Econometric Models for Major Residential Energy End-Uses
Transcript of 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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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
Expenditure Elasticity 1.791 1.755
Cross Price Effect -0.793 -0.606
DHW Heating Energy Consumption
Short-run Price Elasticity -0.534 -0.548
Long-run Price Elasticity -2.510 -1.213 Income Elasticity N/A 0.022
Expenditure Elasticity 1.197 0.860
Cross Price Effect -0.366 N/A
Space + DHW Heating Energy Consumption
Short-run Price Elasticity -0.303 -0.419
Long-run Price Elasticity -1.036 -1.694
Income Elasticity N/A N/A
Expenditure Elasticity 1.733 1.292
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.
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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.
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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
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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
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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
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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
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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:
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- 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
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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)
where variables Xnfor appliance energy consumption model are:
FFAN1E39.31E18.1CDD5E33.7
A_1NFF3E59.12E40.32E26.1a
n
eLIGHTUSAGE_AC
S_1NFFDRYDWX n
=
(10a)
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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)
where variables Xnfor appliance energy consumption model are:
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)
where variables Xnfor appliance energy consumption model are:
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)
where variables Xnfor appliance energy consumption model are:
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,
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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.
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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
presented in Equations 14 to 17.
Natural gas heated household without lagged fuel price:
na
n
1E4.91E2.8
s
2E2.32E5.9
2E3.8E8.1)HHS3E6.1()GT2E1.5HHD2E5.3(
ii
XAPPPBASEAREA
STOREYEYP15.0Q
=
(14)
where variables Xnfor space heating energy consumption model are:
2E5.3a
n WINXn = (14a)
Natural gas heated household with lagged fuel price:
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)
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where variables Xnfor space heating energy consumption model are:
2E7.4a
n WINXn = (15a)
Electric heated household without lagged fuel price:
na
n
1E7.71E1.7
s
2E4.42E0.6
1E1.1E7.1)GT1E5.1HHD1E3.1(
ii
XAPPPAREASTOREY
TEMPEP0011.0Q
=
(16)
where variables Xnfor space heating energy consumption model are:
2E0.31E3.1a
n WINSKYXn = (16a)
Electric heated household with lagged fuel price:
n
1,i
a
n
1E9.71E1.6
s
2E2.6
1E0.1E8.1)GT2E5.2P2E0.4(
ii
XAPPPSTOREY
TEMPEP019.0Q
=(17)
where variables Xnfor space heating energy consumption model are:
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.
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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
presented in Equations 18 to 21.
Natural gas heated household without lagged fuel price:
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na
n
1E66.4
s
1E83.4E18.1)GT2E78.6HHD2E02.7(
ii
XP
TEMPEP08.1Q
=
(18)
where variables Xnfor DHW heating energy consumption model are:
1E01.6a
n TANKXn = (18a)
Natural gas heated household with lagged fuel price:
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)
Electric heated household without lagged fuel price:
na
n
1E06.1
1E60.8)HHS3E70.9()GT2E84.4HHD2E24.5(
ii
XSTOREY
EYP12.0Q
=
(20)
where variables Xnfor DHW heating energy consumption model are:
2E51.1a
n DWXn = (20a)
Electric heated household with lagged fuel price:
na
n
1E06.1
1E60.8)HHS3E70.9()GT2E84.4HHD2E24.5(
ii
XSTOREY
EYP12.0Q
=
(21)
where variables Xnfor DHW heating energy consumption model are:
2E51.1a
n DWXn = (21a)
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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).
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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.
Natural gas heated household without lagged fuel price:
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)
Natural gas heated household with lagged fuel price:
n
1,i
a
n
1E30.81E01.7
s
2E06.32E23.3
1E04.1E73.1)HHD2E04.1P2E48.5(
ii
XAPPPAREASTOREY
TEMPEP1.0Q
+ =(23)
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where variables Xnfor space and DHW heating energy consumption model are:
INSUL2E03.33E01.7
2E13.62E61.11E08.1a
n
eWA
TANKWINSKYX n
=
(23a)
Electric heated household without lagged fuel price:
na
n
E96.21E85.4
s
2E26.32E20.4
2E59.7E29.1)HHS4E82.8()GT2E84.9HHD2E33.8(
ii
XAPPPAREASTOREY
TEMPEYP6.0Q
=
(24)
where variables Xnfor space and DHW heating energy consumption model are:
2E65.12E88.1a
n DWAERATORXn = (24a)
Electric heated household with lagged fuel price:
n
1,i
a
n
1E98.21E57.2
s
2E33.3
2E64.4E29.1)GT2E08.2HHD3E11.9P2E05.3(
ii
XAPPPSTOREY
TEMPEP078.0Q
=(25)
where variables Xnfor space and DHW heating energy consumption model are:
3E68.32E50.12E40.1a
n WAWINDOORXn = (25a)
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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
Long-run Price Elasticity -1.594 -1.746
Own Price Elasticity at Mean+StDev
Short-run Price Elasticity -1.104 -1.150 -0.365 -0.399
Long-run Price Elasticity -1.739 -1.913
Own Price Elasticity at Mean-StDev
Short-run Price Elasticity -1.104 -1.150 -0.250 -0.284
Long-run Price Elasticity -1.472 -1.605
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
Short-run Price Elasticity -0.421 -0.490 -0.430 -0.594
Long-run Price Elasticity -0.739 -1.208
Own Price Elasticity at Mean+StDev
Short-run Price Elasticity -0.421 -0.490 -0.433 -0.594
Long-run Price Elasticity -0.742 -1.208
Own Price Elasticity at Mean-StDev
Short-run Price Elasticity -0.421 -0.490 -0.250 -0.594
Long-run Price Elasticity -0.561 -1.208
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
Variables Name Count Max Min Average Median StDev 25 Percentile 75 Percentile
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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ECONOMETRIC MODEL FOR RESIDENTIAL ENE RG Y EN D-USES
PAGE 47 CREEDAC APRIL 1999
Table 12: Data Statistics for Electric Space Heating Energy Consumption Model in Electric Heated Households
Variables Name Count Max Min Average Median StDev 25 Percentile 75 Percentile
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
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