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vatu ti f a oil r/furace Multiv riate e ressi plac met ilot alysis ersus ram: Iree Iso, Washigto Gas Robert P~ Trost, George Washigto Uiversity Washigto Gas' Boiler/Furace Pilot Program for the

1 vatu ti f a oil r/furace Multiv riate e ressi plac met ilot alysis ersus ram: Iree Iso, Washigto Gas Robert P~ Trost, George Washigto Uiversity Washigto Gas' Boiler/Furace Pilot Program for the District of Columbia is a residetial gas coservatio program. Eergy' savigs from the program are evaluated here usig two regressio methodologies. Oe procedure used is the Priceto Scorekeepig Method (PRISM). Aother method is a geeral multivariate regressio model where some restrictive assumptios are placed o the model parameters; Ordiary Least Squares (OLS) is the used to estimate the eergy savigs. The restricted multivariate model ca be easily estimated with most statistical software packages. However, for some applicatios the implied parameter restrictios may ot be justified. Eergy savigs estimated with PRISM the multivariate model are compared. The PRISM aalysis idicates that high-efficiecy furaces are fairly impressive eergy savers. efficiecy furaces show savigs of 15.7%; high-efficiecy boilers show savigs of 7.4%. Less efficiet heatig equipmet does ot fare as well. Mid-efficiecy furaces saved 1.0%; boilers saved 6.3 %. Oly the estimates for the high-efficiecy furace participats are statistically differet from zero at the 10% level of sigificace. The multivariate aalysis results those of PRISM. High-efficiecy furaces show eergy of 15.2%; high-efficiecy boilers saved 8.9%. Mid-efficiecy heatig shows o eergy savigs; eergy usage icreased after istallatio. Mid-efficiecy furaces used 8.8% more eergy. mid-efficiecy boilers used 1.9% more eergy. the estimates for the high-efficiecy furaces high-efficiecy boilers are statistically differet from zero at the 10% level of l.;jajlw,;ii...iu..ii.j1.v"'-iilav""'. Itroductio W3lsm21to Gas is uder District of Columbia Public Service Commissio PSC) Order No to cost effective Dem Side Maagemet (DSM) programs i order to test the optios available to reach pre-specified coservatio goals. Order No established a collaborative withi a Least Cost to facilitate Washigto Gas' developmet, Im'ple:me~UiUC) test~g of programs. The cosists of DC PSC staff, Office of staff D.C. Office staff. This Group meets 'lr&l>'hi~,1t"~"it to discuss activities. provide iput to the developmet of such activities as program evaluatio. The efforts to date reflect this The work cotaied i this paper has resulted from the Im'pleme;t2Ltlo ' D of a collaborative process, cotiues to be discussed wi be a part of Washigto Gas' 1992 l.east Cost Pla based o further iput from the Workig Washigto Gas' Boiler/Furace Pilot for the District of Columbia is a residetial gas coservatio program. savigs from the program are evaluated here usig two regressio methodologies. Qe pr()ce,qulre used is the Priceto Scorekeepig Method Aother method is a geeral multivariate re12~re~;slc~ where some restrictive assumptios are o the model parameters; Ordiary Least Squares (DLS) is the used to estimate the eergy savigse The restricted multivariate model ca be easily estimated with most statistical software packages. However, for some applicatios the implied parameter' restrictios may ot be ju~tified. Eergy savigs estimated with PRISM the multivariate model are compared. The Boiler/Furace Replacemet Pilot Program The Boiler/Furace Pilot 1II.Jl'1t"f"\C'f1"Q1"It'e $540 cash icetive for the istallatio of a 1k... """h "",i1-h,... o.'>l"'jii"b'llt Multivariate".."... 4" 169

2 + furace or a boiler. Uder certai a icetive will be for a furace rated 80%-89% AFUE" Low-icome customers are for assistace with iterest icurred i the of the ew boiler or furace. ollectio of alysis for the oiler/furace rogra Co:SLlmi)t!C) data for District of Columbia Boiler/Furace R acemet Pilot was collected from Gas records. This icluded all who had ech.l1pjmellt istalled o or before December 1, 1990" A was defmed for each as the twelve to the moth of the was defied as the twelve moths after the istallatio moth. The actual moth of istallatio was deleted. from the data. Savigs=(yp(pre)-yp(post») -(yp(pre)-yp(post» The used eergy echlatllo of the form to the Oll- p;art).cl1j~at:s"... '... "'7.. ''''''... are defied as Weather-ormalized for DSM programs ca be estimated the Priceto Scorekeepig Method re~~re~;slc~ method by the Priceto Ceter for Evirometal Studies. This tecjtmlj(1ue is described i Fels 1986 i Goldberg Pels PRISM has bee used by 1986 to estimate seaso of houses heated atural gas; Stram Pels 1986 estimated eergy of houses heated cooled PRISM to weather-ormalize with the estimatio of a either DalrtlclDBltlOifi or were (1) i the Boiler/Furace program were divided ito low o-low icome A aesllgrlatex:t as low icome if certified Office to be for Assistace All vjju:.':.luja\.# for assistace were as A sig avigs of to Estimate Eergy eatig usto ers is ofte used. whe est~itlrhz eergy achieved DSM rot'~~~'lil,",1~~'11 programs. This of'll ~"'it'il~?"'1ll::!1 ca take oe of three forms. compare DSM program eergy before program to their after the program. I this case, eergy are defied. as where ) ::: m = a moth idex. i = a pre idex. j = a customer idex. k = a idex. A defiitio of variables Table 1. The + o the term that the value of this term be set to zero PaJrethe;ses is e~~ave. + i idicates the value i PRISM differs from other weather-ormalizatio procedures i that is treated as a variable rather tha a COIllStaJt1t such as 65 P The Pij ca be estimated from the M observed eergy customer j i i, stard for ay assumed value of psj"tlcjipwrlts' eergy Co.llsumJ:~tloli the cotrol group of the same 4., 170 w Trost

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3 l~f~i.:-:-.:-:....r....:. :::::::.. Oce the have bee estudjate4cl~ the ormalized aual eergy for customer j i ca be estimated from 365 is the total umber of year relative to the referece year the average weather for a. Give values for attributed to a DSM program ca of the three discussed abovee The ature of the Boiler/Furace program makes the selectio of a cotrol group A ideal cotrol group would cosist of gas customers who ecu.upjmejt1t i the absece of a rebate programe Gas does ot V~A.Jl.""1UUdl. have a database of such customerse l'.h(~re:rore~ it wi ot be to a true measure of free dershro herea ultivariate as sage egressio A researcher may be iterested i gettig estimates of eergy savigs for a DSM programe However, i the begiig moths of a program there may ot be eough mothly observatios i the post period to use PRISMe I this case, a simple multivariate regressio (MVR) model could provide a useful prelimiary estimate a The disadvatage is that some restrictive assumptios o the parameters of the model are ecessary, but these restrictios may ot be justified for all programs a For this reaso it is to carefully state what restrictive assumptios are beig made. Oe possible set of simplifyig restrictive assumptios for a Boiler/Furace program are "ore;seillted below~ Multivariate"",. - 4" 171

4 A Geeral MVR Model of Pre Period as Usage i the The followig describes a model of the mothly gas demed by idividual heatig customers durig the six primary heatig seaso moths of October through March. The model oly cosiders the six heatig seaso moths because, ulike P~SM, it assumes a referece temperature of 65 P. By modelig oly the mo~.ths whe heatig degree days are greater tha zero, the biases caused by specifyig a icorrect referece temperature usig OLS rather tha No-liear Least Squares will be miimized. Let the mothly gas dem for customer j i a give heatig seaso moth m i the period before joiig a pilot'program be give by 6 Ymlj= (X m1ji m,mlj + m=l period, pmlj is the effect of weather o gas dem i the pre period for customer j moth m, E m1j is a rom error term for customer j moth m i the pre period. The term X m1j ( 'tmlj) represets heatig degree days is based o the break-eve or referece tem~erature 'tmlj. For may applicatios this referece temperature 'tmlj is take asa costat of 65 F. Equatio (3) is kow as a "fixed. effects" regressio model sice the itercept terms lxmlj are costat or fixed for a give customer give moth i the pre period. The uderlyig assumptio of this model is that base gas usage represeted by the itercept term C(,mlj for each customer i moth m i the pre period depeds o uobserved exogeous factors. Sice there are 6 itercept terms i Equatio (3), the assumptio is that base gas usage lxmlj is ot oly differet for each of the customers, but for a give customer is also differet i each of the 6 moths. (3) Geeral Post Period VR Model as Usage i the Let the level of gas dem for customer j i a give heatig seaso moth m i the after joiig a program be give by where all variables par'amete:rs are defied i Table 1 6 Ym2j=E E Clm2jI m,m2j + m=l j $ $,U (custome:rs). ecllmtllo is to PRISM that base usage, the effect of weather o gas usage the referece are to be differet i each of the six moths.. differece i the referece temperature over time would occur if iside temperature settig of the house varied from moth to moth, or if the itrisic gais from occupats, appliaces the su varied from moth to moth. For the holiday seaso of November December the idoor temperature settig of the house be to accommodate guests icreases I (3) Ymlj is the average daily use i the pre for customer j i' moth m, Xmlj is the average degree days ifluecig customer j i moth m i the pre period, a m1j is the itercept or "base gas usage" for customer j if Xmlj(1:mlj) = 0 for moth m i the pre where all variables are as previously defied the subscript 2 refers to the post period. Placig Some Restrictios o the Parameters Sice the parameters of Equatios (3) (4) have moth pre/post period subscripts, eve ifheatig degree days are the same i two differet moths, gas dem is differet for each idividual i each moth i each period. There are several reasos why this might occur. For example, the efficiecy of appliaces may deteriorate over time or the itesity of use might vary from moth (4) 4" Olso Trost

5 to moth. Of course, this is a over-parameterizatio of gas dem. Uless somethig is kow about the values of the parameters i Equatios (3) (4), this equatio will ot be useful for estimatig the eergy savigs from a DSM program. The oly alterative is to place some meaigful restrictios o these parameters. Oe possible set of restrictios are those made by PRISM. 1)1ese restrictios are: (a) Base usage is costat over time for ay give customer period.. (b) The referece temperatures do ot vary over time for ay give customer period.. (c) The effect of weather o gas dem does ot vary over time for ay give customer or period. These three restrictios may be writte for all m,i,j as tha 0 for all observatios sice oly witer moths are used i the estimatio. Combiig restrictios (a) (b), these restrictios ca be writte as 2. ~..=6 5 F for all m,i,j m1.j 5. X mij (,;ij) > 0 for all m,i,j.. Placig these five restrictios o the parameters of Equatios (3) (4) yields the followig simple multiple regressio model Puttig the above three restrictios o the parameters of Equatios (3) (4) yields the PRISM model give by y mlj=l exlji mlj + ~ljxm1j ( 1:lj) + mlj Ym2j=L «2jIm2j +P2jXm2j (1: 2j ) +E m2j (3a) (4a) PRISM estimates equatios (3a) (4a) separately with o-liear least squares. A researcher may coduct a paired-compariso t-test to test for the sigificace of eergy savigs betw.ee the pre post period.. A multivariate regressio model ca be used to provide a estimate of DSM savigs while PRISM data is beig collected.. However, this will require some additioal restrictios o the parameters of Equatios (3) (4).. Cosider the followig six restrictios: (a) Base gas usage is the same for each customer i the pre post periods. The replacemet of a boiler or furace should ot have ay o base usage.. (b) Base usage is costat over time for each customer. Although this ~ssumptio is ot ecessary for multivariate regressio aalysis, it reduces the umber of parameters to be estimated.. The referece temperature is costat for all customers i the pre post periods.at 65 P. (d) The effect of weather o gas usage is costat for all customers i the pre period at P1" (e) The effect of weather o gas usage is costat for all customers i the post period at < ~1. (f) Average heatig degree days are greater Ymlj=L CX j I m1j +(31Xmlj (65 F) +Em1j Ym2j= (XjIm2j +P2X m2j (65 F) + m2j where all variables are as previously defied. A Simple MVR Model to Estimate Savigs (3b) (4b) The ultimate goal of ay pilot program evaluatio is to estimate the eergy savigs attributed to the program. These savigs ca be estimated by combiig heatig seaso equatios (3b) (4b) ito oe simple multivariate regressio model of the form Ymij = L tiji mij + P1Xmij (65 F) + where ap= ~ 2 - ~ 1 all other variables are defied i Table I. Ordiary least squares (DLS) wi yield a cosistet efficiet estimate of the mai parameter of iterest a~. The savigs per degree day from the pilot program are measured as () ~.. The' expected sig of this coefficiet is egative.. If six moths of witer data i both the pre (5) Evaluatio of fj Boiler/Furace Replacemet Pilot Program"r4 Multivariate""" - 4,.173

post are used to estimate the model, the t-statistic for the coefficiet estimate 8 from the usual regressio package output will have 1 wi test the ull Vi)otll1eSlS degrees of freedom Estimated avigs

6 post are used to estimate the model, the t-statistic for the coefficiet estimate 8 from the usual regressio package output will have 1 wi test the ull Vi)otll1eSlS degrees of freedom Estimated avigs for the oiler! Furace ilot Program There were 67 partic~pats i the Boiler/Furace program with sufficiet data for evaluatio at the time this work was iitiated~ Of these midfuraces 25 boilers~ Sice eergy o the of the ew boiler or furace relative to the oe ao1'"i"1,..,,1i.:ll>1i"'iir".'tl that was were estimated for each of these groupsg estimated with PRISM with the multivariate re12~re~;slc~ The mea eergy from were presets the mea with PRISM for each u.it as average eergy from PRISM were calculated was used to see if these mea from zero $ Table 2 eergy estimated VU.A" 11>-!l.1VAfJ~&JI.)i"". Percet i:!l1l1 VJB"I~i:'lIM are defmed divided by average NAC i the year to program pattlc:1patloju. was estimated to be 1206 therms per year for pulrch~ase]t"s of hi 1179 therms per year for lc1-e!tl(~leiicv turac~es therms per year for """'JI.&J...a...'JUl...., boilers 1261 therms per year for Pu]~ch:ase:rs 'M>''I!'lIr-lL_ai"i' ll...""o.'ll''il",'![t boilers, The results from the PRISM of Boiler/Furace i ",['able 2 idicate that highfuraces are eergy saversg High-efficiecy furaces show savigs of 15 ~ 7 %; highefficiecy boilers show savigs of 7~4%c Less efficiet heatig equipmet, however, does ot fare as well. Midefficiecy furaces show savigs of oly 100%; midefficiecy boilers show savigs of 6~3 %0 Oly the estimated eergy savigs for the high-efficiecy furace part~cipats are statistically differet from zero at the 10% level of sigificace" Table 3 presets the OLS estimates of equatio (5). The coefficiet o the variable mit is a estimate of 0 ~ represets a measure of the i efficiecy after reljllacid2 a boiler or furace. Percet savigs, give by heatig uit are defied as a The results i Table 3 idicate that furaces show eergy of 1502% highertlclc~c~v boilers show of 809%. heatig equipmet shows o eergy savigs; eergy usage icreased after istallatio~ Mid-efficiecy furaces used 8 G 8% more eergy boilers used 1"9 % more eergy 0 The estimated eergy for the furace h'll.,k~,::;~ m-+1i,""''li0l'1''lo''''''3:1 statlsilcallly differet from zero l,;ila!8.;uju.jll1vu..a..il..vv$ The eergy use icreases are ot stadifferet from zero at the 10% level of The results also idicate that low icome may have had or ma,aecillate i to joiig the Boiler/Furace Ke:plalceleltlt p:rog~rar. These whe examied ofte showed very substatial: icreases i eergy usage after istallatio of the ew heatig Wa.sruglto Gas is a "o-saver" to determie the factors that caused these eergy use icreases for some oclusios evidece that high-efficiecy boilers furaces have to cut heatig eergy use dramatically. This beefits the Compay as we as the customer as measured. by a cost-effectiveess test utilizig the results of this 4" Olso Trost

<:::..' <} '.' : "~Jd" erat". ~. ~. _ : :: :.:..: :.:. :.:-:.'.:.:. :. :.:.. :.:.:.:.:.:.:. :.:~::::.. ::.::::: _ m Paretheses). l~,'.... 1.4........... <::::::. ilii...:. ::: t ( '..%.. :-:. II...... %.

7 <:::..' <} '.' : "~Jd" erat". ~. ~. _ : :: :.:..: :.:. :.:-:.'.:.:. :. :.:.. :.:.:.:.:.:.:. :.:~::::.. ::.::::: _ m Paretheses). l~,' <::::::. ilii...:. ::: t ( '..%.. :-:. II %...:. are.. from 5~1f1 i ~ Disclaimer Ackowledgmets The authors would like to idicate that this paper reflects their views The cotet of this paper is i o way reflective of the views held Washigto Gas or the Public Service Commissio of the District of Columbia. This paper discusses work that is ogoig at Washigto District of Columbia Divisio. At this Gas is i a program stage has ot evaluated all of the programs offered to cosumers i the lacemet Pilof; I"rt,a/~a'l: Multivariate..".. w 4" 175

Statistics for Economics & Business

Statistics for Economics & Business Statistics for Ecoomics & Busiess Cofidece Iterval Estimatio Learig Objectives I this chapter, you lear: To costruct ad iterpret cofidece iterval estimates for the mea ad the proportio How to determie