 17.7 20.7

No. of Storey STOREY 320 3.0 1.0 1.3 1.0 0.4 1.0 1.5

Hted Area (m^2) AREA 320 278.7 46.5 116.4 116.1 46.2 74.3 118.4

BsmtSize (m^2) BASE 320 278.7 13.4 94.9 98.0 33.5 74.3 116.1

DW-Total DW 320 780.0 0.0 102.1 0.0 148.7 0.0 208.0

Wash-Total WA 320 780.0 0.0 340.4 312.0 218.2 156.0 546.0

Dryer-Total DRY 320 780.0 0.0 248.4 195.0 183.5 104.0 364.0

Age-free FREEZER-A 320 28.0 0.0 9.4 9.0 7.9 1.0 13.0

Size-free (ft^3) FREEZER-S 320 25.0 0.0 12.6 16.0 7.7 11.0 16.0

FF-1-Age FF1-A 320 23.0 0.0 7.5 6.5 6.0 2.0 10.8

FF-1-Size (ft^3) FF1-S 320 22.0 0.0 14.4 15.0 6.2 15.0 19.0

NFF-1-Age NFF1-A 320 23.0 0.0 1.6 0.0 4.6 0.0 0.0

NFF-1-Size (ft^3) NFF1-S 320 19.0 0.0 1.9 0.0 5.1 0.0 0.0

FF-2-Age FF2-A 320 23.0 0.0 0.8 0.0 3.6 0.0 0.0

FF-2-Size (ft^3) FF2-S 320 19.0 0.0 0.7 0.0 3.2 0.0 0.0

NFF-2-Age NFF2-A 320 23.0 0.0 1.8 0.0 5.5 0.0 0.0

NFF-2-Size (ft^3) NFF2-S 320 15.0 0.0 1.3 0.0 3.9 0.0 0.0

Range Age RANGE-A 320 23.0 0.0 9.0 9.0 7.0 3.8 13.0

Cooktop (0/1) COOKTOP 320 1.0 0.0 0.1 0.0 0.3 0.0 0.0

CDD (C) CDD 320 189.0 19.0 108.6 125.0 39.1 97.0 138.0

AC usage (%) AC-USAGE 320 100.0 0.0 1.0 0.0 7.8 0.0 0.0

Light LIGHT 320 109.0 5.0 32.7 30.0 16.5 20.0 43.0

Ffan (0/1) FFAN 320 1.0 0.0 0.9 1.0 0.3 1.0 1.0


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Table 7: Appliance Energy Consumption Model Summary for Fossil Fueled Households

Model Coefficients and t Values

Without Lagged Fuel Price With Lagged Fuel Price

Variable Name Variable Variable Description As "ENTER Upto 20% As "ENTER" Upto 20%

Unit Coeff t Coeff t Coeff t Coeff t

LN_CON (kWh) Ln (Appliance Con.)

LN_EXP ($) Ln (Household energy exp) 9.77E-01 13.81 9.68E-01 14.62 1.13E+00 16.24 1.12E+00 17.39

LN_EFF (-) Ln (Heating equipment efficiency) -1.13E-01 -0.63 -2.00E-02 -0.12LN_TEMP (C) Ln (Indoor temp.) 2.64E-01 1.25 3.73E-01 1.84 4.72E-02 0.24

LN_STORE (-) Ln (No. of storey) -1.79E-01 -2.66 -1.93E-01 -3.15 -1.47E-01 -2.35 -1.64E-01 -2.94

LN_AREA (m^3) Ln (Heated area) -2.58E-02 -0.38 -4.86E-02 -0.78

LN_BASE (m^3) Ln (Basement area) -9.69E-02 -2.37 -9.81E-02 -2.60 -7.43E-02 -1.96 -8.68E-02 -2.52

LN_DW_L (-) Ln (No. of dish washer load) -1.10E-02 -1.48 -1.26E-02 -1.75 -8.39E-03 -1.23 -1.00E-02 -1.55

LN_WA_L (-) Ln (No. of clothes washer load) -1.62E-02 -0.67 -5.88E-03 -0.26

LN_DRY_L (-) Ln (No. of clothes dryer load) 4.23E-02 2.11 3.40E-02 2.16 2.88E-02 1.55 2.70E-02 1.87

LN_LIGHT ($) Ln (No of light blubs) 1.12E-01 2.52 1.18E-01 2.80 8.12E-02 1.97 7.91E-02 2.06

HDD_LN_P ($/GJ) HDD*Ln (Price) -1.08E-01 -12.13 -1.12E-01 -12.81 -1.79E-02 -1.07 -2.05E-02 -3.49

GT_LN_P ($/GJ) Ground Temp*LN (Price) -8.30E-02 -9.49 -8.75E-02 10.37 4.05E-03 0.25

HHS_LN_I ($) Household size*Ln (Income) 5.65E-03 3.07 5.75E-03 3.31 3.72E-03 2.17 3.54E-03 2.22

A_N_S_FR (ft^3) Freezer Age*Ln (Size) -4.47E-05 -0.06 -4.45E-04 -0.69

ALN_S_F1 (ft^3) First Frostfree Fridge Age* Ln(Size) -1.47E-03 -1.28 -9.35E-04 -0.88

ALN_SN1 (ft^3) First non-Frostfree Fridge Age* Ln(Size) -2.70E-03 -1.97 -1.59E-03 -1.44 -3.19E-03 -2.52 -2.32E-03 -2.31

ALN_S_F2 (ft^3) Second Frostfree Fridge Age* Ln(Size) 1.94E-03 1.67 1.92E-03 1.79 1.45E-03 1.46

ALN_SN2 (ft^3) Second non-Frostfree Fridge Age* Ln(Size) 8.51E-04 0.93 8.15E-04 0.96

CDD_LN_U (%) CDD*Ln (A/C Usage) 6.59E-05 3.19 7.33E-05 3.70 4.99E-05 2.60 5.33E-05 2.90CT_I (-) Cooktop Indicator (0 or 1) 9.95E-02 1.07 1.18E-01 1.38

FAN_I (-) Furance Fan Indicator (0 or 1) 3.51E-01 1.39 3.39E-01 1.36 1.25E-01 0.53

LN_RAN_A (-) Ln (Range/oven age) 3.32E-02 1.40 3.10E-02 1.42

OP_LN_P ($/GJ) Lag. Price * Ln (Price) -5.75E-02 -6.21 -5.76E-02 -13.39

CONSTANT 4.452 3.797 3.713 4.525 1.828 1.577 2.070 4.537

R-SQUARE 0.706 0.696 0.753 0.746

ADJ. R-SQUARE 0.675 0.678 0.725 0.732


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Table 8: Appliance Energy Consumption Model Summary for Electric Heated Households

Model Coefficients and t Values

Without Lagged Fuel Price With Lagged Fuel Price

Variable Name Variable Variable Description As "ENTER Upto 20% As "ENTER" Upto 20%

Unit Coeff t Coeff t Coeff t Coeff t

LN_CON (kWh) Ln (Appliance Con.)LN_EXP ($) Ln (Household energy exp) 7.97E-01 12.65 8.30E-01 14.54 7.96E-01 12.61 8.30E-01 14.54

LN_EFF (-) Ln (Heating equipment efficiency) 3.65E-01 1.08 4.12E-01 1.77 3.62E-01 1.07 4.12E-01 1.77

LN_TEMP (C) Ln (Indoor temp.) 1.63E-01 1.16 1.62E-01 1.15

LN_STORE (-) Ln (No. of storey) -1.34E-01 -2.00 -1.29E-01 -2.19 -1.34E-01 -2.00 -1.29E-01 -2.19

LN_AREA (m^3) Ln (Heated area) 4.01E-02 0.71 4.16E-02 0.73

LN_BASE (m^3) Ln (Basement area) -8.99E-02 -1.74 -6.86E-02 -1.63 -8.82E-02 -1.70 -6.86E-02 -1.63

LN_DW_L (-) Ln (No. of dish washer load) 1.27E-02 1.70 1.53E-02 2.34 1.23E-02 1.64 1.53E-02 2.34

LN_WA_L (-) Ln (No. of clothes washer load) 8.49E-03 0.51 7.80E-03 0.46

LN_DRY_L (-) Ln (No. of clothes dryer load) 1.94E-02 1.37 2.13E-02 1.80 1.93E-02 1.36 2.13E-02 1.80

LN_LIGHT ($) Ln (No of light blubs) 5.28E-03 0.14 5.59E-03 0.14

HDD_LN_P ($/GJ) HDD*Ln (Price) -4.04E-02 -2.18 -4.73E-02 -2.72 -3.26E-02 -1.18 -4.73E-02 -2.72

GT_LN_P ($/GJ) Ground Temp*LN (Price) -3.69E-02 -2.46 -4.28E-02 -3.03 -2.95E-02 -1.20 -4.28E-02 -3.03

HHS_LN_I ($) Household size*Ln (Income) 9.23E-03 5.22 9.27E-03 5.78 9.28E-03 5.23 9.27E-03 5.78

A_N_S_FR (ft^3) Freezer Age*Ln (Size) -1.76E-04 -0.24 -1.78E-04 -0.24

ALN_S_F1 (ft^3) First Frostfree Fridge Age* Ln(Size) 6.00E-04 0.53 5.79E-04 0.51

ALN_SN1 (ft^3) First non-Frostfree Fridge Age* Ln(Size) -2.28E-03 -1.47 -2.53E-03 -1.90 -2.27E-03 -1.47 -2.53E-03 -1.90

ALN_S_F2 (ft^3) Second Frostfree Fridge Age* Ln(Size) 1.59E-04 0.10 2.09E-04 0.13ALN_SN2 (ft^3) Second non-Frostfree Fridge Age* Ln(Size) 1.59E-03 1.22 1.68E-03 1.47 1.60E-03 1.22 1.68E-03 1.47

CDD_LN_U (%) CDD*Ln (A/C Usage) 3.42E-05 0.23 3.48E-05 0.23

CT_I (-) Cooktop Indicator (0 or 1) 9.81E-02 1.48 9.71E-02 1.46

FAN_I (-) Furance Fan Indicator (0 or 1) 3.79E-03 0.08 3.14E-03 0.07

LN_RAN_A (-) Ln (Range/oven age) 1.55E-02 0.73 1.53E-02 0.72

OP_LN_P ($/GJ) Lag. Price * Ln (Price) -2.41E-03 -0.38

CONSTANT 1.710 1.037 2.108 1.794 1.551 0.910 2.108 1.794

R-SQUARE 0.671 0.665 0.672 0.665

ADJ. R-SQUARE 0.641 0.650 0.640 0.650


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Table 9: Appliance Energy Consumption Model Elasticities Estimates for Natural Gas Fueled Households

Model I (w/o lagged) Model II (w/ lagged)

As Entered 20% As Entered 20%

Variable Coeff

Lagged Price -5.747E-02 -5.756E-02

HDD -1.080E-01 -1.120E-01 -1.794E-02 -2.050E-02GT -8.303E-02 -8.749E-02 4.048E-03 0.000E+00

HHS 5.645E-03 5.746E-03 3.720E-03 3.539E-03

Variable mean

Lagged Price (mean) 3.255 3.255

Lagged Price (mean+StDev) 4.255 4.255

Lagged Price (mean-StDev) 2.255 2.255

HDD 7.511 7.511 7.511 7.511

GT 3.527 3.527 3.527 3.527

HHS 2.433 2.433 2.433 2.433

EXP 1282.418 1282.418 1282.418 1282.418

CON 10207.354 10207.354 10207.354 10207.354

Own Price Elasticity at Mean

Short-run Price Elasticity -1.104 -1.150 -0.308 -0.341


Own Price Elasticity at Mean+StDev



Own Price Elasticity at Mean-StDev



Income Elasticity 0.009 0.009

Expenditure Elasticity 0.977 0.968 1.130 1.115


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Table 10: Appliance Energy Consumption Model Elasticities Estimates for Electric Heated Households

Model I (w/o lagged) Model II (w/ lagged)

As Entered 20% As Entered 20%

Variable Coeff

Lagged Price*P -2.413E-03 0.000E+00

HDD*P -4.041E-02 -4.729E-02 -3.261E-02 -4.729E-02GT*P -3.692E-02 -4.278E-02 -2.950E-02 -4.278E-02

HHS*IN 9.228E-03 9.274E-03 9.282E-03 9.274E-03

Variable mean

Lagged Price (mean) 8.490 8.490

Lagged Price (mean+StDev) 9.490 9.490

Lagged Price (mean-StDev) 7.490 7.490

HDD 5.614 5.614 5.614 5.614

GT 5.253 5.253 5.253 5.253

HHS 2.253 2.253 2.253 2.253

EXP 1535.903 1535.903 1535.903 1535.903

CON 6783.606 6783.606 6783.606 6783.606

Own Price Elasticity at Mean



Own Price Elasticity at Mean+StDev



Own Price Elasticity at Mean-StDev



Income Elasticity 0.021

Expenditure Elasticity 0.797 0.830 0.796 0.830


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Table 11: Data Statistics for Natural Gas Space Heating Energy Consumption Model in Natural Gas Heated Households


SpHt+DHW E Con Q 226.0 181.4 20.6 92.8 87.4 27.8 73.6 108.0

Income IN 190.0 100000.0 6000.0 45144.7 45000.0 24379.3 27500.0 55000.0

HHSize HHS 226.0 7.0 1.0 3.2 3.0 1.2 2.0 4.0

Old Price ($/GJ) P-1 226.0 5.5 3.4 4.7 4.3 0.7 4.3 5.4Price ($/GJ) P 226.0 5.6 3.9 4.9 4.4 0.6 4.4 5.6

Price-s ($/GJ) Ps 226.0 20.8 13.1 15.7 17.3 2.3 13.1 17.3

Energy Exp. ($) EXP 226.0 2499.0 699.3 1190.3 1160.3 288.8 984.0 1336.5

HDD (C) HDD 226.0 6562.0 3962.0 5740.8 5889.0 476.8 5889.0 5920.0

GdTemp (C) GT 226.0 11.1 4.8 5.9 6.1 1.2 4.8 6.1

SHEff (%) EFF 226.0 77.5 57.5 62.5 64.0 6.3 57.5 64.0

Temp (C) TEMP 226.0 23.3 15.0 19.9 20.0 1.5 19.0 21.0

No.Storey STOREY 226.0 2.5 1.0 1.2 1.0 0.4 1.0 1.5

Hted Area (m^2) AREA 226.0 278.7 46.5 117.5 116.1 40.1 74.3 116.1

BsmtSize (m^2) BASE 226.0 223.0 1.3 93.9 93.6 31.3 74.3 111.5

Total Door DOOR 226.0 7.0 1.0 2.6 2.0 0.9 2.0 3.0

Total Sky SKY 8.0 4.0 1.0 1.6 1.0 1.1 1.0 2.0

Total Win WIN 224.0 38.0 3.0 11.2 10.0 5.3 7.8 14.0

App E Con. APP 226.0 98.5 14.0 35.1 32.3 14.4 25.1 39.8


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Table 12: Data Statistics for Electric Space Heating Energy Consumption Model in Electric Heated Households


SpHt+DHW E Con Q 320.0 148.1 8.7 56.0 53.2 21.0 41.8 67.0

Income IN 263.0 100000.0 6000.0 40667.3 37500.0 24397.7 22500.0 55000.0

HHSize HHS 320.0 9.0 1.0 3.0 3.0 1.3 2.0 4.0

Old Price ($/GJ) P-1 320.0 32.5 12.8 15.1 15.6 1.8 15.6 15.6Price ($/GJ) P 320.0 32.5 13.1 15.5 16.1 1.9 16.1 16.1

Price-s ($/GJ) Ps 320.0 11.0 7.3 10.1 10.0 0.7 10.0 10.0

Energy Exp. ($) EXP 320.0 3246.8 490.6 1535.9 1487.2 447.4 1244.0 1806.1

HDD (C) HDD 320.0 7930.0 3007.0 5077.2 4771.0 904.4 4709.0 4884.0

GdTemp (C) GT 320.0 11.3 2.7 7.3 7.7 1.4 7.6 7.7

SHEff (%) EFF 305.0 250.0 100.0 101.1 100.0 10.3 100.0 100.0

Temp (C) TEMP 320.0 25.0 15.0 19.1 19.7 2.1 17.7 20.7

No.Storey STOREY 320.0 3.0 1.0 1.3 1.0 0.4 1.0 1.5

Hted Area (m^2) AREA 320.0 278.7 46.5 116.4 116.1 46.2 74.3 118.4

BsmtSize (m^2) BASE 320.0 278.7 13.4 94.9 98.0 33.5 74.3 116.1

Total Door DOOR 310.0 11.0 1.0 2.7 2.0 1.1 2.0 3.0

Total Sky SKY 7.0 4.0 1.0 2.1 2.0 0.9 2.0 2.0

Total Win WIN 311.0 40.0 2.0 10.7 10.0 4.3 8.0 13.0

App E Con. APP 320.0 69.9 5.8 24.4 23.1 9.7 17.3 29.8

Econometric Models for Major Residential Energy End-Uses

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