ML19329E974
| ML19329E974 | |
| Person / Time | |
|---|---|
| Site: | Midland |
| Issue date: | 07/31/1977 |
| From: | Banks P, Campbell J, Knowles R EQUITABLE ENVIRONMENTAL HEALTH, INC. (SUBS. OF EQUITA |
| To: | |
| References | |
| NUDOCS 8006190751 | |
| Download: ML19329E974 (180) | |
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- IIESIDE':IIAL ELECTRICITY ELASTICITIES I:. <['. .
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4 RESIDENTIAL ELECTRICITY ELASTICITIES IN THE LOWER PENINSULA 0F MICHIGAN VOLUME 3
, Prepared For:
Censumers Power Company and Detroit Edison Company Prepared By: Philip M. Banks John M. Campbell, Jr. Richard K. Knowles E. Kemp Prugh George S. Tolley, Consultant Economic Analysts Division of Equitable Environmental Health, Inc. 455 Fullerton Avenue Elmhurst, Illinois 60126 July 1977 A Sub;idiary of The Equitable Life- Assurance Society of the United States MW 3
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' APPENDIX F -
e n COMPANY LEVEL TIME SERIES
. A model similar-to that used for the regional time series has been developed for: estimating demand elasticities at the company level for Consumers Power Company and Detroit Edison Company. The-company-level data are basically the regional data aggregated to the company level. For the consumption data,~the -
aggregation is straightforward. For the electricity price. variable, no aggre-gation is required since it is already company-wide. The income data ~are aggre-gated using the same procedure applied to the county income data for the Con-sumers Power _ regions. The fuel oil price variable is statewide and'therefore cresents no problem. The gas price variable is aggregated using the number. of customers served by a certain gas company as the weighting factor. .The weather variable was not aggregated, but weather stations representative of the company as a whole were used. Lansing was chosen for Consumers Power and the average of the two Detroit airports was selected for Detroit Edison. .
. A model using these variables was chosen =for each of the companies. A logarithmic specification employing real prices was used, similar to the final regional models. In neither case was the weather variable found significant.
This implies that annual climatic variables do not change enough over the entire service area to significantly explain differences in annual electricity consump-
. . . tion. Also,-the fuel oil price variable was not found to be statist;cally significant in the Detroit Edison service area. Otherwise the model has the ame form as the individual region models. Table F-1 summarizes the estimated coefficients for the company-level demand equations considered most appropriate W
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.t . i - .1 'i l' Table.F-1 Company Time Series Model 1 2 Demand = A* Electricity ** Income"* Gas 6 *0il 6
- Demand (-1)P Short run ' Long run Elasticity Estimates
.+
Detroit Consumers-Consumers' Power Detroit. Edison Power Edison-Coefficient t-statistic ~ Coefficient. t-statistic Electricity - .316 '4.00 .180 2.76 -2.98 -1.15 "
-Income .068 1.'4 .094' 1.24 .64 .60 Gas .187 2.81 .166 1.44 1.76 1 07 Oil .146- 3.09- 1.38 Lagged' dependent variable .899 36.62 . 844 21.47 2 -
R ,9934 .9977 F .2174 2054 Standard Error as percent of Mean Demand .159 .221 N
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o 4 f .J - , .- r i . . L, . 1 Table F - Det'roit' Edison Compa'ny Companywide Time Series Regressions E ND = L1.402* ELECTRICITY .17 88* GAS *16 24*IllCOME.053845* 1 DEMAND (1 ).84407
-R-SQUARED = .99769'
- 24. 0BSERVATI0flS,: 4 '!ARIABLES -
' CORRECTED R-SQUARED = .99721 RESIDUAL SUM SQUARE = .0063166 STANDARD ERROR = .018229 F-RATIO = - 2,054 DEPENDENT MEAN = 8.2634 DEGREES OF FREEDOM = ' 19
- STANDARD ERROR AS % MEAN DEMAND = .22059 .
STANDARD VARIABLE COEFFICIENT
' ERROR BETA- T-STATISTIC PARTIAL-F_
ELECTRICITY .17988 .65091E .13283 -2.7635 7.6473 GAS' .16624 .11528 .51319E-01 1.4420- '2.0794 INCOME- .93845E-01 .75506E-01 .48867E-01 .1.2429 1.5448 DEMAND (-1) .84407 .39309E-01 .87236 ?1.473 461 09-
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' Consumers Power Company _
Companywide Time Series. Regressions O 0 O ND = 0.773* ELECTRICITY -0.31621* GAS .18712* INCOME .068456* FUEL OIL .14649* DEMAND (-1)0.898
'R-SQUARED = .99835' .
24 OBSERVATIONS, 5 VARIABLES
. CORRECTED R-SQUAREC .= .99789 RESIDUAL SUM SQUARE' = 0032081 STANDARD ERROR ,.01335 F-RATIO = '2,173.7 s
=
DEPENDEllT;MEAN = 8.3851 DEGREES OF FREEDOM 18 STAflDARD ERROR AS % MEAft. DEMAND'= .15921 STANDARD.- VARIABLE C0 EFFICIENT ERROR' BETA T-STATISTIC PARTIAL-F ELECTRICITY .31621 .79024 E- 01 16474 -4.0015 16.012 GAS .18712 .66475E-01 . 71041E- 01 2.8149 7.9238-INCOME- .68456E-01 .50921E-01 .41540E-01 1.3444 1.8073
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FUEL OIL- .14649 .47473E-01 .74022E-01 3.0857: 9.5216-DEMAflD(il ) .89892 .24547E-01 .93460 36.621 1341,1 9
_, F-5 _s for each company, and Tables F-2 and F-3 contain the detailed regression results. However, these regression results,'as explained in Section V of _ - Volume 1, are considered inferior to the regional results. The company-level elasticity. estimates obtained by aggregating the regional results together are considered superior. i In the process of developing a company-wide model, a variety of other regressions were run that involved different equation specifications. Each had various problems and/or disadvantages over the model finally chosen. The process began with the most naive model possible--a linear one based ' upon nominal rather than real dollar quantities. Table F-4 gives the results of such a regression, which includes a price for electricity, prices for natu-ral gas, income, heating degree-days, and the percent urbanization as inde-pendent variables. The coefficients all have the expected signs except for the percent urbanization. It was expected that this variable would be nega-tive because consumers in cities tend to use less electricity. The regression shown is for the Consumers Power Company service area. The equation statistics are all very impressive, indicating a high degree of explanatory power. How-ever, there is no explicit control for changes that have occurred over time,
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and the method of interpolation for the percent urban variable makes it very highly correlated with time, thereby muddling its effects. There are a variety of ways to control for changes over time. One com-monly used procedure is to use real prices, meaning prices are divided b;y a price level measure (the consumer price index in this study). Other possi-bilities include explicitly including either the consumer price index or time as an independent variable. All three of these approaches were~im.estigated. N e
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~ Consumers Power Company Regress' ion Not Controlling for Time
. EQUATION DEMAND = -7914 -11109* ELECTRICITY.+ 312.32* GAS + .71468* INCOME + 119.94* URBAN + .16112* HEATING DEGREE DAYS
~R-SQUARED = .9964 STANDARD ERROR RESIDUALS = 125.524 F-RATIO = 529.74 CALCULATED.
ELASTICITY VARIABLE COEFFICIENT STANDARD ERROR T ESTIMATE ELECTRICITY -1109 358.72 -3.092 .454 (500 TEB)
. GAS 312.32 86.792 3.600 .084 INCOME .71468 .061238 11.671 '485
%-URBAN -119.94 13.255- 9.049 IIEATING DEGREE DAYS .16112 .00824 1.956 l
! CONSTANT ' 7914 909.49 -8.702 l I T m
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F-7 An example of a regression for the Consumers Power Company service area that includes the consumer price index as an independent variable is reported in Table F-5. Again, only the percent urban variable is of an unexpected sign. When time is included, the significance of the percent arba variable decreases to almost zero. The major problem with including either time or the consumer price index as an independent variable is that it is tantamount to admitting th.e underlying factors causing changes in consumption cannot be identified. They are " catch-all" variables that do not explain causes, but make the statistics look good. The use of real prices represents one methed of overcoming this problem. Extensive testing of various models was done whera resl prices were employed. Table F-6 reports the results of one of the better real price regressions using a linear specification. This regression, as do the other 7reliminary l r' models that have been discussed, uses the 500 kilowatthour typical electric bill as the basis for the price of electricity. Again, the percent urban variable is positive and highly significant. Also, the inccme variable is
, implausibly negative. The improper signs are the major objections to this model.
The regressions described in this appendix have all been on a company-wide basis, and predominantly for the Consumers Power Company service area. Similar regressions have been run for the Detroit Edison service area. As explained in Section V, the regional level regressions are considered more reliable. Regional level regressions have been run for all of the above ~ specifications and many more. The results of these regressions should be considered developmental and are not reported here. Appendix E reports more fully on regional regressions that overcome the objections to the regressions muses
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- 2- 3- i- b 81 'I-l Table F-5 Consumers' Power Company Regression
' Including the CPI as an Independent Variable l
EQUATION L DEMAllD = -6728.-1716* ELECTRICITY. + 212.22* GAS + .3643*IflCOME + 120.51* URBAN + .3389.1* CPI ~ j- R-SQUARED = .9970 1 . j' STANDARD ERROR RESIDUALS = 114.741-F-RATIO = 634.72 CALCULATED VARIABLE ELASTICITY COEFFICIENT STANDARD ERROR T- ESTIMATE
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ELECTRICITY - (500 TEB) -1716 407.87 - -4.208
.702' GAS 212.22 75.201 2.822 .057.
INLOME .3643 .1409 -2.585 .247
-% URBAN 120.51- 11.604 10.385
- l. CPI .3389.1 1175.2 2.884 C0llSTANT -6728 711.49 -9.456 T
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' DEMAND = -24040 - 826.2* ELECTRICITY + 155.09* FUEL OIL -~.3534* INCOME + 300.07* MULTI' UNIT + 397.76* URBAN R-SQUARED = .9953 -
STANDARD ERROR RESIDUALS = 144.043 F-RATIO ='401.37 - CALCULATED VARIABLE- ELASTICITY COEFFICIErlT STANDARD ERROR T ESTIMATE ELECTRICITY
.(500 TEB). -826.2 549.10 -1.505 .356 FUEL OIL 155.09 38.944 3.982 .404
- IflCOME .3534 .22313 -1.584 .241-
% MULTIUtilT .300.07 35.754 .8.392
% URBAtl 397.76 35.12 11.324 CONSTANT -24040 3066.1 -7.840L 7e e '_ __- B-
F-10 reported in this section. The data utilized in the company-wide regressions are included as part of Appendix D. Section VI of the text details why the regional regressions are considered more reliable. i 4 9 o 6 kW% w
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- APPENDIX G REGIONAL CROSS SECTION MODEL O
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~~ G-1 APPENDIX G REGIONAL CROSS-SECTION MODEL The regional data utilized in the time-series work.were also used in estimating a regional cross-section model. Rather than grouping all obser-vations of a certain region, all 24 regional observations for each year were grouped as a set and an equation estimated for that year. Tables - G-1 through G-10 give the results of this procedure for both linear and . logarithmic specifications. Only the years 1970 through 1974 are reported. These and earlier years' equations have the overriding problem of Wayne County having a high percentage of the sales for Detroit Edison. Company-wide, the Consumers Power Company customers face lower prices and consume more electricity than Detroit Edison customers. But on a regional basis, the Detroit Edison customers outside of Wayne County consume more electricity than the Consumers Power customers. This results in positive electricity l price elasticities in a regional model because each region is weighted . equally. The cause of the difference in consumption levels lies in the degree of urbanization. Outside of the Detroit SMSA, the Detroit Edison service area is almost completely rural, and urban customers tend to use less elect Hcity. All of Consumers Power Company's divisions except the Northwest Division are partially urban. This tends to lower average con-sumption as compared to the rural Detroit Edison counties. The large num-ber of Detroit Edison counties that consume more electricity per customer than Consumers Power divisions and pay higher prices result in a positive price elasticity. This lack of uniformity in consumption rates in the counties for Detroit Edison prevents forming a model that properly takes advantage of the two different price levels (one for each company).
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- _ . . A weighted least squares procedure was considered as a method of overcom-
.ing this problem. However, any rational weighting scheme would have to be based
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on either kilowatthour. consumption or number of customers. Use of either of ~ ' '
.these is objectionable because both are involved in construction of'the depen-
- dent variable. The net effect of such a weighting scheme would be some kind ~
. of implicit modification of the dependent variable, a practice which is highly ,
recommended.against in the literature. Therefore, a weighting scheme was not employed. The regression results reported in this appendix include many variables which are not statistically significant, notably percent urban, percent multi-unit, and heating degree days. The reason these_are included is that the vari-ation of these variables across regions was a source of variation which it was hoped would add additional explanatory power in a cross-section analysis. -The low significance indicates this power was not captured, and is another reason
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why these results are not very useful. These results are included only to demonstrate a plausible method of analyses which was investigated and did not prove fruitful. J e o 4 su 4 cm
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. Table G-1 Regional Cross-Section Model Linear Specification 1970 EQUATION -
DEMAND = - 27,392 +. 9,787.l* ELECTRICITY + 11.056* GAS + .23156* INCOME - 11.355* URBAN + 59.33*MULTIUNIT
+ .49856* DEGREE DAYS R-SQUARED = .55077 24 OBSERVATIONS, 6 VARIABLES CORRECTED R-SQUARED = .39222 RESIDUAL SUM SQUARE = 20,445,298 STANDARD ERROR = 1,096.7 F-RATIO = 3.4737 DEPENDENT MEAN = 6,969 DEGREES OF FREEDOM = 17 STANDARD ERROR AS % MEAN DEMAND = 15.736 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F ELECTRICITY 9787.1 3883.6 .53556 2.4332 2.5201 6.3508 GAS' 11056. 3620.0 .53987 1.8084 3.0543 9.3288 INCOME .23156 .89693 .74706E-01 .10964 .25817 .66652E-01 URBAN -11.355 17.005 .23224 .80825E-01 .66778 .44593 MULTIONIT 59.330- 47.876 .30906 .15995 ,1.2393 1.5358 DEGREE DAYS .49856 .77278 .12789 .50015 .64515 -.41621 p
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' Table G-2 Regional Cross-Section Model Linear Specification 1971 ,
EQUATI0tl DEMAND = - 40.724 + 16,150* ELECTRICITY + 11,078* GAS + .1887* INCOME - 7.8837* URBAN + 72.173*MULTIUNIT
+ 1.0556* DEGREE DAYS R-SQUARED = .58468 24 OBSERVATIONS, 6 VARIABLES CORRECTED R-SQUARED = .4381 RESIDUAL SUM SQUARE = 19,184,720 STANDARD ERROR = 1,062.3 F-RATIO = 3.9887 DEPENDENT MEAll = 7,200.3 DEGREES OF FREEDOM = 17 STAllDARD ERROR AS % MEAN DEMAND = 14,754 STANDARD VARIABLE COEFFICIENT ERROR BriTA ELASTICITY, T-STATISTIC PARTIAL-F ELECTRICITY 16150. 6105.3 .51880 3.7697 2.6452 6.9969 GAS 11078. 3369-9 .58298 1.6720 3.2873 10.806 INCOME .18870 .79754 .69557E-01 .88898E-01 .23660 .55980E-01 URBAll -7.8837 16.809 .16087 .54380E-01' .46902' .21998 MULTIUtlIT 72.173 44.961 .37704 .19458 1.6052' 2.5767 DEGREE DAYS 1.0556 .65562 .30009 .98498 1.6100 2.5923 b
i ; i ; I , 1 , , i . ! , i i i , I ! Table G-3 Regional Cross-Section Model Linear Specification 1972 EQUATION DEMAND = - 6,803.8 - 8,925.3* ELECTRICITY + 16,718* GAS + .16563* INCOME - 10.847* URBAN + 96.972*MULTIUNIT
+ 1.3025* DEGREE DAYS R-SQUARED = .5889 24 OBSERVATIONS, 6 VARIABLES CORRECTED R-SQUARED = .44381 RESIDUAL SUM SQUARE = 20,640,688 STAtlDARD ERROR = 1,101.9 F-RATIO = 4.0588 DEPEllDEllT MEAN = 7,532 DEGREES OF FREEDOM = 17 STANDARD ERROR AS % MEAN DEMAND = 14.629 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F ELECTRICITY -8925.3 ~4392.7 .42616 -2.0390 -2.0318 4.1284 GAS 16718. 4943.5 .63315 2.4004 3.3818 11.436 INCOME .16563 .80923 .61200E-01 .79465E-01 .20467 .41889E-01 URBAN -10.847 18.025 .21319 .71623E-01 .60178 .36214 MULTIUNIT 96.972 47.126 .49187 .25819 2.0577 4.2341 DEGREE DAYS 1.3025 .68182 .36296 1.2759 1.9104 3.6495 T
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~gional Re Cross-Section Model Linear Specificatlon
-1973 EQUATION DEMAND = - 13,794 + 3,297* ELECTRICITY + 6,987.2* GAS + .76354* INCOME - 23.774* URBAN + 84.233*MULTIUNIT
+ .6821* DEGREE DAYS R-SQUARED = .38842 l 24 OBSERVATIONS, 6 VARIABLES l
CORRECTED R-SQUARED = .17257 RESIDUAL SUM SQUARE = 29,702,435 l STANDARD ERROR = 1,321.8 F-RATIO = 1.7995 t DEPENDENT MEAN = 7,547.7 DEGREES OF FREEDOM = 17 STANDARD ERROR AS % MEAff DEMAND = 17.513 STANDARD l ViiRIABLE COEFFICIENT ERROR BETA . ELASTICITY T-STATISTIC PARTIAL-F-l ELECTRICITY 3297.0 3808.3 .22068 .80651 .86574 .74950
-GAS 6987.2 4189.4 .40758 1.0058 1.6678 2.7817 IllCOME .76354 .93989 .30390 .37971 .81238 .65996 l URBAN -23.774 22.001 .47752 .15683 -1.0806 1.1677 MULTIUNIT 84.233 57.987 .44016 .23083 1.4526 2.1101 l DEGREE DAYS .68210 .97494- .16414 .56162 .69963 .48949 l _.
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-EQUATIO!!
DEMAtlD = - 42,162 + 21,294* ELECTRICITY + 4,730.6* GAS + .18631* INCOME - 16.253* URBAN + 50.217*MULTIUNIT
+ .60043* DEGREE DAYS R-SQUARED = .34863 24 OBSERVATIONS, 6 VARIABLES CORRECTED R-SQUARED = .11874 RESIDUAL SUM SQUARE = 33,092,538 STANDARD ERROR = 1,395.2 F-RATIO = 1.5165 DEPENDEllT MEAfl = 7,507 DEGREES OF FREEDOM = 17 STAllDARD ERROR AS % MEAN DEMAND = 18.585 STAllDARD VARIABLE COEFFICIEllT BETA ELASTICITY T-STATISTIC
__ ERROR PARTIAL-F ELECTRICITY 21294. 15077. .37382 5.3198 1.4123 1.9947 GAS 4730.6 -5156.5 .24115 .62575 .91739 .84160 IllCOME .18631 1.0890 .62718E-01 .98927E-01 .17108 .29269E-Ol URBAtl -16.253 22.969 .32085 .10794 .70761 .50072 MULTIUNIT 50.217 62.831 .25959 .14257 .79924 .63878 DEGREE DAYS .60043 .99059 .15324 .54630 .60613 .36739 6
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DEGREE D R-SQUARED = .58164 4 23 OBSERVATIONS, 6 VARIABLES
= .42476 CORRECTED R-SQUARED RESIDUAL SUM SQUARE = .34149 STANDARD ERROR = .14609 F-RATIO = 3.7075 DEPENDENT MEAN = 8.8255 DEGREES OF FREEDOM = 16 STANDARD ERROR AS % MEAN DEMAND = 1.6553 STANDARD VARIABLE COEFFICIENT ERROR BETA T-STATISTIC PARTIAL-F ELECTRICITY 2.5149 1.0222 .58322 2.4603 6.0531 GAS 1.7133 .51240 .58388 3.3437 11.180 INCOME .17806E-02 .32997 .12056-E-02 .45311E-02 .20531E-04 URBAN .26967E-01 .84800E-01 .10049 .31801 .10113 MULTIUNIT .15831 .13669
.27538 1.1582 1.3414 DEGREE DAYS .48761 .75071 .42190
.13045 .64954 c>
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-0.013811* MULTI. UNIT .20769* DEGREE DAYS .9545 R-SQUARED = .62578 23 OBSERVATIONS, 6 VARIABLES' t
CORRECTED R-SQUARED = .48545 RESIDUAL SUM SQUARE = .29043 STAftDARD ERROR = .13473 F-RATIO = 4.4593 DEPENDENT MEAN = 3.861 DEGREES OF FREEDOM = 16 STANDARD ERROR AS % MEAN DEMAND = 1.5205 STANDARD VARIABLE COEFFICIENT ERROR BETA T-STATISTIC PARTIAL-F ELECTRICITY 3.9411 1.4519 .57106 2.7145 7.3686 GAS 1.5757 .42963 . .62652 3.6675 13.451 INCOME .46074E-02 .33597 .35967E-02 .13714E-01 .18806E-03 URBAN .13811E-01 .75835E-01 .53170E-01 .18212 .33167E-01 MULTIUNIT .20769 .12966 .36352 1.6019 2.5660 DEGREE DAYS' .95459 .58038 .30459 1.6448 2.7053 4 b
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1 : Table G-8 Regional Cross-Section Model Logarithmic Specification 1972 2
= 0.100* ELECTRICITY-2.2767,gg3 3483* INCOME-0.03325* URBAN-0.03662*MULTIUNIT O .27482* DEGREE DAYS1 .3326 -
R-SQUARED = .65317 23 OBSERVATIONS, 6 VARIABLES , CORRECTED R-SQUARED
= .52311 RESIDUAL SUM SQUARE = 26666 STANDARD ERROR = .1291 F-RATIO = 5.022 DEPErlDENT MEAN = 8.9056 DEGREES OF FREEDOM' = 16 STAllDARD ERROR AS % MEAN DEMAND = 1.4496 STANDARD VARIABLE C0 EFFICIENT ERROR BETA T-STATISTIC PARTIAL-F
.50057 -2.2797 5.1973 ELECTRICITY -2.2767 .99765 GAS .58172 .67811 4.0368 16.296 2.3.483
.10082 .10165E-01 IllCOME .33250E-01 .32979 .25476E-01
.50658 .25662 URBAN .36620E-01 .72289E-01 .14242 2.1588 4.6602 MULTIUNIT .27482 .12731 .47471 1.3326 .61273 2.1748 4.7297 DEGREE DAYS .39565 G
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, . 2 i i i 3 Table G-9 i
Regional Cross-Section Model Logarithmic Specification 1973 EQUATION 0 I O 0 0
. DEMAND = 0.2898* ELECTRICITY .86695* GAS .446* INCOME .20911* URBAN-0.098751*MUL R-SQUARED = .51412 23 OBSERVATILaS, 6 VARIABLES CORRECTED R-SQUARED = .33192 RESIDUAL SUM SQUARE = .35375 STANDARD ERROR = .1487 F-RATIO = 2.8217 DEPENDENT MEAN = 8.909 '
DEGREES OF FREEDOM = 16 STANDARD ERROR AS % MEAN DEMAND = 1.6691 STAiiDARD VARIABLE COEFFICIENT ERROR BETA T-STATISTIC PARTIAL-F ELECTRICITY .86695 .88288 .25268 .98196 .96424 GAS 1.4460 .51317 .58087 2.8177 7.9396 INCOME .20911 .36888 .16871- .56687 .32134 URBAN .98751E-01 .83701E-01 .39771 -1.1798 1.3920 MULTIUNIT .30356 .15430 .53133 1.9674 3.8706 DEGREE DAYS .83082 .72625 .25356 1.1440 1.3087
?
~t I- i- i 4
. . r- i i . t :
i Table G -10 Regional Cross-Section Model_ Logarithmic Specification 1974 1 3 I O 0 0 = 0.005* ELECTRICITY .8803* GAS .6806* INCOME .14357* URBAN-0.10169*MULTIUNIT .28655* DEGREE I DAYS .154 R-SQUARED = .48168 23 OBSERVATIONS, 6 VARIABLES CORRECTED R-SQUARED
= .2873 RESIDUAL SUM SQUARE = .40405 STANDARD ERROR = .15891 . F-RATIO = 2.4781 DEPENDEllT f1EAN = 8.9013 DEGREES OF FREEDOM = 16 STANDARD ERROR AS % MEAN DEMAND = 1.7853 STANDARD VARIABLE C0 EFFICIENT ERROR BETA T-STATISTIC PARTIAL-F ELECTRICITY 3.8803 3.5736 .28611 1.0858 1.1790 GAS 1.6806 .69764 .56114 2.4090 5.8031 INCOME .14357 .41670 .99669E-01 .34454 .11871 URBAN .10169 .91732E-01 .39895- -1.1086 1.2290 MULTIUNIT .28655 .17605 .47760 1.6276 2.6491 DEGREE DAYS 1.1540 .82521 .33991 1.3984 1.9556 m
to
.m a M APPENDIX H COMBINED CROSS-SECTION/ TIME SERIES ANALYSIS N*-s 4 4 e
O D w 9 5 mem 5 m
_ H-1 COMBINED CROSS-SECTION/ TIME SERIES ANALYSIS An effort at combined cross-section/ time series analysis was made utili-zing the regional level data base. By pooling the data it was possible to do an analysis which considered observations for 13 regions over 25 years at one time. Most procedures for the combining of time series and cross section data fall into the category of generalized least squares estimators. The particu- - lar procedure chosen for use is commonly referred to as " Seemingly Unrelated Regressions". This procedure was chosen because the assumptions required concerning the residuals appears less restrictive and more general than require-ments for other procedures. The precedure is best described in matrix notation. If one has m separate equations (in this case 13 regional equations) with a number of observations for each, the ordinary least squares coefficient estimates for each equation are given by
^
B m . The variance-covariance matrix for each of the equations is given by E (c m 8'm)" mm It where T is the number of observations and mc represents the residuals for the mth equation. The " Seemingly Unrelated Regressions" approach thdn connects the different equations through their residuals by assuming; E(c m S p)""mpk Thus, om p is the covariance of the disturbances of the mth and pth equations, and that covariance is assumed to be constant over time. This says this co-variance is the only link between equations. In this instance this procedure is especially useful because the effect of any omitted variable affecting all the different regions in the same manner would be captured. 4x ink
H-2 This effect captured by the procedure is incorporated into the coefficient estimates by an re-estimation which incorporates the variance-covariance matrix of the ordinary least squares estimates. The variance-covariance matrix for all the equations is denoted n and, in matrix notation again, the new coefficient F
~
estimates are given by;
-l j = (X' n -I X)- (X_'n l) and the variance-covariance matrix of these estimates is given by -
(X'n-1X )-1 It can be shown that in the case of the regressions actually being-unrelated, ie. e mp = 0, then this estimator reduces to the ordinary least squares esti-mator. Further, it can be shown that the variance for the " Seemingly Unrelated Regressions" is snaller or equal to that of the ordinary least squares p'rocedure. This is a relatively straightforward result of the procedure being a maximum likelihood estimator. A different approach which is frequently used is known as an error compo-nents model, often attributed to Balestra and Nerlove. In this procedure the regression disturbance is assumed to be comprised of three separate components-one associated with time, another with cross sectional units, and a third varying in both dimensions. Specifically the assumptions are where cit = "i
- Vt + *it 2
u g s N (0, o ) u 2 v s N (0, o y) t 2 w it s N (0, og) and the components satisfy the following components E (ujty ) = E (ut "it) = E (vt *it) = 0 .'_, .E (ugj u)=0 i+j E (v Vt s) = 0 t+s E (wit"is) = E (wi t"j t) = E (wit"js) = 0 for i + J, t + s
~ --------mm ~mam _ .. . - -
H-3 Again, this procedure requires that the correlation of the disturbances over time remains unchanged no matter how far apart in time the disturbances
. are. But the additional requirements concerning the cross sectional error component are not required in a " Seemingly Unrelated Regressions" approach.
However, in a case where the requirements of the error components model _ are met the two procedures should give the same results because both are unbiased, consistent, and efficient. The " Seemingly Unrelated Regressions" procedures was applied to the regional data for each company. Aggregation into a Lower Peninsula of Michigan data set
^
was not possible because of computer software limitations. The price for elec-tricity used in the analysis that was done is based upon the 500 kWh Typical Electric Bill, rather than the Bill 10 prices. It is felt that this does not -- change the evaluation of the procedure for this study. Table H-1 sunmarizes the results of the procedure for Consumers Power Company and Table H-2 does the same for Detroit. Edison. The equation used to estimate was linear in the independent variables electricity price, gas price, income, and heating degree days. The procedure had somewhat different effects for the two companies. For Consumers Power, as evident in Table H-1, the pro-cedure had relatively major effects. But the effects were counterintuitive. The gas price coefficients all became negative with the exception of Pontiac
. division (which actually faces Detroit Edison rate schedbles). This is not at all expected of an alternative fuel. Also, the electricity price coeffi-
~
cients became much more elastic than in the OLS equations. The income coefficients did respond in an appropriate manner -- the coefficients became much closer to each other and inelastic as compared to the OLS estimates. s 3__ S we w- - ,+c + - e
0 p.t . 1. F . i . , : i . . . i . i i i Table H-1 Seemingi onrelated Regression Results for Consumers Power Company Ordinary Least Squares Estimates Seemingly Unrelated Regression Estimates , Region Price of Electricity Price of Gas Income Price of Electricity Price of Gas Income Coeff. t-s ta t Coeff. t-s ta t Coeff. t-stat Elas. Coeff. t-sta t Coeff. t-stat Coef f. t-stat
' Central -3940 3.17 -451 0.31 1.16 1.95 -2.21 -4819 6.22 -1194 1.14 .465 3. 01 Battle Creek' -3844 3.82 -333 0.62 1.13 2.95 -1.93 -4875 7.29 -1391 1.71 .558 3.98 Northeast -3531 2.91 -485 0.36 .95 2.16 -2.25 -4492 6.50 -1355 1.51 .385 3.27 Pontiac -3531 6.79 3087 0.23 .70 3.05 -2.08 -3850 11.81 1694 1.74 .287 2.04 Flint -4365 3.57 154 0.12 1.42 3.24 -2.13 -5433 7.99 -971 1.15 .673 4.80 Grand Rapids -3362 3.61 -2760 2.24 .52 1.33 -1.78 -3906 7.42 -2462 4.81 .316 1.88 Jackson -3789 2'.94 214 0.15 1.36 3.50 -1.91 -5135 6.84 -1472 1.55 .635 4.65 Kalama zoo -4775 4.38 495 0.38 .94 2.18 -2.18 -5547 8.87 -866 1.19 .286 2.18 Lansin9 -4888 3.15 292 0.17 1.55 2.94 -2.14 -6278 7.11 -1174 0.99 .739 5.51 Muske90n -3058 3.21 -3236 3.15 .15 0.34 -1.75 -3803 6.17 -2820 5.00 .004 .02 Sa91naw -4436 4.71 332 0.27 1.35 4.50 -2.21 -5167 8.28 -1198 1.52 .733 6.34 Northwest -2250 2.02 -4838 3.98 0 0 -1.44 -2969 4.39 -4220 6.92 .138 .54
?
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'l l' ' ~
t 3 . i . . . , . 2 . . . ; . , i . I. Table H-2
, Seemingly linrelated Regression Results for _Jetroit Edison Company Ordinary Least Squares Estimates Seemingly Unrelated Regression Estimates Region Price of Electricity Price of Gas Inco~me Price of Electricity Price of Gas Income Coeff. t-stat Coeff. t-stat Coeff. t-stat Elas. Coeff. t-stat Coeff. t-stat Coeff. t-stat Lapeer -4608 10.17 0.98 0.09 0.27 -2.16 -4425 22.60 964 361 0.63 0.08 0.92 Tuscola -3740 7.08 1926 1.80 0.59 1.57 -1.87 -3720 17.57 840 1.59 0.41 3.73 Iluron -3138 8.91 2183 2.44 - 0.19 0.76 -1.70 -3108 18.75. 1491 3.45 0.10 1.09 Sanilac -3552 3.98 273 0.19 0.17 0.30 -1.88 -4469 11.94 1245 2.21 -0.38 1.73 St. Clair -3466 7.16 1043 1.18 0.09 0.39 -2.23 -3863 21.67 1390 5.57 - 0.16 - 1.75 Macomb -2491 8.90 1366 1.88 0.87 4.02 -1.59 -2457 16.81 792 2.01 0.74 8.84
' 0akland -3531 6.79 3087 2.31 0.70 3.05 -2.24 -3487 13.55 1922 2.71 0.52 7.27 Ingham -4686 9.55 2851 2.20 0.97 2.67 -1.87 -4561 20.99 1779 3.05 0.78 7.85 Livingston -4239 13.79 971 1.01 0.08 9.43 -2.20 -3944 22.73 335 0.59 0.18 3.54 Washtenaw -2954 5.82 2872 2.29 0.68 3.26 -1.64 -2887 14.97 2388 5.48 0.54 5.90 Lenawee -5075 12.18 2288 2.04 0.52 1.65 -1.79 -4970 19.50 1123- 1.67 0.32 1.97 Monroe -2457 10.02 107 0.42 0.79 5.31 -1.52 -2517 22.23 86 0.93 0.71 11.22 Wayne -1954 5.78 467 0.48 0.62 4.49 -l.68 -1977- 17.16 4 81 2.00 0.57 12.89
- x:
-. H-6 The results fur Detroit Edison did not contain so many surprises. The electricity price coefficients were little changed, and the gas price variable had the proper sign. The income coefficients also seemed a little more reason-able than the OLS estimates, though not greatly changed.
The sof tware limitation and lack of identifiable benefits limited use of , this comparatively expensive procedure. Because nothing in it changes greatly from the OLS estimates this is not considered a major shortcoming. The standard error of the residuals in the OLS procedure is so small it is unlikely that a combined approach will significantly alter coefficients or decrease the standard error. 4 i i~
.w.
ee w
.- - -- * -g - w, r y-
APPENDIX I INDIVIDUAL :USTOMER CROSS SECTION REGRESSIONS . we
- M S
NT I-1 APPENDIX I INDIVIDUAL CUSTOMER CROSS-SECTION REGRESSIONS This appendix contains detailed results of cross-sectional regressions using individual customer data with annual kilowatthour consumption as the dependent variable. The first group of 36 tables does not include average price per kilowatthour as an independent variable; the next group of 36 does. The final 9 tables present the regression results of an attempt to use price variables in the manner described in the Taylor article in the literature review. The first seventy two tables in this appendix provide empirical verifica-tion of two expectations relating to the use of average price of electricity -- the two being the reversal of cause-and-effect and the biasir.g of the income coefficient. As detailed in the text, average price is not a viable variable because it reverses cause-and-effect. The group of re;*essions including it as an explanatory variable demonstrate the degree to which it merely re-
~
flects the slope of the supply curve. Two data bases are used -- one for each . company. The Detroit Edison data, based on a 1973 appliance survey, was collected when Detroit had a traditional declining block rate structure. In contrast the Consumers Power data, based on a 1976 appliance survey, was collected when Consumers Power customers were facing a flat rate structure. The differences in the electricity price elasticity are striking. The time series regressions previously indicated that the Consumers Power customers tended to be somewhat more elastic in their responses to price changes than the Detroit Edison customers. However, in these individual customer regres- __ - sions the price elasticity estimates are negative, and sometimes elastic, for the Detroit Edison data but very inelastic or even positive for the Consumers Power dita. This difference is attributable to the difference in rate structure. H
I-2 Another expectation that is verified by these regressions is that delet-ing the average price variable would increase the importance of the income variable. This expectation applies in the instance of the traditional declin-ing block rate-structure. Thus, comparison of the results, of including and-
, not including average price in regressions utilizing the Detroit Edison appli-
~'
ance ownership data, with particular emphasis on the income variable, reveals
~
the truth of this expectation. The income e1asticity is doubled in most cases, and definitely is more important when the average price variable is not present.
. As mentioned earlier, the major portion of this a'ppendix is divided into two subsets -.one that includes average price and one that does not. Each of these two categories is further divided into regressions that do not ex-plicitly include appliance ownership variables (Tables I-1 to I-9, I-19 to I-27, I-37 to I-45, and I-55 to I-63) and those that do (Tables I-10 to I-18,
. I-28 to I-36, I-46 to I-54, and I-64 to I-72). This separates long-term -
'i L .- appliance-buying decisions from short-term usage decisions. The equations r~ that include appliance variables also indicate average annual electricity i usage by an appliance. These groupings are also ordered by company. The data for each company
- survey was partitioned by income and consumption and individual regressions c
~.
.were run for each usage block and each income block as well as for the sample as a whole. The following table will clarify the breakdown of the-first 72 tables.
69 ( e se iN
.~ .w _ - - -
I-3 l Regressions Including Regressions Excluding Average Price Average Price CPC DEC CPC DEC Including Appliance Variables
~
Total sample 46 64 10 28 Usage block 47-49 65-67 11-13 29-31 Income block 50-54 68-72 14-18 32-36' Excluding Appliance Variables L Total sample 37 55 1 19 r- Usage block 38-40 56-58 2-4 20-22 {- ' In.come block 41-45 59-63 5-9 23-27 1-As discussed in the literature review section, one method, suggested by saylor, to overcome the problems associated with selecting a proper electricity price variable is to include both an average and a marginal price variable. l' [, Specifically, average price is to be calculated based on consumption up to, ,- but not including, that in the last block consumed in. Marginal price is then the price from the rate schedule that corresponds to the block at the { actual level of consumption. Thus, if a h'ypothetical consumer uses 609 kWh t., per month, and the rate schedule is as follows: [, 0-100 kWh 5.0c/kWh 101-250 kWh 4.04/kWh 251-500 kWh 3.04/kWh ['w > 500 kWh 2.5c/kWh jI t F*
I _4 average price is calculated as 3.74c/kWh = (.05*100 + .04
- 150 + .03
- 250)/500, and marginal price is 2.5c/kWh. In this manner the pure price effect,* repre-sented by the coefficient of the marginal price variable, !s supposed to be separated from the income effect,* represented by the cor fficient of the aver- .
age price variable. Thus Taylor hypothesizes that inclusion of both prices will eliminate the likely upward bias in the elasticity estimate if only one price variable is included. Furthermore, he indicates that the coefficient of the average price variable should be equal in magnitude, but opposite in sign to the coefficient of the income variable.
" TAYLOR PRICES"
~
Detroit Edison " Average Price" " Marginal Price"
- I' 0-15 $ 1.50 0 li 15-100 10.0d 3.24 ,
^l 100-200 4.22c 2.8d over 200 3.51c 2.6c ~~ As a test of the methodology, individual customer data from the 1973 i' Detroit Edison saturation survey were utilized. This resulted in a sample of 711 customers. All equations were estimated in linear fashion with ten ~L. - independent variables: 1) marginal price, 2) average price, 3) income, 4)
; presence o'f an air conditioner, 5) size of the family, 6) age of the hea'd L.
-
- Any price change has ssociated with it a pure price (or substitution) effect and an income effect. For details, see any intermediate price theory te.,t.
u w
+
We
I-5
-N of the family, 7) . presence of a freezer, 8) number of rooms in the domicile,
. 9) presence of a dryers, and 10) presence of a stove. Of the above, variables 4, 7, 9, and 10 were binary variables. In addition, the income variable was an ordinal type variable.
, several regressions-were run, including one for the overall sample, -
, five for the data partitioned by income levels, and three for the data parti-tioned by usage level. Table I-73 presents the results.for the overall sample; Tables I-74 through I-78 for income partitions of $0 to $5,000 per year,
$5,001 to $10;000 per year, $10,001 to $15,000 per year, $15,001.to $25,000 per yaar, and greater than $25,000 per year, respectively; Tables I-79 through
_ I-81 for monthly usage partition of 0 to.500 kWh per month, 501 to 1,000 kWh. j
. per month, and greater than 1,000 kWh per month, respectively.
Examination of these tables reveals rather disappointing results. First, the elasticities obtained in all cases are extremely large, ranging from: approximately -8 to -34. Furthermore, the sign associated with the average
, price variable coefficient is consistently the opposite of a priori expecta- -
. tions. In addition, in several instances the signs associated with several'
[- appliance't coefficients are also opposite to what one would logically expect. The above aspects of these results seem to indicate the inappropriate-iL. ness of Taylor's methodology to individual customer data, especially within a single service area. Indeed, Taylor implies in his article that the method-
- '. ology is best suited for a national study with the state as the observational unit. For all of the above reasons, not much confidence is put in the results obtained from this approach,. and hence the reporting of results has- been relegated to this appendix.
4 m
i -!- c I: i , . Table I-1 Consumers Power Individual Customer Cross-Section Model Regression Excluding Average Price and Excluding Appliance Variables _ Total Sample ._ EQUATION KWH = - 28.925 + 356.7* INCOME + 684.67*R00MS + 511.72* FAMILY R-SQUARED = .094574 1533 OBSERVATIONS, 3 VARIABLES CORRECTED R-SQUARED = .092797 RESIDUAL SUM SQUARE = 5.5279E+10 STAtlDARD ERROR = 6,012.8 F-RATIO = 53.236 DEPENDENT MEAN = 6,914.7 ' DEGREES OF FREEDOM = 1529 STANDARD ERROR AS % MEAN KWH = 86.957 4 STANDARD VARIABLE C0 EFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F IllCOME - 356.70 93.379 .10029 .17/80 3.8199 14.592 ~ ROOMS 684.67 91.823 .18993 .57356 7.4564 55.598 FAMILY 511.72 93.283 .14069 .23283 5.4856 30.092-4 ---~_ - _ _
~
i- i . . . .
. i i I Table I-2 Consumers Power Individual Customer Cross-Section Model Regression Excluding Average Price and Excluding Appliance Variables Consumption Less Than 500 Kilowatthours/ Month EQUATION KWH = 2,028.3 + 317.13*R00MS - 121.62* FAMILY R-SQUARED = .1198' 783 OBSERVATIONS, 2 VARIABLES
' CORRECTED R-SQUARED = .11754 RESIDUAL SUM SQUARE = 1.8304E+09 STANDARD ERROR = 1,552.6 F-RATIO = 53.082 DEPENDENT MEAN = 3,370.9 DEGREES OF FREEDOM = 780 STANDARD ERROR AS % MEAN KWil = 46.060 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ROOMS 317.13 32.569 .32774 .49778 9.7370 94.809 FAMILY -121.62 30.605 .13376 .994b3E-01 -3.9739 15.792
~
- s
- 1. . I' l- ! . i Table 1-3 Consumers Power Individual Customer Cross-Section Model Regression Excluding Average Price and Excluding Appliance Variables
_ Consumption 500-1,000 Kilowatthours/ Month EQUATION
.KWH = 7,745 + 194.43* FAMILY R-SQUARED = .03048 581 OBSERVATIONS, 1 VARIABLE -
CORRECTED R-SQUARED = .028805 RESIDUAL SUM SQUARE = 1.5828E+09 STANDARD ERROR = 1,653.4 F-RATIO = 18.203 DEPENDENT MEAN = 8,401.3 DEGREES OF FREEDOM = E'9 STANDARD ERROR AS % MEAN KWH = 19.680 4 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F FAMILY 194.43 45.573 .17459 .78114E-01 4.2605 18.203 s Mm ehe .O, ee g e ee. O 4 i g%e 0 0
y __ ,
; 3 9
Q Table I-4 Consumers Power Individual Customer Cross-Section Model-Regression Excluding Average Price - and Excluding Appliance Variables Consumption Over 1,000 Kilowatthours/ Month PROCEDURE SuttMARY NO INDEPENDENT VARIABLE QUAL.IFIED FOR ENTRY PROCEDURE ENDED WHEN MAXIMUM F TO ENTER = 1.92 for "R0 OMS" FAILED TO MEET "F ACCEPT = 3.90" 9 i-l e o e
I a 1 Table I-5 Consumers Power Individual Customer Cross-Section Model _ Regression Excluding Average Price-and Excluding Appliance Variables Income Less Than $4,000 ~ PROCEDURE
SUMMARY
NO INDEPENDENT VARIABLE QUALIFIED FOR ENTRY ._ PROCEDURE ENDED WilEN MAXIMUM F TO ENTER = .20 FOR " ROOMS" FAILED TO MEET "F ACCEPT = 3.90" W$sp
.g- 7 ,
g ;- ; , , , i . 't i Table I-6 Consumers Power Individual Customer Cross-Section Model Regression Excluding Average Price and Excluding Appliance Variables
- . _ - . . _ . . Income M ,000-10,000 EQUATION KWH = 1, "?0.4 + 496.65*R00MS + 761.29* FAMILY R-SQUARED = .043741 451 OBSERVATIONS, 2 VARIABLES i 8 CORRECTED R-SQUARED = .039472 RESIDUAL SUM SQUARE = 2.4711E+10 STANDARD ERROR = 7,426.9 F-RATIO = 10.246 DEPENDENT MEAN = 6,190.1 DEGREES OF FREEDOM = 448 STANDARD ERROR AS % MEAN KWH = 119.98 STANDARD
, VARIABLE COEFFICIENT ERROR BEFA ELASTICITY T-STATISTIC PARTIAL F ROOMS 496.65 215.33 .10687 .43354 2.3065 5.3200 FAMILY 761.29 205.28 .17184 .35314 3.7086 13.753
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Table I-7 Consumers Power Individual Customer Cross-Section Model Regression Excluding Average Price and Excluding Appliance Variables Income n $10,000-15,000 EQUATION KWH = 1,738.5 + 530.68*R00MS + 753.31* FAMILY R-SQUARED = .074387 387 OBSERVATIONS, 2 VARIABLES CORRECTED R-SQUARED = .069566 RESIDUAL SU.4 SQUARE = 1.1745E+10 STANDARD ERROR = 5,530.5 F-RATIO = 15.43 DEPENDENT MEAN = 7,189.1 DEGREES OF' FREEDOM = 384 STANDARD ERROR AS % MEAN KWH = 76.929 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ROOMS 530.68 181.84 .14704 .42459 2.9185 8.5174 FAMILY 753.31 190.67 .19905 .33358 3.9508 15.609 6
.e =
6
i 1 , I i~. i : . ,. .
. i , ! i 1 i i Table I-8 Consumers Power Individual Customer Cross-Section Model Regression Excluding Average Price and Excluding Appliance Variat>1es Income $15,000-25,000 _
EQUATION KWil = 974.75 + 889.33*R00MS + 376.33*FAMILV R-SQUARED = .11638 387 OBSERVATIONS. 2 VARIABLES CORRECTED R-SQUARED = .11178 RESIDUAL SUM SQUARE = 9.4972E+09 STANDARD ERROR = 4,973.2 F-RATIO = 25.288 DEPENDENT MEAN = 7,772.8 DEGREES OF FREEDOM = 384 STANDARD ERROR AS % MEAN KWH = 63.982 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ROOMS 889.33 141.63 .30424 .69832 6.2792 39.428 FAMILY 376.33 155.38 .11735 .17627 2.4219 5.86S8.
~~
T'
~ . . . . . . . _ . ._ _-. _.-.
_____ G
; 3 -; ; ; - -- - - - '
i [ . I ; Table I-9 Consumers Power Individual Customer Cross-Section Model Regression Excluding Average Price and Excludinq Appliance Variables
-- Income Over $25,000 EQUATION KWH = - 2,414.7 + 1,642.9*R00MS R-SQUARED = .14255 138 OBSERVATIONS, 1 VARIABLE CORRECTED R-SQUARED = .13624 RESIDUAL SUM SQUARE = 7.1421E+09 STANDARD ERROR = 7,246.8 F-RATIO = 22.609 DEPENDENT MEAN = 9,133.5 DEGREES OF FREEDOM = 136 STANDARD ERROR AS % NEAN KWH = 79.343 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ROOMS 1642.9 345.52 .37755 1.2644 4.7549 22.609 T
****No ein, e , m == .s ,w ,w . * * * " " 1=*,% .. , . =
-m. _
g . _. 7 ;. , , ,-_ , Table t-10 Consumers Power Individual Customer Cross-Section Model ' Regressions Excluding Average Price and Including Appliance Variables _ Total Sample EQUATION KWH = - 10,388 + 227.3* INCOME + 432.87*R00MS + 493.24* FAMILY + 728.74* FREEZER + 2,547.5* DRYER + 394.31*ST0VE
+ 2,0249.9*AC + 2,696.1* WATER R-SQUARED = .28013 1310 OBSERVATIONS, 8 VARIABLES CORRECTED R-SQUARED = .2757 RESIDUAL SUM SQUARE = 4.1160E+10 STANDARD ERROR = 5,624.7 F-RATIO = 63.283 DEPENDENT MEAN = 7,142.3 DEGREES OF FREEDOM = 1301 STANDARD ERROR AS % MEAN KWH = 78.752 STANDARD VARIABLE C0 EFFICIENT ERROR _ BETA ELASTICITY T-STATISTIC PARTIAL F INCOME 227.30 97.899 .60195E-01 .12436 2.3218 5.3908 ROOMS 432.87 98.603 .11322 .35629 4.3901 19.273 FAMILY 493.24 96.113 .12801 .21814 5.1319 26.338 FREEZER 728.74 93.729 .19512 .27299 7.7750 60.451 DRYER 2547.5 338.76 .19113 .51161 7.5203 56.554 ST0VE 394.31 189.20
~
.56104E-01 .12790 2.0841 4.3436 AC 2024.9 324.49 .14938 4
.32008 6.2401 38.939 WATER 2696.1 358.57 .19863 .52301 7.5191 56.537
i r~n f : ; .T F-~ 7 : . _. 1 : : 3 . T 'l J i . r . i Table I-11 Consumers Power Individual Customer Cross-Section Model Regressions Excluding Average Price and Including Appliance Variables Consumption Less Than 500 Kilowatthours/ Month EQUATION KWH = 2,251.9 + 206.61*R00MS - 89.84* FAMILY + 229.95* FREEZER + 420.45* DRYER - 503.74* WATER R-SQUARED = .1801
- 648 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .17371 RESIDUAL SUM SQUARE = 1.3775E+09 STANDARD ERROR = 1,464.8 F-RATIO = 28.204 DEPENDENT MEAN = 3,456.3 DEGREES OF FREEDOM = 642 STANDARD ERROR AS % MEAN KWH = 42.380 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ROOMS 206.61 35.891 .21581 .32176 5.7565 33.138 FAMILY -89.840 33.058 .98205E-01 .71480E-01 -2.7177 7.3857 FREEZER 229.95 39.239 .21710 .12988 5.8603 34.343 4
DRYER 420.45 133.30 .11572 .15431 3.1541 9.9485 1 WATER -503.74 132.09 .13988 .18600 -3.8135 14.543
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7 _. Table I-12 ; i< Consumers Power Individual Customer Cross-Section Model Regressions Excluding Average Price and Including Appliance Variables Consumption 500-1,000 Kilowatthours/ Month EQUATION . KWH = 2,679.8 + 107*R00MS + 315.16* FAMILY + 132.95* FREEZER + 439.46* DRYER + 197.43*ST0VE + 546.98*AC
+ 1,228.6* WATER R-SQUARED = .24281 509 OBSERVATIONS, 7 VARIABLES CORRECTED R-SQUARED = .23223 RESIDUAL SUM SQUARE = 1.0973E+09 STANDARD ERROR = 1,480 - F-RATIO = 22.951 DEPENDENT MEAN = 8,370.3 DEGREES OF FREEDOM = 501 STANDARD ERROR AS % MEAN KWH = 17.681 i
STANDARD j VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ROOMS 107.00 44.111 .98636E-01 .79260E-01 2.4257 5.8838 FAMILY 315.16 45.583 .28449 .12642 6.9140 47.803 FREEZER 132.95 38.627 .13638 .51986E-01 3.4418 11.846 DRYER 439.46 136.64 .13011 .79836E-01 3.2161 10.343 ST0VE 19,7.43 82.178 .99359E-0'. .59455E-01 2.4025 5.7720 AC 546.98 121.80 .17838 .76132E-01 4.4907 20.167 WATER 1228.4 149.78 .35792 .20676 8.2026 67.282
. . . _ .. . ~
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~ ~~i ~ ~ ~1 ~~'l ~! 1 I Table I-13 Consumers Power Individual Customer Cross-Section Model Regressions Excluding Average Price and Including Appliance Variables Consumption Over 1,000 Kilowatthours/ Month PROCEDURE SlH4ARY NO INDEPENDENT VARIABLE QUALIFIED FOR ENTRY PROCEDURE ENDED WilEN MAXIMUM F TO ENTER = 3.22 FOR " WATER" FAILED TO MEET "F ACCEPT = 3.90" 6
5
, 7. ._ . . . 7..
, , ; 3 Table I-14 Consumers Power Individual Customer Cross-Section Model Regressions Excluding Average Price and Including Appliance Variables Income under $4,000 EQUATION 2 KWil = - 26.957 + 425.96* FREEZER + 1,252.1* DRYER + 1,342.9* WATER R-SQUARED = .2805 ,
125 OBSERVATIONS, 3 VARIABLES CORRECTED R-SQUARED = .26266 RESIDUAL SUM SQUARE = 599,429.760 STANDARD ERROR = 2,225.8 F-RATIO = 15.724 DEPENDENT MEAN = 4,520.6 DEGREES OF FREEDOM = 121 STANDARD ERROR AS % MEAN KWH = 49.235 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTICS PARTIAL F FREEZER 425.96 127.86 .27523 .21257 3.3316 11.099 ORYER 1252.1 459.83 .22625 .36562 2.7230 7.4149 WATER .1342.9 410.14 .25821 .42777 3.2743 10.721-we qu 4 Og . ga G
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Table I-15 Consumers Power Individual Customer Cross-Section Model Regressions Excluding Average Price and Including Appliance Variables Income $4,000-10,000 EQUATION KWH = - 10,195 + 554.48* FAMILY + 876.78* FREEZER + 2,233.8* DRYER + 4,599.7*AC + 3,257* WATER R-SQUARED = .2167 382 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .20629 _ RESIDUAL SUM SQUARE = 1.9499E+10 STANDARD ERROR = 7,201.4 F-RATIO = 20.805 DEPENDENT MEAN = 6,400 DEGREES OF FREEDOM = 376 STANDARD ERROR AS % MEAN KWH = 112.52 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F FAMILY 554.48 220.28 .11795 .24948 2.5171 6.3360 FREEZER .876.78 216.81 .19250 .35110 4.0441 16.355 DRYER 2233.8 798.32 .13573 .48974 2.7981 7.8293 AC 4599.7 841.55 .25046 .79396 5.4657 29.874 WATER 3257.0 777.00 .19703 .70875 4.1918 17.571 .
- g. .; r 7. r- , r- l [-- i~ i [- - , , ~ ~1 (( ] ; i " ! [ I 4 1 . -) . l . 1 Table I-16 ,
Consumers Power Individual Customer Cross-Section Model Regressions Excluding Average Price and Including Appliance Variables Irtcome $10,000-15,000 EQUATION KWH =-- 5.230.2.+ 630.82* FAMILY + 630.3* FREEZER + 2.246* DRYER + 723.55*ST0VE + 2,782.8* WATER
; R-SQUARED = .28325
! 338 OBSERVATIONS, 5 VARIABLES - CORRECTED R-SQUARED = .27245 RESIDUAL SUM SQUARE = 8.4988E+09 i STANDARD ERROR = 5,059.5 F-RATIO = 26.24
= 7,339 DEPENDENT MEAN .. DEGREES OF FREEDOM = 332 STANDARD ERROR AS % MEAN KWH = 68.940 STANDARD VARIABLE .C0 EFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F j ,
FAMILY 630.82 194.05 .15858 .27083 3.2508' 10.568 FREEZER 630.30 164.23 .18782 .22767 3.8379 14.730 DRYER 2246.0 592.30 .18939 .45181 3.7920- 14.379 ST0VE 723.55 325.17 .11578 .22722 2.2251 4.9513 WATER 2782.8 638.12 .23119' .53512 4.3610 19.018 N- .
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1 j7 r r- i ; ; , , ; Table I-17 Consumers Power Individual Customer Cross-Section Model Regressions Excluding Average Price and Including Appliance Variables Income $15,000-25,000 EQUATION KWH = - 7,724 + 688.77*R00MS + 358.98* FAMILY + 782.85* FREEZER + 2,858.8* DRYER + 2,769.9* WATER R-SQUARED = .37414 343 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .36485 RESIDUAL SUM $QUARE = 6.2202E+09 STANDARD ERROR = 4,296.2 F-RATIO = 40.291 DEPENDENT MEAN = 7,846.7 DEGREES OF FREEDOM = 337 STANDARD ERROR AS % MEAN KWH = 54.752 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY. T-STATISTIC PARTIAL F-ROOMS 688.77 138.70 .22604 .53793 4.9660 24.661 FAMILY 358.98 143.93 .10990 .16632 2.4940 6.2202 FREEZER 782.85 137.50 .25745 .28709 5.6933 32.414 DRYER 2858.8 494.57 .26382 .52578 5,7804 33.413 i WATER 2769.9 515.50 .24075 .46724 5.3732 28.871 wm , Y M
._,u ., e . -= * * - * * ' ' * ** "" ' " ~ * '~ ~ ' ' ' Table I-18 Consumers Power Individual Customer Cross-Section Model Regressions Excluding Average Price and Including Appliance Variables Income Over $25,000. __ . EQUATION KWH = - 8,854.4 + 802.69* FAMILY + 1,068.2* FREEZER + 6,009.8* DRYER + 2,449.4*AC R-SQUARED = .32822 122 OBSERVATIONS, 4 VARIABLES CORRECTED R-SQUARED = .30525 RESIDUAL SUM SQUARE = 5,1372E+09 STANDARD ERROR = 6,626.3 F-RATIO = 14.291 DEPENDENT MEAN = 9,627.5 DEGREES OF FREEDOM = 117 STANDARD ERROR AS % MEAN KWH = 68.827 STANDARD VARIABLE' COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F FAMILY 802.69 336.53 .18431 .32667 2.3852 5.6892 FREEZER 1068.2 358.16 .23586 .32832 2.9825 8.8955 DRYER 6009.8 1275.0 .37949 .94147 4.7136 22.218 AC 2449.4 901.13 .20975 .32324 2.7182 7.3886 U
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. Table I-19 Detroit Edison Individual Customer Cross-Section Model Regressions Excluding Average Price and Excluding Appliance Variables Total Sample _, _ _ _ _ , _ _ _
EQUATION KWH = - 4,309.2 + 654.71* INCOME + 750.57*R00MS + 701.03* FAMILY + 271.37* AGE HEAD 4 R-SQUARED = .28403 711 OBSERVATIONS, 4 VARIABLES 4 CORRECTED R-SQUARED = .27997 RESIDUAL SUM SQUARE = 1.3009E+10 STANDARD ERROR = 4,292.6 F-RATIO = 70.017 DEPENDENT MEAN = 7,044 DEGREES OF FREEDOM = 706 STANDARD ERROR AS % MEAN KWH = 60.940 STANDARD VARIABLE COEFFICIENT ERROR BETA
~
ELASTICITY T-STATISTIC PARTIAL F INCOME . 654.71 94.955 .25848 .49832 6.8950 - 47.541 , ROOMS 750.57 126.89 .21753 .61984 5.9151 34.988 FAMILY 701.03 111.70 .25155 .34280 6.2758 39.385 AGE HEAD 271.37 130.97 .78533E-01 .15079 2.0720 4.2932
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l . ! I L J t I - - I Table 1-20 Detroit Edison Individual Customer Cross-Section Model Regressions Excluding Average Price and Excluding Appliance Variables Consumption Less Than 500 Kilowatthours/ Month _ EQUATION - KWH = 1,387.6 + ..'02.73* INCOME + 147.82*R00MS + 280.22* FAMILY R- SQUARED = .32868 . 342 OBSERVATI0tC, 3 VARIABLES CORRECTED R-SQUARED = .32273 RESIDUAL SUM SQUARE = 425,658,707 STAflDARD ERROR = 1,122.2 F-RATIO = 55.163 DEPEllDENT MEAN = 3,780 DEGREES OF FREEDOM = 338 STANDARD ERROR AS % MEAN KWH = 29.6P.8 i
- STANDARD.
VARIABLE COEFFICIENT ERROR BETA _ ELASTICITY T-STATISTIC PARTIAL F INCOME 202.73 31.734 .31138 .23759 6.3884 40.812 ROOMS 14 E'. 82 .49.879 .14049 .20457 -2.9636 8.7830 FAMILY 1d0.22 46.373 .30225 . 19075 6.0428 36.515 m-f
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, , i Table I-21 Detroit Edison Individual Customer Cross ,Section Model Regressions Excluding Average Pr ice and Excludir,' Appliance Variables Consumption 500 i,000 Kilowatthours/ Month EQUATION '
KWH = 5,943.2 + 217.3* INCOME + 134.36*R00MS R-SQUARED = .057275 294 OBSERVATIONS, 2 VARIABLES CORRECTED R-SQUARED = .050796 RESIDUAL SUM Sy0ARE = 673,664,034 STANDARD ERROR = 1,521.5 F-RATIO = 8.8399 DEPENDENT MEAN = 8,110.8 DEGREES OF FREEDOM = 291 STANDARD ERROR AS % MEAN KWH = 18.759 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F INCOME 217.30 61.419 .20206 .16431 . 3.5381 12.518 ROOMS 134.36 - 68.035 .11278 .10294 1.9748 3.8998 I 4 N
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Table I-22 Detroit Edison Individual Customer Cross-Section Model Regressions Excluding Average Price and Excluding Appliance Variables ~ Conr_amption Over 1,000 Kilowatthours/ Month PROCEDURE
SUMMARY
NO INDEPENDENT VARIABLE QUALIFIED FOR ENTRY PROCEDURE ENDED WHEN MAXIMUM F TO ENTER = 3.86 FOR " ROOMS" FAILED TO MEET "F ACCEPT = 3.97" \ h-*w % eM pa a esse m,.gg-- e 0
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i ; [ -', [9 f- ^, t , t . : , i~ l .; . . . . 1 . t . 3 I i v l Table I-23 Detroit Edison Individual Customer Cross-Section Model' Regression Excluding Average Price and Excluding Appliance Variables Incom_e,U_n_ der $5,000 _ EQUATION KWll = 1,541.6 + 1,038.3* FAMILY R-SQUARED = .26484 i 122 OBSERVATIONS, 1 VARIABLE , CORRECTED R-SQUARED = .25871 RESIDUAL SUM SQUARE = 619,915,214 STANDARD ERROR = 2,272.9 F-RATIO = 43.229 DEPENDENT MEAN = 3,745.8 DEGREES OF FREEDOM = 120 STANDARD ERROR AS % MEAN KWil = 60.678 STANDARD ; VARIABLE COEFFICIENT ERROR BETA ELASTICITY .T-STATISTIC PARTIAL F i FAMILY 1038.3 157.92 .51462 .58845 6.5749 43.229 J em i 8h-g.e a 'I D!
-li ~; I j i i . f -~1 r~l i 1 i , ! , r~~ i : ; i .~ ~l ~1 ~ ~7 ~~7 r 71 'l ) ll Table I-24 Detroit Edison Individual Customer Cross-Section Model Regression Excluding Average Price and Excluding Appliance Variables Income $5,000-10,000 EQUATION .
KWH = 1,527.3 + 507.65*R00MS + 421.73* FAMILY R-SQUARED = .12357 141 OBSERVATIONS, 2 VARIABLES CORRECTED R-SQUARED = .11087 RESIDUAL SUM SQUARE = 1.0534E+09 STANDARD ERROR. = 2,762.8 F-RATIO = 9.7282 DEPENDENT MEAN = 5,360.4 DEGREES OF FREEDOM = 138 - STANDARD ERROR AS % MEAN KWH = 51.541 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ROOMS 507.65 210.48 .20595 .49636 2.4119 5.8174 FAMILY 421.73 163.40 .22037 .21873 2.5809 6.6611
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g; ;-- ;-- ; -- - r-i ; ; ,1 -l Table I-25 Detroit Edison Individual Customer Cross-Section Model Regression Excluding Average Price and Excluding Appliance Variables Income $10,000-15,000 EQUATION KWH = - 1,289.4 + 1,227.7*R00MS + 442.39* FAMILY R-SQUARED = .12942 216 OBSERVATIONS, 2 VARIABLES CORRECTED R-SQUARED = .12124 RESIDUAL SUM SQUARE = 5.6405E+09 STANDARD ERROR = 5,146 F-RATIO = 15.832 DEPENDENT MEAN = 7,684.7 DEGREES OF FREEDOM = 213 STANDARD ERROR AS % MEAN KWH = 66.964 STANDARD VARIABLE C0 EFFICIENT ERROR BETA ELASTICITY T-STATISTIC FARTIAL F ROOMS 1227.7 301.84 .27875 .93193 4.0674 16.544 4 FAMILY 442.39 204.60 .14818 .23586 2.1623- 4.6753
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i ; f -~ ' , 1 f~ T- I' i -~' I i ' . I '~ I~l ' - 8 'l i l I ) Table I-26 Detroit Edison Individual Customer Cross-Section Model Regression Excluding Average Price and Excluding Appliance Variables Income $15,000-25,000 EQUATION KWil = 5,412.5 + 815.6* FAMILY R-SQUARED = .083549 170 OBSERVATIONS, 1 VARIABLE CORRECTED R-SQUARED = .078094 RESIDUAL SUM SQUARE = 3.4753E+09 STANDARD ERROR = 4,548.2 F-RATIO = 15.316 DLPENDENT MEAN = 8,622.1 DEGREES OF FREEDOM = 168 STANDARD ERROR AS % MEAN KWH = 52.750 STANDARD
' VARIABLE COEFFICIENT ERROR BETA . ELASTICITY T-STATISTIC PARTIAL F FAMILY 815.60 208.40 .28905 .37225 3.9135 15.316 i
~~
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q ._. j.__._ g__. 3 , ; ;3 l 0 Table I-27 Detroit Edison Individual Customer Cross-Section Model Regression Excluding Average Price and Excluding Appliance Variables Income Over $25,000 EQUATION , KWH = - 1,577.9 + 965.28*R00MS + 1,460.9* FAMILY R-SQUARED = .30627 62 OBSERVATIONS, 2 VARIABLES CORRECTED R-SQUARED = .28275 RESIDUAL SUM SQUARE = 1.8997E+09 STANDARD ERROR = 5,674.4 F-RATIO = 13.023-DEPENDENT MEAN = 10,804 DEGREES OF FREEDOM = 59 STANDARD ERROR AS % MEAN KWH = 52.522 STANDARD VARIABLE COEFFICIENT ERROR 8 ETA ELASTICITY T-STATISTIC PARTIAL F ROOMS 965.28 453.24 .26537 . 61389 2.1298 4.5358 FAMILY 1460.9 489.08 .37219 .53216 2.9870 8.9224 ~- j k!
i . F~ i - F f~~ i i i , _ , ; ~i ~ ~ ~ ~; ; , . 1 i : , i i Table 1-28 Detroit Edison Individual Customer Cross-Section Model Regressions Excluding Average Price and Including Appliance Variables Total Sample EQUATION KWH = - 9,814.8 + 309.07* INCOME + 733.56*AC + 685.69* FAMILY + 1,932.7* FREEZER + 468.45*R00MS
+ 2,423.4* DRYER + 2,279.9*ST0VE R-SQUARED = .4566 l 711 OBSERVATIONS, 7 VARIABLES 1
CORRECTED R-SQUARED = .45119 RESIDUAL SUM SQUARE = 9.8735E+09 STANDARD ERROR = 3,747.6 F-RATIO = 84.387 DEPENDENT MEAN = 7,044 DEGREES OF FREEDOM = 703 STANDARD ERROR AS % MEAN KWH = 53.203 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F INCOME 309.07 82.328 .12202 .23524 3.7541 14.093 AC 733.56 150.89 .14156 .17415 4.8617 23.636 FAMILY 685.69 91.645 .24605 .33529 7.4820 55.980 FREEZER 1932.7 317.85 .17650- .35888 6.0804 36.972 l ROOMS 468.45 111.14 .13577 .38686 4.2148 17.765 DRYER 2423.4 342.18 .21069 .43403 7.0822 50.158 ST0VE 2279.9 299.96 .22431 .46888 7.6006 57.770 7' tl
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7__ _ Table I-29 Detroit Edison Individual Customer Cross-Section Model Regressions Excluding Average Price and Including Appliance Variables Consumption Less Than 500 Kilowatthours/ Month EQUATION KWH = - 551.03 + 170.4* INCOME + 262.39*AC + 328.05* FAMILY + 548.58* FREEZER + 129.78*R00MS + 522.38* DRYER
+ 349.4*ST0VE R-SQUARED = .40504 342 OBSERVATIONS, 7 VARIABLES CORRECTED R-SQUARED = .39257 RESIDUAL SUM SQUARE = 377,242,154 STANDARD ERROR = 1,062.8 F-RATIO = 32.484 DEPENDENT MEAN = 3,780 DEGREES OF FREEDOM = 334 STANDARD ERROR AS % MEAN KWH = 28.116 STANDARD VARIABLE C0 EFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F INCOME 170.40 31.117 .26172 .19969 5.4761 29.988 AC 262.39 83.295 .13851 .97833E-01 3.1502 9.9236 FAMILY 328.05 44.899 .35383 .22331 7.3063 53.38E FREEZER 548.58 161.85 .14466 .16719 3.3894 11.488 ROOMS 129.78 47.971 .12335 .17960 2.7054 7.3193 DRYER 522.38 174.93 .12845 .15598 2.9863 8.9178 ST0VE 349.40 125.75 .11986 .12217 2.7785 7.7201
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. 4 i ~l Table I-40 Detroit Edison Individual Customer Cross-Section Model Regressions Excluding Average Price and Including Appliance Variables
_ Consumption 500-1,000 Kilowatthours/ Month EQUATION KWH = 3,290.3 + 142.81* INCOME + 303.61*AC + 178.57* FAMILY + 384.08* FREEZER + 758.13
- DRYER + 755.56*ST0VE R-SQUARED = .2091 294 OBSERVATIONS, 6 VARIABLES CORRECTED R-SQUARED = .19256 RESIDUAL SUM SQUARE = 565,172,145 STANDARD ERROR = 1,403.3 c-RATIO = 12.646 DEPENDENT MEAN = 8,110.8 DEGREES OF FREEDOM = 287 STANDARD ERROR AS % MEAN KWH = 17.302 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F INCOME 142.81 58.011 .13279 .10798 2.4617 6.0600 AC 303.61 81.331 .20067 .68754E-01 3.7330 13.935-FAMILY 178.57 50.858 ,
.19439 .90685E-01 3.5111 12.328 FREEZER 384.08 167.39 .12108 .66683E-01 2.2945 5.2649 DRYER 758.13 183.48 .22481 .12240 4.1319 17.072 ST0VE 755.56 176.66 .24211 .13783 4.2769 18.292
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Table I-31 Detroit Edison Individual Customer Cross-Section Model
, Regressions Excluding Average Price and
- Including Appliance Variables Consumption Over 1,000 Kilowatthours/ Month j
4 PROCEDURE
SUMMARY
NO INDEPENDENT VARIABLE QUALIFIED FOR ENTRY PROCEDURE ENDED WHEN MAXIMUM F TO ENTER = 3.86 FOR "R0 OMS" . I FAILED TO MEET "F ACCEPT = 3.97" i I-
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Table I 32 Detroit Edison Individual Customer Cross-section Model Regressions Excluding Average Price and Including Appliance Variables Income Less Than $5,000 EQUATION KWH = - 4,131.4 + 891.57* FAMILY + 1,603* FREEZER + 2,725* DRYER + 135.03*ST0VE R-SQUARED = .50166 122 OBSERVATIONS, 4 VARIABLES CORRECTED R-SQUARED = .48462 RESIDUAL SUM SQUARE = 420,222,266 STANDARD ERROR = 1,895.2 F-RATIO = 29.444 DEPENDENT MEAN = 3,745.8 DEGREES OF FREEDOM = 117 STANDARD ERROR AS % MEAN KWH = 50.594 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F FAMILY 891.57 137.92 .44191 .50530 6.4643 41.787 FREEZER 1603.0 458.25 .24238 .51213 3.4981 12.237 DRYER 2725.0 535.92 .34036 .81691 5.0847 25.854 ST0VE 735.03 362.49 .13490 .26860 2.0277 4.1117 D 0
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Table I,33 Detroit Edison Individual Customar Cross-Section Model Regressions Excluding Average Price and Including Appliance Variables Income $5,000-10,000 EQUATION i KWil = - 5,405.5 + 470.27*AC + 483.2* FAMILY + 2,199.9' FREEZER + 382.05*R00MS + 1,491.9*0RYER + 1,471.1*ST0VE R-SQUARED = .4472 141 OBSERVATIONS, 6 VARIABLES . CORRECTED R-SQUARED = .42245 RESIDUAL SUM SQUARE = 664,392,644 STANDARD ERROR = 2,226.7 F-RATIO = 18.067 DEPENDENT fiEAN = 5,360.4 DEGREES OF FREEDOM = 134 STANDARD ERROR AS % MEAN KWH = 41.540 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F AC 470.27 220.37 .13907 .13440 2.1340 4.5541 FAMILY 483.20 132.72 .25250 .25061 3.6406 13.254 FREEZER 2199.9 434.32 .33967 .52683 .5.0652- 25.656 ROOMS 382.05 172.95 .15499 .37355 2.2090 '4.8797 DRYER 1491.9 467.89 .21859 - - r34543 3.1886 10.167 ST0VE 1471.1 402.41 .24405 .37759 3.6557- 13.364 - M
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Table I-34 Detroit Edison Individual Customer Cross-Section Model Regressions Excluding Averaga Price and Including Appliance Variables
-Income $10,000-15,000 EQUATION KWH = - 10,803 + 586.39* FAMILY + .2,891.8* FREEZER + 578.73*R00MS + 3,799.2* DRYER + 2,931*ST0VE R-SQUARED = .39049 216 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED =. 37598 RESIDUAL SUM SQUARE = 3.9490E+09 STANDARD ERROR = 4,336.4 F-RATIO = 26.908 DcPENDENT MEAN = 7,684.7 DEGREES OF FREEDOM = 210 STANDARD ERROR AS % MEAN KWil = 56.429 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F FAMILY ,
586.39 177.55 .19642 .31264 3.3026 10.907 FREEZER 2891.8 647.56 .24713 .49826 4.4657 19.943 ROOMS 578.73 263.84 .13140 .43930 2.1935 4.8113 DRYER 3799.2 722.38 .30909 .62943 5.2593 27.660 ST0VE 2931.G 658.99* .25971 .52620 4.4477 19.782
i 'r FD' f f. - t' i ! . ! - i 4 . . ._i .I ;- I . i . ~1 1 . i 4 i 'l 1 Table I-35 Detroit Edison Individual Customer Cross-Section Model Regress 13ns Excluding Average Price and Including Appliance Variables Income $15,000-25,000 , EQUATION KWil = - 3,423.1 + 692.28* FAMILY + 1,856.7* FREEZER + 2,024.5* DRYER + 2,785.4*ST0VE R-SQUARED = .28578 170 OBSERVATIONS, 4 VARIABLES S CORRECTED R-SQUARED = .26847 RESIDUAL SUM SQUARE = 2,7084E+09 STANDARD ERROR = 4,051.5 F-RATIO = 16.505 DEPENDENT MEAN = 8,622.1 DEGREES OF FREEDOM = 165 STANDARD ERROR AS % MEAN KWH = 46.989 STANDARD 4 VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC P_ARTIAL F FAMILY 692.28 188.64 .24534 .31597 3.6698 13.467 FREEZER 1856.7 671.86 .18638 .28881 2.7635 7.6370 DRYER 2024.5 714.22 .19531 .30386 2.8345 8.0345 ST0VE 278S.4 645.58 .29480 .48838 4.3146 18.615
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Table I-36 Detroit Edison Individual Customer Cross-Section Model Regressions Excluding Average Price and Including Appliance Variables Income Over $25,000 EQUATION KWH = - 5,834.8 + 1,846.8*AC + 1,420.9* FAMILY + 1,000.8*R00MS R-SQUARED = .43304 62 OBSERVATIONS, 3 VARIABLES CORRECTED R-SQUARED = .40372 RESIDUAL SUM SQUARE = 1.5525E+09 STANDARD ERROR = 5,173.8 F-RATIO = 14.767 DEPENDENT MEAN = 10,804 DEGREES OF FREEDOM = 58 STANDARD ERROR AS % MEAN KWH = 47.888 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F AC 1846.8 512.81 .35620 .38599 3.6013 12.970 . FAMILY 1420.9 446.07 .36200 .51759 3.1854 10.147 ROOMS 1000.8 413.37 .27514 .63649 2.4211 5.8618
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rc . p- . 7, g-- q 7--- -) p- ,----- p-- 7 ; - ;- , , - 3 3 3 g. ; 3 Table I-37 Consumers Power Individual Customer Cross-Section Model Regressions Including Average Price and Excluding Appliance Variables _. Total Sample I EQUATION KWH = 29.215 - 2.4467* CENTS KWH + 357.78* INCOME + 676.56*R00MS + 511.66* FAMILY I ! R-SQUARED = .095327 1533 OBSERVATIONS, 4 VARIABLES 4 CORRECTED R-SQUARED = .092959 RESIDUAL SUM SQUARE = 5.5233E+10 STANDARD ERROR = 6,012.3 F-RATIO = 40.252 , DEPENDENT MEAN = 6,914.7 DEGREES OF FREEDOM = 1528 l STANDARD ERROR AS % MEAN KWH = 86.949 l. STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F CENTS KWH -2.4467 2.1696 .27527E-01 .21864E-02 -1.1277 1.2717 INCOME 357.78 93.375 .10059 .19839 3.8316 14.681 ROOMS 676.56 92.096 .18768 .56677 7.3463 53.968 FAMILY 511.66 93.275 .14068 .23280 5.4855 30.091 R;
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_ _ _ Consumption Less Than 500 Kilowatthours/ Month EQUATION KWH = 2,080.4 - 1.3634* CENTS /KWH + 309.53*R00MS - 121.43* FAMILY R-SQUARED = .12645 783 OBSERVATIONS, 3 VARIABLES CORRECTED R-SQUARED = .12309 RESIOUAL SUM SQUARE = 1.8661E+09 STANDARD ERROR = 1,547.8 F-RATIO -= 37.589 DEPENDENT.MEAN = 3,370.9 DEGREES-0F FREEDOM = 779 STANDARD ERROR AS % MEAN KWH = 45.915 STANDARD
- VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH -1.3636 .55982 .81943E-01 .36725E-02 -2.4358 5.9331 ROOMS 309.53 32.516 .31988 .48585 9.4899 90.057 FAMILY -121.43 30.509 .13355 - 99327E-01 -3.9802 15.842 1~~" n,. ,. .-. ~_
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. Regressions Including Average Price and Excluding Appliance Variables Consumption 500-1,000 Kilowatthours/ Month EQUATION KWil = 11,113 - 1,087.5* CENTS /KWH + 219.15* FAMILY R-SQUARED = .03953 581 OBSERVATIONS, 2 VARIABLES CORRECTED R-SQUARED = .036207 RESIDUAL SUM SQUARE = 1.5680E+09 STANDARD ERROR = 1,647 F-RATIO = 11.894 '
DEPENDENT MEAN = 8,401.3 DEGREES OF FREEDOM = 578 STANDARD ERROR AS % MEAN KWH = 19.605 ! STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS / KWH -1087.5 466.01 .97686E-01 .41087 -2.3337 5.4462 FAMILY 219.15 46.618 .19678 .88045E-01 4.7010 22.100 1 1 ~. a
- Table T 40 Consumers Power Individual Customer Cross-Section Model Regressions Including Average Price and Excluding Appliance Variables
_ Consumption Greater Than 1,000 Kilowatthours/ Month EQUATION KWH = 642,779 - 201,894* CENTS / KWH - 773.52* INCOME R-SQUARED = .58658 169 OBSERVATIONS, 2 VARIABLES CORRECTED R-SQUARED = .5816 RESIDUAL SUM SQUARE = 1.0152E+10 STANDARD ERROR ' = 7,820.4 F-RATIO = 117.77 DEPENDENT MEAN = 18,223 DEGREES OF FREEDOM = 166 STANDARD ERROR AS % MEAN KWH = 42.916 STANDARD VARIABLE C0 EFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH .20189E+06 13161. .77017 -34.064 -15.341 235.34
- INCOME -773.52 367.41 .10570 .20998 -2.1053 4.4325
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i , Table I-41 Consumers Power Individual Customer Cross-Section Model Regressions Including Average Price and Excluding Appliance Variables Income Less Than $4,000 EQUATION KWH = 4,754.8 - 55.498* CENTS /KWH ' R-SQUARED = .070153 170 OBSERVATIONS,'1 VARIABLE CORRECTED R-SQUARED = .064618 RESIDUAL SUM SQUARE = 1.1d53E+09 STANDARD ERROR = 2,565 F-RATIO = 12.675 DEPENDENT MEAN = 4,457.7 DEGREES OF FREEDOM = 168 STANDARD ERROR AS % MEAN KWH = 57.541 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH -55.498 15.588 .26486 .66647E-01 -3.5602 12.675 i On e-
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Table I-42 Consumers Power Individual Customer Cross-Section Model Regre_ssions Including Average Price and Excluding Appliance Variables _ ._ _ _ . _ Income $4,000-10,000 EQUATION KWil = 1,420.2 - 1.4427* CENTS KWil + 481.68*R00MS + 759.74* FAMILY R-SQUARED = .044342 451 OBSERVATIONS, 3 VARIABLES CORRECTED R-SQUARED = .037929 RESIDUAL SUM SQUARE = 2.4695E+10 STANDARD ERROR = 7,432.8 F-RATIO = 6.9136 DEPENDENT MEAN = 6,190.1 DEGREES OF FREEDOM = 447 STANDARD ERROR AS % MEAN KWH = 120.08 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F CENTS KWil -1.4427 2.7198 .24743E-01 .23325E-02 .53045 .28137 ROOMS 481.68 217.34 .10365 .42048 2.2163 4.9119 FAMILY 759.74 205.47 .17148- -
.35242 3.6976 13.673 s
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. i~~' . , j i i i [1 ~) .i Table I-43 Consumers Power Individual Customer Cross-Section Model Regressions Including Average Price and Excluding Appliance variables
~ --Income $10,000-15,000 EQUATION ,
KWH = 3,928.3 - 375.67* CENTS /KWH + 367.08*R00MS + 827.1* FAMILY R-SQUARED = .12812 387 OBSERVATIONS, 3 VARIABLES CORRECTED R-SQUARED = .12129 RESIDUAL SUM' SQUARE = 1.1063E+10 STANDARD ERROR = 5,374.6 F-RATIO = 18.76 DEPENDENT MEAN = 7,189.1 DEGREES OF FREEDOM = 383 STANDARD ERROR AS % MEAN KWH = 74.760 STANDARD YARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH -375.67 77.324 .23616 .20636 -4.8584 23.604 ROOMS 367.08 179.89 .10171 .29369 2.0406 4.1639 FAMILY 827.10 185.92 .21855 .36625 4.4487 19.791 t w
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F~ F~ " ' F~ . - . ; . i i i Table I-44 Consumers Power Individual Customer Cross-Section Model Regressions Including Average Price and Encluding Appliance Variables Income $15,000-25,000 EQUATION. KWH = 1,287.2 - 63.582* CENTS /KWH + 889.28*R00MS + 376.58* FAMILY R-SQUARED = .14635 387 OISERVATIONS, 3 VARIABLES CORRECTED R-SQUARED = .13966 RESIDUAL SUM SQUARE = 9.1751E+09 STANDARD ERROR = 4,894.5 F-RATIO = 21.886 DEPENDENT MEAN = 7,772.8 DEGREES OF FREEDOM = 383 STANDARD ERROR AS % MEAN KWH = 62.969 , STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH -63.582 17.341 .17310 .40280E-01 -3.6665 13.443 ROOMS 889.28 139.39 .30422 .69828 6.3798 40.702 FAMILY 376.58 152.92 .11743 .17639 2.4625 6.0641
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. DEPENDENT h 4 = 9,133.5 DEGREES OF FREEDOM = 135 STANDARD ERROR AS % MEAN KWH = 78.807 ,
VARIABLE STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F ^ CENTS KWH -168.15 99.497 . 13885 .82003E-01 -1.6900 2.8563 ROOMS 1473.6 357.51 .33864 1.1341 4.1218 16.989 i E?
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.q 7__, (_ . 7 _ .. _ q Table I-46 Consumers Power Individual Customer Cross-Section Model Regressions Including Average Price and Including Appliance Variables Total Sample N
EQUATION KWH = -22,123 - 104.97* CENTS /KWH + 358.22*R00MS + 560.56* FAMILY + 942.39* FRIDGE 2 + 842.07* FRIDGE
+ 670.31* WASHER + 679.13* FREEZER + 1,797.2* DRYER + 2,398.3*AC + 3,156.3* WATER + 8.156.l* SPACE R-SQUARED = .34467 1000 OBSERVATIONS,11 VA;d?.BlES ; CORRECTED R-SQUARED = .33737 RESIDUAL SUM SQUARE = 3.285E+10
- STANDARD ERROR = 5,766.3 F-RATIO = 47.239 DEPENDENT MEAN = 7,395.5 DEGREES OF FREEDOM = 988 STANDARD ERROR AS % MEAN KWH = 77.971 l
STANDARD VARIABLE C0 EFFICIENT ERROR BETA ELASTITICTY T-STATISTIC PARTIAL-F CENTS /KWH -104.97 19.179 .14296 .61336E-01 -5.4733 29.958 ROOMS 358.22 118.04 .86806E-01 .28786 3.0346 9.2088 FAMILY 560.56 112.18 .13220 .24467 4.9969 24.969 FRIDGE 2 942.39 454.02 .55227E-01 .15559 2.0757 4.3084 PEiCGE 824.07 220.48 .10039 .36270 3.7376 13.970 W f.tR 670.31 192.14 .11320 .30092 3'.4886 12.170 FREEZER 679.13 113.05 .17006 .24812 6.0072 36.087 DRYER 1797.2 432.44 .12644 .35406 4.1559 17.271 AC 2398.3 398.99 .15633 .36126 6.0110 36.132 WATER 3156.3 415.27 .21857 .59835 7.6005 57.768 SPACE 8156.1 1058.3 .20578 1.1392 7.7070 59.398 [ t . - . -
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i i i l' ~ I ~'I [ ] ~i , o i , 1 . . > Table I-47 Consumers Power Individual Customer Cross-Section Model Regressions including Average Price ' and Including Appliance Variables . Consumption Less Than 500 Kilowatthours/ Month
~~-
EQUATION KWH = -179.5 - 38.992* CENTS /KWH + ll2.85*R00MS + 769.52* MICRO-0VEN + 356.46* FRIDGE + 360.25* WASHER
+ 193.26* FREEZER R-SQUARED = .3685 474 OBSERVATIONS, 6 VARIABLES CORRECTED R-SQUARED = .36038 RESIDUAL SUM SQUARE = 799,392,222
. STANDARD ERROR = 1,308.3 F-RATIO = 45.417 DEPENDENT MEAN = 3,485 DEGREES OF FREEDOM = 467 STANDARD ERROR AS % MEAN KWH = 37.542 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F CENTS /XWH -38.992 4.4740 .33142 .62865E-01' -8.7152 75.954 ROOMS 112.85 37.742 .11802 .17605 2.9900 8.9399 MICR0 OVEN 769.52 371.31 .79723E-01 .22733 2.0724 4.2950
' FRIDGE 356.46 69.441 .19631 .30815 5.1333 26.350 WASliER 360.25 48.527 .30252 .29638 7.4239 55.114 1
FREEZER 193.26 42.676 .17693 .10646 4.5285 20.507
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i ~~i , f .' ~. f' I i ( . i i _. 1 ! ) i i 1 71 .~l Table I-48 Consumers Power Individual Customer Cross-Section Model Regressions Including Average Price and Including Appliance Variables Consumption 500-1000 Kilowatthours/ Month EQUATION KWH = -4,524.7 + 1,633.6* CENTS /KWH + 103.92*R00MS + 296.43* FAMILY + 305.61* FRIDGE + 212.51* WASHER
+ 137.2* FREEZER + 236.42*ST0VE + 449.97*AC + 1,875.3* WATER
, R-SQUARED = .28217 400 OBSERVATIONS, 9 VARIABLES CORRECTED R-SQUARED = .2656 RESIDUAL SUM SQUARE = 938,596,226 STANDARD ERROR = 1,467.2 F-RATIO = 17.033 DEPENDENT MEAN = 8,382.5 DEGREES OF FREEDOM = 390 STANDARD ERROR AS % MEAN KWH = 17.504 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY. T-STATISTIC PARTIAL-F' CENTS /KWH 1633.6 664.88 .14242 .61923 2.4570 6.0370 ROOMS 103.92 50.302 .93418E-01 .77141E-01 2.0659 4.2679 FAMILY 296.43 53.316 .25525 .11917 5.5598 30.911 FRIDGE 305.61 98.122 .13655 .12633 3.1146 9.7005 WASHER 212.51 88.735 .11082 .93104E-01 2.3949 5.7354 FREEZER 137.20 43.056 .13997 .53564E-01 3.1866 10.154 ST0VE 236.42 94.100 .11320 .72413E-01 2.5124 6.3121 AC 449.97 139.11 .14278 .62269E-01 3.2347 10.463 WATER 1875.3 208.50 .54035 .31656 8.9942 80.896
- 4
., y g . . __, 7__ . p. _ . , , Table I-49 Consumers Power Individual Customer Cross-Section Model Regressions Including Average Price _and Including Appliance Variables Consumption over 1000 Kilowatthours per Month EQUATION KWH = 757.606 - 238,303* CENTS /KWH - 5,881.3* SPACE R-SQUARED = .59803 126 OBSERVATIONS, 2 VARIABLES
= .59149 RESIDUAL SUM SQUARE
= 9.3119E+09 CORRECTED R-SQUARED
= 8,700.9 F-RATIO = 91.946 STANDARD ERROR =
= 18,974 DEGREES OF FREEDOM 123 DEPENDENT MEAN STANDARD ERROR AS % MEAN KWH = 45.858 STANDARD ERROR BETA ELAS ICITY' T-STATISTIC PARTIAL-F VARIABLE COEFFICIENT
.23830E+06 18355. .83037 -38.573 -12.983 168.57 CENTS /KWH
-5881.3 2423.4 .15521 .35671 -2.4269 5.8896 SPACE
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Table I -50 Consumers Power Individual Customer Cross-Section Model Regressions Including Average Price ~ and Including Appliance Variables Income Less Than $4,000
. EQUATION KWil = - 3,092 - 164.06* CENTS /KWil + 863.15* FRIDGE + 1,684.4*DISHWASliER + 420.5* FREEZER
+ 2,012.7* WATER R-SQUARED = .55751 89 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .53085 RESIDUAL SUM SQUARE = 227,275,988 STANDARD ERROR = 1,654.8 F-RATIO = 20.915 DEPENDENT MEAN = 4,208.9 DEGREES OF FREEDOM = 83 STANDARD ERROR AS % MEAN KWH = 39.316 STANDARD VARIABLE C0 EFFICIENT ERROR BpETA_ ELASTICITY T-STATISTIC, PARTIAL-F CENTS /KWH -164.06 29.696 .40727 .17626 -5.5247 30.523 FRIDGE 863.15 200~.72 .31515 .58067 4.3003 18.492 DISHWASHER 1684.4 539.95 .23023 .42718 3.1196 9.7319 FREEZER 420.50 115.10 .28388 .20992 3.6534 13.347 WATER 2012.7 375.66 .41676 .G9312 5.3577 28.705
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Table I-51 1 Consumers Power Individual Customer Cross-Section Model Regressions Including Average Price and Including Appliance Variables Income $4,000-10,000 EQUATION KWH = - 22,403 - 91.249* CENTS KWH + 741.57* FAMILY + 9,037*MICR0 OVEN + 1,026.3* FREEZER l
- + 2,165.9* DRYER + 7,229.8*AC + 3,183.5* WATER R-SQUARED = .26764 266 OBSERVATIONS, 7 VARIABLES CORRECTED R-SQUARED = .24777 RESIDUAL SUM SQUARE =
1.6995E+10: STANDARD ERROR = 8,116.1 F-RATIO = 13.47 DEPENDEN1 MEAN = 6,739.7 DEGREES OF FREEDOM = 258
- STANDARD ERROR AS % MEAN KWH = 120.33 STANDARD VARIABL2 COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F CENTS KWH -91.2G 119.19 .41500E-01 .52418E-01 .76557 .58610 FAMILY 741.57 304.17 .13237 '
.32140 2.4380 5.9437 MICR0 OVEN 9037.0 3386.3 .14366 1.3711 2.6687 7.1220 FREEZER 1026.3 288.11 .19678 .39155 3.5621 12.688 DRYER 2165.9 1065.6 .11463 .45788 2.0326 4.1315 AC 7229.8 1252.9 .3D824 1.1614 5.7705 33.299 WATER 3183.5 1036.6 16848 .67302 3.0712
-a 9.4323 M
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Table 1-52 Consumers Power Individual Customer Cross-Section Model Regressions Including Average Price 4 and Including Appliance Variables Income $10,000-15,000 _
~ ._ _
EQUATION ) KWH = - 14,061 - 1,170.7* CENTS /KWH + 676.83* FAMILY + 2,798.7* MICRO-0VEN + 836.33* FRIDGE + 583.21* FREEZER (
+ 1,616.8* DRYER + 3.115.4* WATER + 9,199.3* SPACE R-SQUARED = .42303 263 OBSERVATIONS, 8 VARIABLES CORRECTED R-SQUARED = .40486 RESIDUAL SUM SQUARE = 5.6376E+09 STANDARD ERROR = 4,711.2 F-RATIO = 23.279 DEPENDENT MEAN = 7,623.7 DEGREES OF FREEDOM = 254 STANDARD ERROR AS % MEAN KWH = 61.796 1
STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F
< CENTS /KWH Y -1170.7 256.65 .-23714 .54728 -4.5614 20.807 i , FAMILY 676.83 211.48 .16004 .28659 3.2005 10.243 HICR0 OVEN 2798.7 1418.9 .95817E-01 .38386 1.9725 3.8909 FRIDGE 836.33 369.85 .11252 .36164 2.2613 5.1133 FREEZER 583.21 177.34 .17007 .20943 3.2887 10.815 DRYER 1616.8 641.99 .13258 .32093 2.5184 6.3423 4
WATER 3115.4 632.68 .25329 .58578 4.9242 23.248 SPACE 9199.3 1734.0 .25919 1.2434 5.3052 28.145 7' a am e , ym
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t' . I _ f' , I~~ . 'i _ i Table I-53 Consumers Power Individual Customer Cross-Section Model Regressions Including Average Price and Including Appliance Variables Income $15,000-25,000 EQUATION KWH = - 22,218 - 96,16* CENTS /KWH + 533.11*R00MS + 474.75* FAMILY + 1,113.7tFRIDGE + 1,223.1* WASHER
+ 677.34* FREEZER + 1,493.2* DRYER + 3,246.5* WATER + 8,695.l* SPACE R-SQUARED = .59378 285 OBSERVATIONS, 9 VARIABLES CORRECTED R-SQUARED = .58049 RESIDUAL SUM SQUARE = .3.5681E+09 STANDARD ERROR = 3,602.1 F-RATIO
= 44.665 DEPENDENT MEAN = 7,988.8 DEGREES OF FREEDOM = 275 STANDARD ERROR AS % MEAN KWH = 45.089 STANDARD VARIARLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F CENTS /KWH -96.160 13.294 .28838 .64283E-01 -7.2334 52.322 ROOMS 533.11 138.04 .16860 .41117 3.8620 14.915 FAMILY 474.75 132.67 .14118 .22228 3.5784 12.805 FRIDGE 1113.7 272.03 .17172 .47055 4.0940 16.761 WASilER 1223.1 265.48 .23666 .54148 4.6070 21.224 FREEZER 6/7.34 133.59 .21415 .24573 5.0705 25.710 DRYER 1493.2 497.69 .13404 .27282 3.0002 9.0015 WATER 3246.5 535.86 .27639 .54327 6.0585 36.706 SPACE 8695.1 1115.6 .32679 1.1381 7.7939 60.745 e g
i 1. . , i -i i F _. i . . I _ i Table I-54 - Consumers Power Individual Customer Cross-Section Model Regressions Including Average Price and including Appliance Variables Income Greater Than $25,000 EQUATION KWH = - 25,779 - 106.18* CENTS KWH + 799.39* FAMILY + 3,891.1* FRIDGE 2 + 1,337.7* WASHER + 3,757* DRYER
+ 2,268.8*AC + 13,508* SPACE R-SQUARED = .48621 97 OBSERVATIONS, 7 VARIABLES .
i CORRECTED R-SQUARED = .4458 RESIDUAL SUM SQUARE = 3.1768E+09 STANDARD ERROR = 5,974.5 F-RATIO = 12.032 DEPENDENT MEAN = 9,755.9 DEGREES OF FREEDOM = 89 STANDARD ERROR AS % MEAN KWH = 61.240 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F CENTS KWH -106.18 92.006 .96520E-01 .48190E-01 -1.1540 1.3318 FAMILY 799.39 372.17 .17208 .31762 2.1480 4.6137 FRIDGE 2 3891.1 1281.7 .23674 .55099 3.0360 9.2171 WASHER 1337.7 659.57 .18804 .47636 2.0281 4.1131. 0RYER 3757.0 1430.1 .23497 .58757 2.6271 6.9015 AC 2268.8 875.79 .20058 .30208 2.5905 6.7109 SPACE 13508. 2761.8 .37409 1.4560 4.8909 23.921
i i i - i Table I-55 Detroit Edison Individual Customer Cross-Section Model Regressions Including Average Price and Excluding Appliance Variables Total Sample EQUATION KWH = 15,776 - 5,095.2* CENTS /KWH + 265.52* INCOME + 502.49*R00MS + 464.88* FAMILY + 304.13* AGE HEAD R-SQUARED = .44834 711 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .44442 RESIDUAL SUM SQUARE = 1.0024E+10 STANDARD ERROR = 3,770.7 F-RATIO = 114.59 DEPENDENT MEAN = 7,044 DEGREES OF FREEDOM = 705 STANDARD ERROR AS % MEAN KWH = 53.530 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH -5095.2 351.61 .47501 -2.2529 -14.491 209.98 INCOME. 265.52 87.626 .10483 .20210 3.0301 9.1817 ROOMS 502.49 112.77 .14563 .41497 4.4559 19.855 FAMILY 464.88 99.466 .16681 .22732 4.6738 21.844 AGE HEAD 304.13 115.06 .88015E-01 .16900 2.6431 6.9860
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Table I-56
- Detroit Edison Individual Customer Cross-Sectien'Model Regressions Including Average Price
, and Excluding Appliance Variables Consumption Less Than 500 Kilowatthours/ Month EQUATION KWH = 10,428 - 2,276.4* CENTS /KWH + 92.47* INCOME + 173.12* FAMILY + 66.339* AGE HEAD R-SQUARED = .79137 342 OBSERVATIONS, 4 VARIABLES CORRECTED R-SQUARED = .78889 RESIDUAL SUM SQUARE = 132,286,595 STANDARD ERROR = 626.53 - F-RATIO = 319.57 DEPENDENT MEAN = 3,780 DEGREES OF FREEDOM = 337 STANDARD ERROR AS % MEAN KWH = 16.575
\
STANDARD
-VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F-CENTS /KWH -2276.4 81.989 .76426 -2.0594 -27.765 770.90 INCOME 92.470 19.260 .14203 .10837 4.8010 23.050 l FAMILY 173.12 27.302 .18673 .11785 6.3409 40.207 4
AGE HEAD 66.339 25.442 .77411E-01 .74512E-01 2.6075 6.7791 N
- i
i { '~ ' :~', , Table I-57. Detroit Edison Individual Customer Cross-Section Model Regressions Including Average Price and Excluding Appliance Variables Consumption 500-1000 Kilowatthours/ Month EQUATION KWH = 12,015 - 2,219.9* CENTS /KWH + 222.74* INCOME + 178.56*R00MS R-SQUARED = .18438 294 OBSERVATIONS, 3 VARIABLES CORRECTED R-SQUARED = .17594 RESIDUAL SUM SQUARE = 582,835,242 STANDARD ERROR = 1,417.7 F-RATIO = 21.853 DEPENDENT MEAN = 8,110.8 DEGREES OF FREEDOM = 290 STANDARD ERROR AS % MEAN KWH = 17.479 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH -2219.9 330.22 .35852 .78658 -6.7226 - 45.193 INCOME 222.74 57.233 .20711 .16842 3.8919 15.147 ROOMS 178.56 63.732 .14988 .13680 2.8017 7.8493
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l Table I-58 Detroit Edison Individual Customer Cross-Section Model Regressions Including Average Price and Excluding Appliance Variables Consumption Over 1,000 Kilowatthours/ Month EQUATION KWH = 46,958 - 10,947* CENTS /KWH R-SQUARED = .11381 75 OBSERVATIONS, 1 VARIABLES CORRECTED R-SQUARED = .10167 RESIDUAL SUN SQUARE = 3,7682E+09 STANDARD ERROR = 7,184.6 F-RATIO DEPENDENT HEAN = 17,747
. = 9.375 DEGREES OF FREEDOM = 73 STANDARD ERROR AS % HEAN KWH = 40.484 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY- T-STATISTIC PARTIAL F CENTS /KWH -10947 3575.3 .33735 -1.6460 -3.0619 9.3750
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Table I-59 Detroit Edison Individual Customer Cross-Section Model Regressions Including Average Price and Excluding Appliance Variables Income $0-5,000 EQUATION KWH = 13,535.- 3,031.4* CENTS /KWH + 470.19* FAMILY R-SQUARED = .64033 122 OBSERVATIONS, 2 VARIABLES CORRECTED R-SQUARED = .63428 RESIDUAL SUM SQUARE = 303,288,575 STANDARD ERROR = 1,596.4 F-RATIO = 105.93 DEPENDENT MEAN = 3,745.8 DEGREES OF FREEDOM = 119 STANDARD ERROR AS % MEAN KWH = 42.620 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH -3031.4 271.97 .67437 -2.8798 .-11.146 124.23 FAMILY 470.19 122.07 .23305 .26648 3.8518 14.837
l~ , . _ i i .
. . .i 1 Table I-60 Detroit Edison Individual Customer Cross-Section Model Regressions Including Average Price and Excludina Appliance Variables Income $5,000-10,000 F0llATION -
KWH = 16,575 - 3,885.2* CENTS /KWH + 364.12* FAMILY R-SQUARED = .54581 . 141 OBSERVATIONS, 2 VARIABLES , CORRECTED R-SQUARED = .53923 RESIDUAL SUM SQUARE = 545,877,882 STANDARD ERROR = 1,988.9 F-RATIO = 82.919 DEPENDENT MEAN = 5,360.4 DEGREES OF FREEDOM = 138 STANDARD ERROR AS % MEAN KWH = 37.103 STANDARD VARIABLE . COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWil -3885.2 328.92 .68558 -2.2810 -11.812 139.52 FAMILY 364.12 111.07 .19027 . 18885 3.2782 10.747
- i - :
1 - Table I-61 Detroit Edison Individual Customer Cross-Section Model Regressions Including Average Price and Excluding Appliance Variables
.,, Income $10,000-15,000 ~~ ~
EQUATION KWH = 30,531 - 9,231.1* CENTS /KWH + 893.09*R00MS R-SQUARED = .38602
.216 OBSERVATIONS, 2 VARIABLES 1
CORRECTED R-SQUARED = .38025 RESIDUAL SUM SQUARE = 3.9780E+09 STANDARD ERROR = 4,321.6 F-RATIO = 65.958 DEPENDENT MEAN = 7,684.7 DEGREES OF FREEDOM = 213 STANDARD ERROR AS % MEAN KWH = 56.236 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F 4 CENTS /KWH -9231.1 943.88 .54078 -3.6509 -9.7800 95.648 ROOMS 893.09 243.54 .20278 .67793 3.6672 13.448 3 - ~ . _ . -- mt - o,
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I I I' ; , 1 ,} Table I-62 Detroit Edison Individual Customer Cross-Section Model Regressions Including Average Price and Excluding Appliance Variables Income $15,000-25,000 -- EQUATION ' KWH = 30,991 - 8,061.9* CENTS /KWH + 355.34* FAMILY R-SQUARED = .38043 170 OBSERVATIONS, 2 VARIABLES CORRECTED R-SQUARED = .37301 RESIDUAL SUM SQUARE = 2.3495E+09 STANDARD ERROR = 3,750.8 F-RATIO = 51.271 DEPENDENT MEAN = 8,622.1 DEGREES OF FREEDOM = 167 STANDARD ERR 0R AS % MEAN KWH = 43.502 STANDARD VARIABLE COEFFICIENT ERROR 8 ETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH -8061.9 901.22 .56876 -2.7566 -8.9455 80.023 FAMILY 355.34 179.40 .12593 .16219 1.9807 3.9232
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l 1 Table I -63 Detroit Edison Individual Customer Cross-Section Model Regressions Including Average Price and Excluding Appliance Variables Income Over $25,000 EQUATION KWH = 40,061 - 12,541* CENTS /KWH + 1,010.7*R00MS R-SQUARED = .41958 62 OBSERVATIONS, 2 VARIABLES CORRECTED R-SQUARED = .39991 RESIDUAL SUM SQUARE = 1.5894E+09 STANDARD ERROR = 5,190.3 F-RATIO = 21.326 DEPENDENT MEAN = 10,804 DEGREES OF FREEDOM = 59 STANDARD ERROR AS % MEAN KWH = 48.041 STANDARD . VARIABLE COEFFICIENT ERROR 8 ETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH -12541 2662.7 .49741 -3.3508 -4.7099 22.183 ROOMS 1010.7 384.15 .27787 .64281 2.6311 6.9229 N
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Table I-64
. Detroit Edison Individual Customer Cross-Section Model .
Regressions Including Average Price and including Appliance Variables Total Sample EQUATION KWil = -22,278 - 1,243.4* CENTS /KWH + 279.28* INCOME + 481.53*R00MS + 645.16* FAMILY + 1,127.6* FREEZER
+ 942,.99* DRYER + 1,166.9*ST0VE + 936.86*AC + 4.340.9* WATER + 15,695* SPACE R-SQUARED = .68C91 711 OBSERVATIONS, 10 VARIABLES RESIDUAL SUM SQUARE = 5.7978E409 CORRECTED R-SQUARED
= .67635 149.37
=
= 2,877.9 F-RATIO STANDARD ERROR = 700
= 7,044 DEGREES OF FREEDOM DEPENDENT MEAN STANDARD ERROR AS % MEAN KWil = 40.587 STANDARD BETA ELASTICITY T-STATISTIC PARTIAL-T VARIABLE COEFFICIENT ERROR
.11592 .54979 -3.7569 14.114
., CENTS /KWil -1243.4 330.96
.21257 4.2138 17.756 j INCOME 279.28 65.276 85.947
.11026
.13956 .39766 5.6027 31.390 i ROOMS 481.53
.23150 .31548 8.8788 78.834 FAMILY 645.16 72.663
.10298 .20939 4.5348 20.565 FREEZER 1127.6 248.66
.81984E-01 .16889 3.4490 11.896 DRYER 942.99 273.41
.11481 .23999 4.9101 24.109 ST0VE 1166.9 237.66
.18079 .22241 7.8796 62.089 AC 936.86 118.90
.28821 .69599 10.814 116.94 WATER 4340.9 401.42
.30653 2.2600 13.870 192.37 SPACE 15695. 1131.6 a
l i' ~ i , i i . Table I-65 Detroit Edison Individual Customer Cross-Section Model Hegrs :sions Including Average Price
+
and including Appliance Variables _ _ _ Consumption Less Than 500 Kilowatthours/ Month 2 EQUATION KWH = -12,246 - 2,506* CENTS /KWH + 81.685* INCOME + 135.12* FAMILY + 70.167* AGE HEAD + 281.88* FREEZER
- 1,186.9* WATER R-SQUARED = .81703 342 OBSERVATIONS, 6 VARIABLES CORRECTED R-SQUARED = .81375 RESIDUAL SUN SQUARE = 116,014,389 STANDARD ERROR = 588.48 F-RATIO = 249.32 DEPENDENT MEAN = 3,780 DEGREES OF FREEDOM = 335 STANDARD ERROR AS % MEAN KWH = 15.568 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F CENTS /KWH -2506.0 89.223 .84135 -2.2671 -28.087 788.89 INCOME 81.685 18.172 .12546 .95729E-01 4.4952 20.207
[ FAMILY 135.12 26.286 .14574 .91976E-01 5.1401 26.421 AGE HEAD 70.167 24.125 .81878E-01 .78811E-01 2.9085 8.4594 I 281.88 FREEZER 89.994 .74334E-01 .85911E-01 3.1322 9.8107 WATER -1186.9 200.89 .16040 .32503 -5.9085 34.911 7* y
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l i- Table 1,66 Detroit Edison Individual Customer Cross-Section Model Regressions Including Average Price and Including Appliance Variables Consumption 500-1000 Kilowatthours/ Month EQUATION KWH = 8,865.8 - 1,827.1* CENTS /KWH + 158.67* INCOME + 202.44* FAMILY + 325.19* FREEZER + 636.37
- DRYER + 576.86*ST0VE + 296.2*AC R-SQUARED = .28881 294 OBSERVATIONS, 7 VARIA8LES CORRECTED R-SQUARED = .2714 RESIDUAL SUM SQUARE = 508,210,487 STANDARD ERROR = 1,333 F-RATIO = 16.592 DEPENDENT MEAN = 8,110.8 DEGREES OF FREEDOM = 286 STANDARD ERROR AS % MEAN KWH = 16.435 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F CENTS /KWH -1827.1 322.71 .29508 .64738 -5.6618 32.056 INCOME 158.67 55.177 .14753 .11997 2.8756 8.2691 FAMILY 202.44 48.495 .22038 .10281 4.1745 17.427 FREEZER 325.19 159.35 .10252 .56458E-01 2.0407 4.1646 DRYER 636.37 175.62 .18870 .10275 3.6237 13.131 ST0VE 576.86 170.75 .18485 .10523 3.3783- 11.413 AC 296.20 77.270 .19577 .67076E-01 3.8333 14.694 T
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j , Table I-67 Detroit Edison Individual Customer Cross-Section Model Regressions Including Average Price and Including Appliance Variables _ Consumption Greater Than 1000 Kilowatthours/ Month __, EQUATION KWH = -30,494 + 1,529.9* INCOME + 1,709.4*R00MS + 7,563.2* WATER + 13,438* SPACE R-SQUARED = .50702 75 OBSERVATIONS, 4 VARIABLES CORRECTED R-SQUARED = .47885 RESIDUAL SUN SQUARE = 2.0962E+09 STANDARD ERROR = 5,472.3 F-RATIO = 17.998 DEPENDENT MEAN = 17,747 DEGREES OF FREEDOM = 70 STANDARD ERROR AS % MEAN KWH = 30.836 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F INCOME 1529.9 566.62 .27178 .56783 2.7001 7.2905 ROOMS 1709.4 451.60 .36387 .66784 3.7852 14.328 WATER 7563.2 1567.3 .49861 .66484 4.8256 23.286 SPACE 13438. 2467.7 .48417 .81778 5.4454 29.653 ~ d'
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l i i Table I-68 Octroit Edison Individual Customer Cross-Section Model Regressions Including Average Price j and Including Appliance Variables Income $0_-5t000 i EQUATION KWH = 215.02 - 1,908.8* CENTS /KWH + 669.2* FAMILY + 1,503.7* DRYER + 2,920.l* WATER + 4,012.8* SPACE . R-SQUARED = .81056 122 OBSERVATIONS, 5 VARIABLES , CORRECTED R-SQUARED = .8024 RESIDUAL SUM SQUARE = 159,742,153 STANDARD ERROR = 1,173.5 F-RATIO = 99.267 4 DEPENDENT MEAN = 3,745.8 DEGREES OF FREEDOM = 116 , STANDARD ERROR AS % MEAN KW!! = 31.328 STANDARD
- VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F CENTS /KWH -1908.8 230.29 .42466 -1.8134 -8.2887 68.703 FAMILY 669.20 92.154 .33169 .37927 7.2618 52.733 DRYER 1503.7 342.93 .18783 .45080 4.3849 19.228 WATER 2920.1 468.31 .29034 .83707 6.2354 38.880 SPACE 4012.8 869.52 .19382 1.0888 4.6149 21.297 7
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, j i Table I-69 Detroit Edison Individual Customer Cross-Section Model_
Regressions Including Average Price and Including Appliance Variables Income $5,000-10,000 EQUATION KWH = -4,7128 - 2,792.2* CENTS /KWH + 297.22*R00MS + 388.55* FAMILY + 1,426* FREEZER + 886.77*ST0VE
+ 317.48*AC + 12,597* SPACE R-SQUARED = .77441 141 OBSERVATIONS, 7 VARIABLES CORRECTED R-SQUARED = .76253 RESIDUAL. SUM SQUARE
= 271,136,978 STANDARD ERROR = 1,427.8 F-RATIO = 65.222 DEPENDENT MEAN = 5,360.4 DEGREES OF FREEDOM = 133 STANDARD ERROR AS % MEAN KWH = 26.636 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL- F CENTS /KWH -2792.2 260.03 .49272 -1.6394 -10.738 115.30 ROOMS 297.22 110.85 .12058 .29061 2.6814 7.1897 FAMILY 388.55 85.786 .20304 .20152- 4.5292 20.514 FREEZER 1426.0 282.84 .22017 .34149 5.0552 25.555 ST0VE 886.77 259.84 ! .14711 .22761 3.4127 11.647 AC 317.48 142.67 .93887E-01 .90731E-01 2.2252 4.9517 SPACE 12597. 1471.1 .36206 2.3666 8.5626 73.318
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= _ _ _ _
Ii ; j i - , Table I-70 -- Detroit Edison Individual Customer Cross-Section Model l Regressions Including Average Price and Including Appliance Variables Income $10,000-15,000 EQUATION KWH = -23,001 - 2,847.4* CENTS /KWH + 519*R00MS + 373.08* FAMILY + 1.056.5* FREEZER + 1,730* DRYER
+ 741.97*AC + 5,598* WATER + 23,332* SPACE R-SQUARED = .73663 216 OBSERVATIONS, 8 VARIABLES i =
CORRECTED R-SQUARED = .72645 RESIDUAL SUM SQUARE 1.7064E+09 STANDARD ERROR = 2,871.1 F-RATIO = 72.371 DEPENDENT MEAN = 7,684.7 DEGREES OF FREEDOM = 207 STA!!DARD ERROR AS % MEAN KWH = 37.361 STANDARD VARIABLE COEFFICIENTS ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F CENTS /KWH -2847.4 775.07 .16681 -1.1261 -3.6738 13.497 ROOMS 519.00 175.55 .11784 .39396 2.9564 8.7403 FAMILY 373.08 119.64 .12497 .19891 3.1183 9.7239 1056.5 441.53 .90287E-01 .18204 2.3929 5.7259 f FREEZER DRYER 1730.0 498.59 .14075 .28661 3.4697 12.039 AC 741.97 225.58 .12181 .15690 3.2891 10.818 WATER 5598.5 700.97 .36314 .83646 7.9869 63.790 SPACE 23332. 2137.8 .40803 3.0643 10.914 119.12 l
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Table I-71 Detroit Edison Individual Customer Cross-Section Model } Regressions Including Average Price ! and Including Appliance Variables _Incpme $1L 000-25,000 ._ l I EQUATION KWH = -21,238 - 1,839.7* CENTS /KWH + 736.18* FAMILY + 1.578.l* FREEZER + 1.449.8*ST0VE + 815.58*AC
+ 4,074.2* WATER + 21,621* SPACE R-SQUARED = .71978 170 OBSERVATIONS, 7 VARIABLES CORRECTED R-SQUARED = .70767 RESIDUAL SUM SQUARE = 1.0626E+09 STANDARD ERROR = 2,561.1 '
F-RATIO = 59.445 DEPENDENT MEAN = 8,622.1 DEGREES OF FREEDOM = 162 STANDARD ERROR AS % MEAN KWH = 29.704 - STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F CENTS /KWH -1839.7 829.88 .12979 .62905 -2.2169 4.9145 FAMILY 736.18 127.15 .26090 .33601 5.7898 33.522 FREEZER 1578.1 439.80 .15841 .24547 3.5881 12.875' ST0VE 1449.8 432.02 .15344 .25420 3.3559 11.262 AC 815.58' 189.85 .18744 .18306 4.2959 18.455 WATER 4074.2 721.55 .29506 .53646 5.6465 31.883 ST0VE 21621. 1952.4 .49360 2.5371 11.074 122.64 7 M
- i, ! i' . . .
. , ; i , .
Table I-72
, Detroit Edison Individual Customer Cross-Section Model i Regressions Including Average Price and Including Appliance Variables
_. Income Greater Than $25,000 __ EQUATION KWil = 12,244 - 6,972.6* CENTS /KWH + 870.26*R00MS + 904.33* FAMILY + 1,169.7*AC + 5,007.2* WATER
.f R-SQUARED = .56465 5 62 OBSERVATIONS, 5 VARIABLES ,
CORRECTED R-SOUARED = .52578 RESIDUAL SUM SQUARE = 1.1922E+09 i STANDARD ERROR = 4.613.9 F-RATIO = 14.526
- DEPENDENT MEAN = 10,804 DEGREES OF FREEDOM = 56 STANDARD ERROR AS % MEAN KWH = 42.706 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F CENTS KWH -6972.6 2745.2 .27655 -1.8630 -2.5399 6.4512 ROOMS 870.26 373.58 .23925 .55346 2.3295 5.4265 FAMILY 904.33 431.44 .23040 .32942 2.0961 4.3935 AC 1619.7 476.16 .31241 .33853 . 3.4016 11.571
- WATER 5007.2 2072.1 .22275 .50832 2.4165 5.8393 1
I-78 a Table I-73 i. Cross Sectional Regressions for Detroit Edison Customers Using Both a Marginal and an Average Price for Electricity Total Sample
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I th-e o+ house
=
I-80 Table I 7.4 . Cross Sectional Ragressions for Detroit Edison Customers Using
. Both a Marginal and an Average Price for Electricity Income 50 to 5,000 Per Year v.c .a : : ..
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1 . . .. .. .
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I-81 1 Table I-74(Cont.) l l l 1
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54 9 % h w t-W
I-82 Table I-75 Cross Sectional Regressions for Detroit Edison Customers Using Both a Marginal and an Average Price for Electricity Income 55,001 to 10,000 Per Year C..'.. .b.
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I-83 Table I-75 (Cont.) s , 4 - # . e, , s -r ,- F r- e I- . .. 4- .. . . ..
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i
Table I-76 Cross Sectional Regressions for Detroit Edison Customers Using Both a Marginal and an Average Price for Electricity Income $10,000 to 15,000 Per Year ,v , I s e. s . s.
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- I-85 l Table I-76 (Cont. )
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I-86 Table I -77
' Cross Sectional Regressions for Detroit Edison Customers Using
< Both a Marginal and an Average Price for Electricity
- ' Income 515,001 to 25,000 Per Year G
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Table I-77 rone 9 e ( f 4
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.he i
soe h
Table I-78 Cross Sectional Regressions for Detroit Edison Customers Using Both a Marginal and an Average Price for Electricity Income Greater Than $25,000 Per Year
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l I-89 Table I-78 (Cont.) . 4
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I-90 Table 1 79
, Cross Sectional Regressions for Detroit Edison Customers Using Both a Marginal and an Average Price for Electricity usage Less Than 500 kWh Per Month e
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. Cross Sectional Regressions for Detroit Edison Customers Using
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e 4 4 .. 6 APPENDIX J APPLIAllCE SATURATI0fl REGRESSIONS ( LM es L
J-1
- APPENDTX J APPLIANCE SATURATION REGRESSIONS Detailed output from regressions using either appliance saturation levels or appliance ownership variables as dependent variables are reported. The first set of seventy two tables are concerned with regional time-series re-
_ gressions for electric space heating, electric water heating, and air condi-
~
tioning. 'The second grouping of twelve tables report regression results utilizing individual customer data for Detroit Edison where dummy variables indicating appliance ownership _ are used as dependent variables. The time-series regressions use the percentage of customers owning the particular appliance as ti,2 dependent variable. When these regressions were run they were meant to be the first part of an analysis aimed at separating appliance ownership and electricity use decisions. However, the results that were obtained, especially for water heating, were of such a nature as to
~
/ cast serious doubt on the accuracy of the procedure. The best regression results obtained leave a lot to be explained as to why the saturation level -
is what it is. Relying on these specifications to appropriately separate the appliance buying decision from other electricity usage does not seem justifiable . To simplify interregional comparison, the identical set of indepen-dent variables was used for all regressions reported, regardless of the statis-tical significance of the coefficients. Income and the price of electricity (based on marginal price at average consumption) were included because they are the focus of this study. Degree days were included because the three appliances
^
for which regressions were'run are expected to be weather sensitive -- less so with water heating than with the'other two. Price variables for natural gas and fuel oil were also included as representing competitive fuels. Fuel 1 N9 *** , - - , - , 4-,. ,.y,f wr% . ., - - w ,- , - ,--- ., .- , vv.4m - . -
J-2 ; I oil is especially appropriate for space heating, but not so much so for the
~~~
other two. Its inclusion in the other appliance equations does not present ' a serious problem in interpretation. These equations could be made to have somewhat better statistical properties by deleting some variables, but the
. changes would not be major. Including too many variables can only increase the R2 and decrease the standard error.
~
Large favorable changes in both of these statistics would be required to justify continuing investigation along these lines. Deleting variables will not bring about such changes. The equations utilizing individual customer data, reported in Tables J-73 through J-84, are further divided into two types of specifications -- linear and logarithmic. The independent variables used for a given appliance are the same so the linear and logarithmic specification can be directly compared, except for FREEZERS. One of the variables used for that equation, TEENS, can take a value of zero, for which the logarithm is - . All these observations were excluded so the' logarithmic case has only 298 obser- - vations and therefore is not readily comparable. The choice of independent variables for each appliance.was based upon our opinion as to which variables might be important. Other regressions deleting some of the less significant variables have been run, but no great improvements in the equation statistics were noted. The most telling statistic in this case is the standard error as a percent of mean of the dependent variable. In all cases this number is large. The usefulness of these equations with such large problems is very small. Therefore the equations reported include all variables so that it is clear what has been considered. The definitions of two of the variables he
- . . , - . _ _ _ . _ . -__ ,. -, ,y ---*___--,__._y _,y_..-,_g-,,m_ wy,,,,e ,ee-- -. . . , - -.-- ._.-.7 -,p.._,--, . - , , - ,-
3-3 are not obvious. CENTS /KWH is average price calculated by dividing total dollars billed for the year by total consumption for the year. TYPE HOUSE - relates to home, condiminium, or mobile homes, etc. The other variables are all self-explanatory. The tables in this appendix are indexed below. Individual Customer Acoliance Ownership Ecuations Table Index Linear Logarithmic Apoliance Specification Specification Electric space heating 73 79 Electric water heating 74 80 Air Conditioning 75 81
$ Electric stove 76 82 Freezer 77 83 ,
Electric dryer 78 84 In addition to the regression analysis concerning appliance saturatica levels, a simple comparison was done between 19i0 census data and the 1970 Consumers Power appliance survey. This compa-ison, given in Table J-85, indicates the census data and Consumers Power data are compatible. Division 4 data represents Pontiac and measurement difference accounts for the disparity. 1 .L r b-W vw w, ._._ .._,.. -_, , , . - -
l i ; .. , ; Table J-1 Appliance Saturation -Time Ser)*s Electric Space Heating
~ . . . . . _ .
CENTRAL . EQUATION . SPACE HEAT = 2.7887 .22205* ELECTRICITY - 7.2328* GAS + .34493* FUEL OIL + .0022542* INCOME .00015507* DEGREE DAYS R-SQUARED = .81264 25 OBSERVATIONS, 5' VARIABLES 4 CORRECTED R-SQUARED = .76334 RESIDUAL SUM SQUARE = 9.6073 i STANDARD ERROR = .71109 F-RATIO = 16.482 , DEPENDENT MEAN = 1.192 DEGREES OF FREEDOM = 19 j STANDARD ERROR AS % MEAN SPACE HEAT = 59.655 STANDARD
; VARIABLE COEFFICIENT ERROR BETA -ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .22205 1.9396 .50674E-01 .40003 .11448 .13106E-01 1 GAS -7.2328 2.5590 .549415 -7.5809 -2.8264 7.9887 FUEL OIL .34493 .21645 .41631 3.3662 1.5936 2.5395 INCOME .22542E-02 .12333E .61990 4.1675 1.8277 3.3406
. DEGREE DAYS .15507E-03 .53006E-03 .30588E-01 .89232 , .29255 .85584E-01 Cs e e
; 4 -
i , 2 . Table J-2 Appliance Saturation Time Series Electric Space Heating BATTLE CREEK . EQUATION SPACE HEAT = - 3.4121 + .90274* ELECTRICITY - 3.5039* GAS + .14679* FUEL OIL + .0023149* INCOME .00016856* DEGREE DAYS R-SQUARED = .92575 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .90621 RESIDUAL SUM SQUARE = 2.4013 STANDARD ERROR = .35551 F-RATIO = 47.377 DEPENDENT MEAN = 1.02 DEGREES OF FREEDOM = 19 STANDARD RROR AS % MEAN SPACE HEAT = 34.853 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .90274 .87935 .25941 1.9006 1.0266 1.0539 GAS -3.5039 1.3505 .36244 -4.2919 -2.5946 6.7319 FUEL OIL .14679 .11461 .22309 1.6741 1.2808 1.6404 INCOME .23149E-02 .40634E-03 1.0307 6.1705 5.6968 32.454 DEGREE DAYS .16856E-03 .26348E-03 .45368E-01 -1.1081 - 63975
, .40928 .
% ' u?,
g c , .-~, i , Table J-3 Appliance Saturation Time Series Electric Space Heating NORTHEAST EQUATION SPACE HEAT = -1.27 + 1.0038* ELECTRICITY - 5.3626* GAS + .20114* FUEL OIL + .0024278* INCOME .00026656* DEGREE DAYS R-SQUARED = .86605 25 OBSERVATIONS, 5 VARIA8LES CORRECTED R-SQUARED = .8308 RESIDUAL SUM SQUARE = 5.6257 STANDARD ERROR = .54414 F-RATIO = 24.568 DEPENDENT MEAN = 1.036 DEGREES OF FREEDOM = 19
~ ~ ~ ~ ~
STANDARD ERROR AS % MEAN SPACE HEAT = 52.523 ~ STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY 1.0038 1.5120 .25313 2.0807 .66387 .44073 GAS- -5.3626 2.0120 .48676 -6.4670 -2.6653 7.1036 FUEL OIL .20114 .18136 .26825 2.2585' 1.1091 1.2301 INCOME .24278E-02 .77621E-03 .94909 6.1197 3.1277 9.782G DEGREE DAYS .26656E-03 .35788E-03 .89176E-01 -1.7660 .74482 .55476 b 4
e t ,. ! . , i i Table J-4 Appliance Saturation Time Series Electric Space Heating FLINT EQUATION
- SPACE HEAT = .87802
.68548* ELECTRICITY - 1.9117* GAS + .1679* FUEL OIL + .00076445* INCOME __.0001128* DEGRE R-SQUARED = .90943 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .8856 RESIDUAL SUM SQUARE = .82538 STANDARD ERROR = .20842 F-RATIO = 38.159 DEPENDENT MEAN = .584 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 35.689 4
STANDARD j VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .68548 .51725 .37107 -2.5206 -1.3252 1.7562
- GAS -1.9117 .72230 .37251 -4.0899 -2.6467 7.0052 FUEL OIL .16790 .61763E-01 .48069 3.3444 2.7185 7.3900 INCOME .76445E-03 .25576E-03 .63708 4.1248 2.9890 8.9340
. DEGREE DAYS .11280E-03 .14915E-03 .60452E-01. - -1.3622 .75625 .57191
~
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Table J-5 Appliance Saturation Time Series Electric Space Heating GRAND RAPIDS EQUATION
- SPACE HEAT = .43425 .38432* ELECTRICITY .50209* GAS + .14912* FUEL OIL + .0006379* INCOME .00017586* DEGREE DAYS R-SQUARED = .84323 25 OBSERVATIONS, 5 VARIABLES -
i CORRECTED R-SQUARED = .80198 RESIDUAL SUM SQUARE = .41599
- STANDARD ERROR = .14797 F-RATIO = 20.44 DEPENDENT MEAN = .484 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 30.572 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .38432 .41977 .38555 -1.7052 .91554 .83821 GAS .50209 .60663 .27859 -1.3425 .82768 .68505 FUEL OIL .14912 .48111E-01 .79121 3.5841 3.0996 9.6075 INCOME .63790E-03 .21404E-03 .90533 3.8232 2.9803 8.8821 ,
DEGREE DAYS .17586E-03 .91765E-04 .22231- -2.4625 -1.9164 3.6725 c b -- -
; i ; , , , ; , 1 . ; . . ; ! i i i Table J-6 Appliance Saturation Time Series Electric Space Heating JACKSON EQUATION SPACE HEAT = - 3.5144 + .58429* ELECTRICITY - 2.9109* GAS + .15593* FUEL OIL + .0016332* INCOME + .000072207* DEGREE DAYS R-SQUARED = .91644 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .89445 RESIDUAL SUM SQUARE = 1.7861
' STANDARD ERROR = .3066 F-RATIO = 41.676 DEPENDENT MEAN = .832 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 36.851 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .58429 .75318 .20653 1.5081 .77577 .60181 GAS -2.9109 1.1335 .37038 -4.3712 -2.5682 6.5957 FL'EL OIL .15593 .95757E-01 .29150 2.1801 1.6284 2.6516 INCOME .16332E-02 .31926E-03 1.0248 5.3142 5.1156 26.169 DEGREE DAYS .72207E-04 .20728E-03 .25159E-01 .59286 .34836 .12135 4 c e e
g- ; s , Table J-7 . Appliance Saturation Time Series Electric Space Heating KALAMAZOO EQUATION SPACE HEAT = - 2.778 + .084904* ELECTRICITY - 1.1037* GAS + .15429* FUEL OIL + .0011717* INCOME .000073116* DEGREE DAYS R-SQUARED = .87893 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .84707 RESIDUAL SUM SQUARE = .87382 STANDARD ERROR = .21445 F-RATIO = 27.587 DEPENDENT MEAN = .636 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 33.719 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .84904E-01 .55758 . 51646E-01 GAS -1.1037 .83224 .24167 -2.1682 -1.3262 1.7589 FUEL OIL .15429 .66322E-01 .49637 2.8221 2.3264 5.4121 INCOME .11717E-02 .29397E-03 1.1129 5.1454 3.9857 15.886 DEGREE DAYS .73116E-04 .17746E-03 .37654E-01 .71797 .41203 .16977 c
^
b o
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Table J-8 Appliance Saturation Time Series ( Electric Space Heating
. LANSING EQUATION SPACE HEAT = .65065 .6923* ELECTRICITY - 6.2096* GAS + .32013* FUEL OIL + .0019427* INCOME + .0001788* DEGREE DAYS R-SQUARED = .89162 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .8631 RESIDUAL SUM SQUARE = 7.6208 STANDARD ERROR = .63332 F-RATIO =.31.261 DEPENDENT MEAN = 1.584 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 39.982 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .69230 1.7144 .13492 .93855 .40382 .16307 GAS -6.2096 2.4213 .43561 -4.8978 -2.5645 6.5768 FUEL OIL .32013 .21012 .32997 2.3510 1.5236 2.3214 INCOME .19427E-02 .73485E-02 .666,93 3.2904 2.6437 6.9893 DEGREE DAYS .17888E-03 .46973E-03 .38754E-01 .78411 .38081 .14502
= i'
~~
7_..
- -; , , -; r Table J-9
~
Appliance Saturation Time Series Electric Space Heating MUSKEGON - EQUATION SPACE HEAT = .26284 + .39926* ELECTRICITY - 2.8645* GAS + .053004* FUEL OIL + .0012879* INCOME + .000015684* DEGREE DAYS R-SQUARED = .91511 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .89277 RESIDUAL SUM SQUARE = 1.6093
= .29103
~
STANDARD ERROR F-RATIO = 40.965 DEPENDENT MEAN = .836 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 34.812 ' STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .39926 .87256 .14985 1.0256 .45757 .20937 GAS -2.'8645 1.0537 .59464 -4.4340 -2.7186 7.3906 FUEL OIL .53004E-01 .94489E-01 .10522 .73754 .56096 .31468 INCOME .12879E-02 .47736E-03 .59609 3.8582 2.6979 - 7.2788 - DEGREE DAYS .15684E-04 .18065E-03 .74178E-02 .12715 .86817E-01 .75372E-02 c e
's
- i. i . l~ f . i i
Table J-10 Appliance Saturation Time Series
- Electric Space Heating SAGINAW EQUATION SPACE HEAT = - 3.1303 + .039452* ELECTRICITY - 1.5131* GAS + .18653* FUEL OIL + .0011506* INCOME + 4.7488E-06* DEGREE DAYS
! R-SQUARED = .92477 25 OBSERVATIONS, 5 VARIABLES 1 CORRECTED R-SQUARED = .90497 RESIDUAL SUM SQUARE = .70739 STANDARD ERROR = .19295 F-RATIO = 46.709 DEPENDENT MEAN =. 548 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 35.210 STANDARD VARIABLE COEFFICIENT ERROR 8 ETA ELASTICITY T-STAT',STIC . PARTIAL F ELECTRICITY .39452E-01 .45305 .21026E-91 .15460 .87081E-01 .75830E-02 GAS -1.5131 .70184 .29028 -3.4497 -2.1559 4.6481 FUEL OIL .18653 .58056E-01 .52577 3.9597 3.2130 10.323 INCOME .11586E-02 .17918E-03 1.0936 5.9859 6.4663 41.813 DEGREE DAYS .47488E-05 .13266E-03 .23670E-02 .61797E-01 .35798E-01 .12815E-02 z' S w
- e
L , , - ' ~ Table J-11 Appliance Saturation Time Series Electric Space Heating a.
, [..
NORTHWEST ' EQUATION SPACE HEAT = - 9.3768 + 4.5949* ELECTRICITY - 12.706* GAS + .25181* FUEL OIL + .0050193* INCOME + .00059271* DEGREE DAYS R-SQUARED = .94578 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .93151 RESIDUAL SUM SQUARE = 12.2 STANDARD ERROR = .8013 F-RATIO = 66.284
. DEPENDENT MEAN = 2.64 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 30.352 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY 4.5949 2.5351 .50059 3.7376 1.812 3.2851 GAS -12.706 3.3955 .76562 -6.2281 -3.7419 14.001 FUEL OIL .25181 .26500 .14509 1.1096 .95024 9.0295 INCOME .50193E-02 .15558E-02 .78238 4.1152 3.2261 10.408 DEGREE DAYS .59271E-03 .50122E-03 .66066E-01 1.8176 1.1825 1.3984 c_s ..
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1 : - Table J-12 Appliance Saturation Time Series Electric Space Heating HURON EQUATION SPACE HEAT = 2.8167 .94142* ELECTRICITY - 2.636* GAS + .34688* FUEL OIL + .0012604* INCOME .00037463* DEGREE DAYS R-SQUARED = .91734 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = . 89559 RESIDUAL SUN SQUARE = 3.1539 STANDARD ERROR = .40742 F-RATIO = 42.171 DEPENDENT MEAN = 1.032 DEGREES OF FREEDOM = 19 STANDARD'Eh20R AS % MEAN SPACE HEAT = 39.479
. STANDARD i VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F 1
ELECTRICITY .94142 .69498 .50326
-2.4855 -1.3546 1.8349 GAS -2.6360 1.6636 .25104 -3.1913 -1.5846. 2.5108 FUEL OIL .34688 .16407 .48536 3.9100 2.1142 4.4698 INCOME .12604E-02 .49327E-03 .67120 2.5289 2.5553 6.5294 DEGREE DAYS .37463E-03 .26411E-03 .13149 -2.4916 -1.4184 2.0120
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I i i i . i- i . - Table J-13 Appliance Saturation Time Series Electric Space Heating . LAPEER EQUATION SPACE HEAT = 19.009 - 4.2576* ELECTRICITY - 7.1624* GAS + 1.0784* FUEL OIL .00082055* INCOME .0010637* DEGREE DAYS R-SQUARED = .88147 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .85027 RESIDUAL SUM SQUARE = 9.7271 STANDARD ERROR = .71551 F-RATIO = 28.258 DEPENDENT MEAN = 1.456 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 49.142 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -4.2576 1.2143 -1.5519 -7.9671 -3.5061 12.292 GAS -7.1624 2.4314 .46510 -6.1459 -2.9458 8.6778 FUEL OIL 1.0784 .23990 1.0289 8.6160 4.4953 20.208 INCOME .82055E-03 .10588E-02 .22887 -1.4062 .77498 .60060 DEGREE DAYS .10637E-02 .48113E-03 .18999 -5.1526 -2.2109 4.8881
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I i ! . , ; -s I 6. , s , Tabl e 'J-1'4 Appliance Saturation Time Series Electric Space Heating
. SANILAC I
EQUATION . . SPACE HEAT = - 1.1017 + .018002* ELECTRICITY - 5.424* GAS + .57207* FUEL OIL + .0025233* INCOME .00023968* DEGREE DAYS R-SQUARED = .88559 l 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .85548 RESIDUAL SUM SQUARE = 6.979 ' STANDARD ERROR = .60607. F-RATIO = 29.414 DEPENDENT MEAN = 1.64 DEGREES OF FREEDOM = 19 STANDARD EP.R0R AS % MEAN SPACE HEAT = 36.955 i STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .18002E-01 1.5269 .76111E-Q2 .29908E-01 n11790E-01 .13901E-03 GAS -5.4240 2.6209 .68458 -4.7906 -2.0695 4.2830 FUEL OIL .57207 .22863 .63306 4.0578 2.5021 6.2606 INCOME .25233E-02 .11343E-02 .80849 3.3975 2.2246 4.9488 DEGREE DAYS .23968E-03 .44887E-03 .50595E-01 -1.0227 .53396 .28511 i'
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. Table J-15 Appliance Satiuration Time Series Electric Space Heating ST. CLAIR EQUATION SPACE HEAT = .29787 .41493* ELECTRICITY - 3.9246* GAS + .59666* FUEL OIL + .0013496* INCOME .00044955* DEGREE DAYS - R-SQUARED = .80488 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .75354 RESIDUAL SUM SQUARE = 5.8821 STANDARD ERROR = . 5564 F-RATIO = 15.675 DEPENDENT MEAN = 1.088 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 51.140 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .41493 1.3216 .24954 -1.0391 .31396 .98574E-01 GAS -3.9246 2.5011 .70462 -5.2250 -1.5692 2.4623 FUEL OIL .59666 .20754 .93923 6.3794 2.8749 8.2652 INCOME .13496E-02 .79629E-03 .70375 3.2630 1.6948 2.8725 DEGREE DAYS .44955E-03 .44074E-03 .11497 -2.6521 -1.0200 1.0404
I . t [ i - m Table J-16 Appliance Saturation Time Series Electric Space Heating TUSCOLA EQUATION SPACE HEAT = 1.0413
.10173* ELECTRICITY - 4.6803* GAS + .3625* FUEL OIL + .0020988* INCOME .00036599* DEGREE DAYS R-SQUARED = .93601 .
25 OBSERVATIONE,.5 VARIABLES CORRECTED R-SQUARED = .91917 RESIDUAL SUM SQUARE = 2.9114 STANDARD ERROR = .39145 F-RATIO = 55.586 DEPENDENT MEAN = 1.208 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 32.404 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .10173 .76640 .49801E-01 .22945 .13274 .17620E-01 GAS -4.6803 1.4458 .40816 -4.8406 -3.2371 10.479 FUEL OIL .36250 .15888 .46449 3.4908 2.2816 5.2058 INCOME .20988E-02 .58154E-03 .92664 3.7967 3.6090 13.025 DEGREE DAYS .36599E-03 .25653E-03 .11764 -2.0795 -1.4267 2.0354 H c_. _ a
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Table J-17 . Appliance Saturation Time Series Electric Space Heating 0AkLAND 1 EQUATION SPACE HEAT = 5.8342 - 1.0999* ELECTRICITY - 2.2036* GAS + .24477* FUEL OIL .00021523* INCOME .00023412* DEGREE DAYS i R-SQUARED = .84294 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .80161 RESIDUAL SUM SQUARE = .8858 STANDARD ERROR = .21592 F-RATIO = 20.395 DEPENDENT MEAN = .5 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 43.184 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -1.0999 .32024 -1.4809 -5.9585 -3.4346 11.796 i GAS -2.2036 .75028 .52453 -5.4797 -2.9370 8.6263 FUEL OIL .24477 .74860E-01 .82803 5.6614 3.2698 10.691
, INCOME .21523E-03 .20431E-03 .34630 -1.7908 -1.0535 1.1098 DEGREE DAYS .23412E-03 .15174E-03 .15770 -3.1008 -1.5429 2.3806 lt 1
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I , t 1._, I. I i . .- 1 i . . 1 i . m ' Table J-19 1 Appliance Saturation Time Series Electric Space Heating
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4 MACOMB EQUATION SPACE HEAT = .97858 .80984* ELECTRICITY - 1.5199* GAS + .2595* FUEL OIL + .00061305* INCOME .00017297* DEGREE DAYS R-SQUARED = .90815 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .88398 RESIDUAL SUM SQUARE = 1.0122 STANDARD ERROR = .23081 F-RATIO = 37.573 DEPENDENT MEAN = .82 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 28.147
- STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .80984 .38725 .80555 -2.6908 -2.0912 4.3733 l GAS -1.5199 .82938 .26933 -2.3158 -1.8326 3.3585 FUEL OIL .25950 .86414E-01 .67563 '3.6813 3.0381 9.2303 INCOME .61305E-03 .31717E-03 .47457 2.4859 1.9329 3.7360 DEGREE DAYS .17297E-03 .17318E-03 .73166E-01 -1.3539 .99879 .99758 a
b
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;l Table J-19 Appliance Saturation Tir.e Series
. Electric Space Heating WASHTENAW i EQUATION SPACE HEAT = 1.1067 + .55678* ELECTRICITY - 4.9268* GAS + .035457* FUEL OIL + .00077638* INCOME + .00027454* DEGREE DAY R-SQUARED = .94724 25 GBSERVATIONS,' 5 VARIABLES CORRECTED R-SQUARED = .93335 RESIDUAL SUM SQUARE = 1.2864 STANDARD ERROR = .26021 F-RATIO = 68.222 DEPENDENT MEAN = 948 DEGREES OF FREEDOM = 19 I STANDARD ERROR AS % MEAN SPACE HEAT = 27.448 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .55678 .65420 .37233 1.6002 .85108 .72434 GAS -4.9268 1.2454 .90185 -6.7254 -3.9560' 15.650 FUEL OIL .35457E-01 .11618 .62062E-01 .43509 .30518 .93137E-01 INCOME .77638E-03 .38092E-03 .46922 2.6474 2.0382 4.1541.
DEGREE DAYS .27454E-03 .23490E-03 .85393E-01 1.8754 1.1688 1.3660 c
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Table J-20
- Appliance Saturation Time Series Electric Space Heating LENAWEE -
EQUATION SPACE HEAT = - 1.7483 - 1.0431* ELECTRICITY - 3.5971* GAS + .5745* FUEL OIL + .001674* INCOME .00013836* DEGREE DAYS r R-SQUARED = .84543 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .80475 RESIDUAL SUM SQUARE = 7.0206 STANDARD ERROR = .60787 F-RATIO = 20.784 DEPENDENT MEAN = .98 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 62.028 4 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -1.0431 1.0729 .51109 -2.9001 .97228 .94532 l GAS -3.5971 2.1829 .31397 -4.5858 -1.6478 2.7154 FUEL'0IL .57450 .22851 .73676 6.8193 2.5141 6.3205 INCOME .16740E-02 .85448E-03 .69417 4.4149 1.9591 3.8379 i DEGREE DAYS .13836E-03 .42121E-03 .33070E-01 .96442 .32847 .10789.
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Table J-21 Appliance Saturation Time Series Electric Space Heating LIVINGSTON t EQUATION SPACE HEAT = 9.5904 - 2.2325* ELECTRICITY - 3.6228* GAS + .44112* FUEL OIL .00043304* INCOME .00028161* DEGREE DAYS R-SQUARED = .92165 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .90103 RESIDUAL SUM SQUARE = 1.9104 STANDARD ERROR = .31709 F-RATIO = 44.699 DEPENDENT MEAN = .948 DEGREES OF FREEDOM = 19 STANDARD ERROR'AS % MEAN SPACE HEAT = 33.449 . STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F
~
ELECTRICITY -2.2325 .42693 -1.4929 -6.4163 -5.2293 27.345 GAS -3.6228 1.1249 .43158 -4.7748 -3.2206 10.372 . FUEL OIL .44112 .10111 .77211 5.4129 4.36'7 2 19.033 INCOME .43304E-03 .30771E-03 .25568 -1.3236 -1.4073 1.9805 DEGREE DAYS .28161E-03 .22961E-03 .93531E-01 -2.0149 -1.2264 1.5041 a*6'
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Table J-22 , Appliance Saturation Time Series Electric Space lieating INGHAM ) EQUATION SPACE HEAT = .27093 { .75514* ELECTRICITY - 2.5004* GAS + .27699* FUEL OIL + .0010566* INCOME - 5.0135E-06* DEGREE DAYS R-SQUARED = .93788 25 OBSERVATIONS, 5 VARIABLES - CORRECTED R-SQUARED = .92153 RESIDUAL SUN SQUARE = 1.5147 STANDARD ERROR = .28235 F-RATIO = 57.37 $ DEPENDENT MEAN = .948 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 29.783 --- --
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STANDARD . VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F ELECTRICITY .75514 .49591 .50498 -2.1703 -1.5227 2.3187 GAS -2.5004 1.0240 .29787 -3.2953 -2.4418 5.9622 FUEL OIL .27699 .10361 .48482 3.3989 2.6733 7.1465 INCOME .10565E-02 .39831E-03 .60348 3.3889 2.6524 7.0352 DEGREE DAYS .50135E-05 .21175E-03 .16275E-02 .36425E-01 .23677E-01 . 56059E-03 t Un
g [ ;- r Table J-23
- Appliance Saturation Time Series l Electric Space Heating l
b MONR0E EQUATION SPACE HEAT = - 8.9436 - 1.6482* ELECTRICITY + 4.7982* GAS + .19411* FUEL OIL + .0024279* INCOME .000081021* DEGREE DAYS R-SQUARED = .9012 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .8752 RESIDUAL SUM SQUARE = 4.4873 STANDARD ERROR = .48598 F-RATIO = 34.663 DEPENDENT MEAN = .98 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 49.590 STANDARD . VARIABLE C0 EFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -1.6482 .94529 .78202 -4.5556 -1.7436 3.0401 GAS 4.7982 1.6459 .89523 6.2039 2.9152 8.4983 FUEL OIL .19411 .22332 .23139 2.2906 .86919 .75550 INCOME .24279E-02 .66948E-03 1.0979 6.7248 3.6266 13.152 DEGREE DAYS .81021E-04 .36780E-03 .18061E-01 .53745 .22029 .48526E-01 c. h
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] Table J-24 . Appliance Saturation Time Series Electric Space Heating WAYNE i i EQUATION SPACE HEAT = .13138 + .20413* ELECTRICITY - 1.658* GAS + .025027* FUEL- OIL + .00022685* INCOME + .000098844*0EGREE DAYS l 1 R-SQUARED = .79614 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .74249 RESIDUAL SUM SQUARE = .24088 STANDARD ERROR = .1126 F-RATIO = 14.84 DEPENDENT MEAN = .244 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN SPACE HEAT = 46.146 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F 4 ELECTRICITY .20413 .27970 .60048 2.2661 .72982 .53264 GAS -1.6580 .65219 .97360 -7.5073 -2.5422 6.4627 FUEL OIL .25027E-01 .56589E-01 .18496 1.1862 .44226 .19559 INCOME .22685E-03 .13151E-03 .62921 3.0180 1.7249 2.9753 i DEGREE DAYS .98844E-04 .10700E-03 .12137 2.5755 .923/9 .85338 i g
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p-, p- 3 ,; o Table J-25 a Appliance Saturation Time Series Electric Water Heating -l ]:- CENTPAL - d EQUATION
]
- i WATER HEAT = 74.008 + 12.191* ELECTRICITY + .0074316* INCOME - 28.434* GAS - 2.7907* FUEL OIL .0016043* DEGREE DAYS S
R-SQUARED = .93162 20 OBSERVATIONS, 5 VARIABLES - CORRECTED R-SQUARED = .90719 RESIOUAL-SUM SQUARE = 61.893 STANDARD ERROR = 2.1026 F-RATIO = 38.145 DEPENDENT MEAN = 39.095 DEGREES OF FREEDOM = 14 STANDARD ERROR AS % MEAN WATER HEAT = 5.3782 STANDARD . VARIABLE . ' COEFFICIENT ERROR 8 ETA ELASTICITY T-STATISTIC PARTIAL-F ELECTRICITY 12.191 6.6328 .49730 .63681 1.8380 3.3781 INCOME .74316E-02 .39960E-02 .39479 .43964 1.8598 3.4587 GAS -28.434 11.285 .48235 .89111 -2.5197 6.3489 FUEL OIL -2.7907 .66019 .65923 .29572 -4.2272 17.869 1 DEGREE DAYS .16043E-02 .19438E-02 .58577E-01 28264 .82536 .68122 M
y i ! . . . .~ . . i i x~, ; 4 Table J-26 Appliance Saturation Time Series Electric Water Heating n BATTLE CREEK EQUATION WATER HEAT = 56.543 + 6.3039* ELECTRICITY + .0017648* INCOME - 18.185* GAS .61107* FUEL OIL .0015034* DEGREE DAYS R-SQUARED = .8345 20 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .7754 RESIDUAL SUM SQUARE = 16.892 STANDARD ERROR = 1.0984 F-RATIO = 14.119 DEPENDENT MEAN = 35.26 DEGREES OF FREEDOM = 14 STANDARD ERROR AS % MEAN WATER HEAT = 3.1153 , STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F d ELECTRICITY 6.3039 3.5055 .76578 .36511 1.7983 3.2338 INCOME .17648E-02 .15291E-02 .38236 .14237 1.1541 1.3321 GAS -18.185 5.9206 91861 .63189 -3.0715 9.'4341 FUEL OIL .61107 .37815 .42985 -119319 -1.6160 2.6113 DEGREE DAYS .15034E-02 .10130E-02 .18534 .28601 -1.4841 2.2025 t M
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Table J-27 - Appliance Saturation Time Series Electric Water Heating NORTHEAST EQUATION WATER HEAT = 73.68 + 13.748* ELECTRICITY + .0050592* INCOME - 35.338* GAS - 2.6222* FUEL OIL .001012* DEGREE DAYS R-SQUARED = .90394 20 OBSERVATIONS, 5 VARIA8LES CORRECTED R-SQUARED = .86964 RESIDUAL SUM SQUARE = 80.337 STANDARD ERROR = 2.3955 F-RATIO = 26.35 . DEPENDENT MEAN' = 36.06 DEGREES OF FREEDOM = 14 STANDARD ERROR AS % MEAN WATER HEAT = 6.6430 , STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F ELECTRICITY 13.748 8.2105 .58344 .77862 1.6745 2.8039 INCOME .50592E-02 .38322E-02 .37101 .38523 1.3202 1.7428 ]
- GAS -35.338 12.896 .62360 -1.2007 -2.7402 7.5089 i FUEL OIL -2.6222 .90668 .64437 .81059 -2.8920 8.3639 I DEGREE DAYS .10120E-02 .21148E-02 55955E-01 .19586 .47855 .22901 c
O
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i ! i -- Table J-28 Appliance Saturation Time ~eries Electric Water HerliF FLINT EQUATION WATER HEAT = 63.508 + 15.709* ELECTRICITY .0036497* INCOME - 20.249* GAS - 2.7065* FUEL OIL'+ .00031409* DEGREE DAYS R-SQUARED = .70992 20 OBSERVATIONS, 5 VARIA8LES CORRECTED R-SQUARED = .60632 RESIDUAL SUM SQUARE = 48.272 STANDARD ERROR = 1.8569 F-RATIO = 6.8525 DEPENDENT MEAN = 30.85 DEGREES OF FREEDOM = 14 STANDARD ERROR AS % MEAN WATER HEAT = 6.0191 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F ELECTRICITY 15.709 5.4771 1.4944 1.0399 2.8680 8.2256 INCOME .36497E-02 .24799E-02 .59519 .38862 -1.4717 2.1660
. GAS -20.249 9.6267 .80107 .80418 -2.1034 4.4243 FUEL OIL -2.7065 .56772 -1.4910 .97794 -4.7673 22.727
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DEGREE DAYS .31409E-03 .16740E-02 .32643E-01 .72264E-01 .18762 .35203E-01 o
N l- ' Table J-29 GRAND RAPIDS l EQUATION WATER HEAT = 1.3267 + 13.026* ELECTRICITY + .0041249* INCOME + 1.5954* GAS - 1.6254* FUEL OIL .00060269* DEGREE DAYS R-SQUARED = .65491
- 20 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .53167 RESIDUAL SUM SQUARE = 15.839 STANDARD ERROR = 1.0636 F-RATIO = 5.3139 DEPENDENT MEAN = 20.075 .
DEGREES OF FREEDOM = 14 STANDARD ERROR AS % MEAN WATER HEAT = b 2983 STA.NDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F
' ELECTRICITY 13.026 3.4258 2.3597 1.3251 3.8023 14.457 INCOME .41249E-02 .18255E-02 1.2109 .61991 2.2597 5.1061 GAS 1.5954 4.6255 .17439 .98861E-01 .34492 .11897 -
FUEL OIL -1.6254 .35660 -1.7050 .90255 -4.5580 20.775 ! DEGREE DAYS 60269E-03 .89481E-03 .12412 .20742 .67353 .45365 . G
' - ~; m I $ i. I~ ! _.
j , , i Table J-30 , , Appliance Saturation Time Series Electric Water Heating JACKSON EQUATION WATER HEAT = 79.962 + 3.4312* ELECTRICITY + .00029896* INCOME - 13.214* GAS - 2.3304* FUEL OIL .00013775* DEGREE DAYS I R-SQUARED = .95427 20 OBSERVATIONS, 5 VARIABLES 4 CORRECTED R-SQUARED = .93794 RESIDUAL SUM SQUARE = 17.143 STANDARD ERROR = 1.1066 F-RATIO = 58.433 DEPENDENT MEAN = 44.71 DEGREES OF FREEDOM = 14 STANDARD ERROR AS % MEAN WATER i1 EAT = 2.4750 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F ELECTRICITY 3.4312 3.6270 .21748 .15673 .94602 .89496 INCOME .29896E-03 .14022E-02 .38637E-01 .19072E-01 .21320 .45454E-01 GAS -13.214 5.8801 .34829 .36211 -2.2472 5.0600 FUEL OIL -2.3304 .36888 .85535 .58102 -6.3175 39.910 DEGREE DAYS .13775E-03 .92698E-03 .94258E-02 .21129E-01 .14860 .22083E-01
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Table J-31 Appliance Saturation Time Series Electric Water Heating KALAMAZOO EQUATION WATER HEAT = 104.12 + 4.7985* ELECTRICITY .0079664* INCOME - 27.752* GAS - 1.2764* FUEL OIL .00052118* DEGREE DAYS R-SQUARED = .74182 20 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .64961 RESIDUAL SUM SQUARE = 26.212 STANDARD ERROR = 1.3683 F-RATIO = 8.0452 DEPENDENT MEAN = 39.115 DEGREES OF FREEDOM = 14 STANDARD ERROR AS % HEAN WATER HEAT = 3.4982 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F ELECTRICITY 4.7985 4.4523 .58446 .25053 1.0778 1.1616 INCOME .79664E-02 .22387E-02 -1.7123 .59580 -3.5585 12.663 GAS -27.752 7.9167 -1.4056 .86929 -3.5056 12.289 FUEL OIL -1.2764 .44977 .90023 .36374 -2.8378 8.0533 DEGREE DAYS .52118E-03 .14936E-02 .56141E-01 .83687E-01 .34895 .12176 c
i i i , f . . . i , , , Table J-32 Appliance Saturation Time Series Electric Water Heating LANSING-EQUATION WATER HEAT = 81.888 .81674* ELECTRICITY .004367* INCOME - 18.891* GAS .99443* FUEL OIL + .0010491* DEGREE DAYS R-SQUARED = .83009 20 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .76941 RESIDUAL SUM SQUARE = 20.252 STANDARD ERROR = 1.2027 F-RATIO = 13.679 DEPENDENT MEAN = 40.92 DEGREES OF FREEDOM = 14 STANDARD ERROR AS % MEAN WATER HEAT = 2.9392 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F ELECTRICITY .81674 3.8598 .91811E-01 .40761E-01 .21160 .44774E-01 INCOME .43670E-02 .15113E-02 .94602 .30313 -2.8895 8.3495 GAS -18.891 6.4166 .88306 .56562 -2.9441 8.6675 i FUEL OIL .99443 .42121 .64732 .27090 -0.3609 5.5739 DEGREE DAYS .10491E-02 .10219E-02 .14944 .17924 1.0266 1.0538 l c
i , . Table J-33 Appliance Saturation Time Series Electric Water Heating 1 1 MUSKEGON
! EQUATION l WATER HEAT = 39.566 + 9.6543* ELECTRICITY + .00036006* INCOME - 11.701* GAS - 1.5212* FUEL OIL .00015454* DEGREE DAYS R-SQUARED = .79541 20 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .72234 RESIDUAL SUM SQUARE = 14.376 STANDARD ERROR = 1.0133 F-RATIO = 10.886 DEPENDENT MEAN = 27.64 DEGREES OF FREEDOM = 14 STANDARD ERROR AS % MEAN WATER HEAT = 3.6662 STANDARD '
, VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F ELECTRICITY 9.6543 3.5197 1.4134 .71332 2.7429 7.5236 INCOME .36006E-03 .18598E-02 .73961E-01 .33960E-01 ,19360 .37482E-01 GAS -11.701 3.7255 -1.0337 .52663 -3.1409 9.8654
- FUEL OIL -1.5212 .34311 -1.2897 .61350 -4.4335 19.656 DEGREE DAYS .15454E-03 .83132E-03 .25722E-01 .38628E-01 .18589 .34557E-01
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.3 Table J-34 Appliance Saturation Time Series Electric Water Heating
~ SAGINAW EQUATION WATER HEAT = 37.42 + 2.5211* ELECTRICITY .0028407* INCOME - 13.552* GAS + .10707* FUEL OIL + .00079339* DEGREE DAYS R-SQUARED = .56319 20 OBSERVATIONS, 5 VARIABLES i CORRECTED R-SQUARED = .40719 RESIDUAL SUM SQUARE = 21.083 STANDARD ERROR = 1.2272 F-RATIO = 3.6101 DEPENDENT MEAN = 24.385 DEGREES OF FREEDOM = 14 STANDARD ERROR AS % MEAN WATER HEAT = 5.0324 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F ELECTRICITY 2.5211 3.7274 .44535 .21113 .67635 .45745 INCOME .28407E-02 .13197E-02 -1.0175 .34683 -2.152S 4.6336 GAS -13.532 6.4716 .99408 .67992 -2.0910 4.3725 ., FUEL OIL .10707 .38729 .10952 .48944E-01 .27645 .76424E-01 - DEGREE DAYS .79339E-03 .10272E-02 .14311 .23213 .77239 .59659 . c N
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,s Table J-35 , _ Appliance Saturation Time Series Electric Water Heating 1
i NORTHWEST EQUATION WATER HEAT = 140.47 + .024564* ELECTRICITY .008193* INCOME - 29.507* GAS - 3.2666* FUEL OIL + .00061544* DEGREE DAYS R-SQUARED = .93236 20 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .90821 RESIDUAL SUM SQUARE = 52.369 STANDARD ERROR = 1.9341 F-RATIO = 38.598 DEPENDENT MEAN = 53.635 DEGREES OF FREEDOM = 14 STANDARD ERROR AS % MEAN WATER HEAT = 3.6060 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL-F ELECTRICITY .24564E-01 7.1856 .10834E-02 .93531E-03 .34185E-02 .11686E-04 INCOME .81930E-02 .41345E-02 .57158 .34992 -1.9816 3.9268 , d GAS -29.507- 8.4065 .78527 .68436 -3.5101 12.321 FUEL OIL -3.2666 .67194, .83430 .67892 -4.8614' 23.634 DEGREE DAYS .61544E-03 .14547E-02 .31080E-01 .93191E-01 .42306 .17898
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7 , Table J-36 Appliance Saturation Time Series Electric Water Heating i HURON EQUATION WATER HEAT = 51.806 - 10.47* ELECTRICITY + 26.538* GAS - 1.6694* FUEL OIL .000539%* INCOME + .0016105* DEGREE DAYS i R-SQUARED = .79749 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .74419 RESIDUAL SUM SQUARE = 341.22 STANDARD ERROR = 4.2378 F-RATIO = 14.964 DEPENDENT MEAN = 46.952 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN WATER HEAT = 9.0258 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -10.470 7.2288 .84223 .60756 -1.4483 2.0977 , GAS 26.538 17.304 .38031 .70616 1.5337 2.3521 FUEL OIL -1.6694 1.7066 .35151 .41361 .97822 .95691 INCOME .53996E-03 .51308E-02 .43269E-01 .23812E-01 .10524 .11075E-01 DEGREE DAYS .16105E-02 .27472E-02 .85065E-01 .23543 .58625 .34369
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m ,, 1 Table J-37 Appliance Saturation Time Series Electric Water Heating LAPEER - EQUATION . WATER HEAT = - 5.0939 - 4.3324* ELECTRICITY + 19.795* GAS - 2.6876* FUEL OIL + .0079006* INCOME + .0059491* DEGREE DAYS R-SQUARED = .87247 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .83891 RESIDUAL SUM SQUARE = 319.8 STANDARD ERROR = 4.1026 F-RATIO = 25.997 DEPENDENT MEAN = 38.24 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN WATER HEAT = 10.729 STANDARD VARIABLE C0 EFFICIENT ERROR BETA - ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -4.3324 6.9629 .28568 .30869 .62222 .33716
~
GAS 19.795 13.941 .23253 .64674 1.4199 2.0161 FUEL OIL -2.6876 1.3755 .46386 .81756 ,
-1.9538 3.8175 INCOME .79006E-02 .60710E-02 .39864 .51552 1.3014 1.6936 DEGREE DAYS .59491E-02 .27587E-02 .19221 1.0972 2.1565 4.6503 c
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3 i _ f I . l lN i t 6 a Table J-38 ' ~ Appliance Saturation Time Series Electric Water Heating SANILAC EQUATION WATER HEAT = 72.369 - 11.748* ELECTRICITY + 19.864* GAS - 3.0061* FUEL OIL .0013046* INCOME + .0021641* DEGREE DAYS i I R-SQUARED = .77052 3 4 3 25 OBSERVATIONS, 5 VARIABLES
- CORRECTED R-SQUARED = .71013 RESIDUAL SUN SQUARE = 566.03 STANDARD ERROR = 5.4581 F-RATIO = 12.759 ;
4 DEPENDENT MEAN = 46.428 - DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN WATER HEAT = 11.756 ' STANDARD , VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -11.748 13.751 .78107 .68941 .85434 .72990 l GAS 19.864 23.603 .39426 .61972 .84157 .70825 i FUEL OIL -3.0061 2.0590 .52313 .75318 -1.4600 2.1315 ! INCOME .13046E-02 .10215E-01 .65737E-01 .62049E-01 .12772 .16311E-01 i DEGREE DAYS .21641E .40425E-02 .7184]E-01 .32618 .53535 .28660 i
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.t f..,. 'i i- m. l 3, Table J-39 l Appliance Saturation Time Series Electric Water Heating ST. CLAIR
- ~ EQUATION WATER HEAT = 99.031 - 18.821* ELECTRICITY + 17.273* GAS .51695* FUEL OIL .0092548* INCOME- .0013%2 ~* DEGREE DAYS i
i
- R-SQUARED = .67936 25 OBSERVATIONS, 5 VARIABLES i CORRECTED R-SQUARED = .59499 RESIDUAL SUM SQUARE = 321.89 i -STANDARD ERROR = 4.116 F-RATIO = 8.0515 I DEPENDENT MEAN = 33.452 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN WATER HEAT = 12.304 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F
-1.5329 -1.9251 3.7060 ELECTRICITY -18.821 9.7765 -1.9614.
GAS 17.273 18.502 .53739 .74794 .93357 .87156 FUEL OIL .51695 1.5353 .14101 .17977 .33671 .11337 , INCOME .92548E-02 .58906E-02 . .83628 -
.72776 -1.5711, 2.4684
! 3EGREE DAYS -.13962E-02 .32604E-02 .61874E-01 -
.26788 .42811 .18337 l
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. Table J-40 - Appliance Saturation Time Series Electric Water Heating TUSCOLA EQUATION WATER HEAT = 44.009 - 10.174* ELECTRICITY + 25.073* GAS - 2.4479* FUEL OIL .00049733*1NCOME + .003217* DEGREE DAYS
- R-SQUARED = .82867 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .78358 RESIDUAL SUM SQUARE = 426.97 STANDARD ERROR = 4.7404 F-RATIO = 18.379
, DEPENDENT MEAN = 40.132 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN WATER HEAT = 11.812 i STANDARD l VARfABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F, ELECTRICITY -10.174 9.2812 -
.67296 .69071 -1.0962 1.2016 GAS 25.073 17.509 .29545 .78055 1.4320 2.0506 FUEL OIL -2.4479 1.9241 -
.42382 .70957 -1.2723 1.6187 INCOME .49733E-03 .70425E-02 -
.29669E-01 .27080E-01 .70618E-01 .49869E-02.
DEGREE DAYS .32170E-02 .31067E-02 .13972 .55020 1.0355 1.0723
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Table J-41 Appliance Saturation Time Series i Electric Water Heating OAKLAND EQUATION WATER HEAT = -23.114 + 2.6271* ELECTRICITY + 30.382* GAS - 2.3477* FUEL OIL + .0040195* INCOME + .0016139* DEGREE DAYS R-SQUARED = .60179 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .49699 RESIDUAL SUM SQUARE = 175.02 STANDARD ERROR = 3.0351 F-RATIO = 5.7426 DEPENDENT MEAN = 22.036 DEGREES OF FREEDOM. = 19 STANDARD ERROR AS % MEAN WATER HEAT = 13.773 STANDARD ' VARIABLE C0 EFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ' ELECTRICITY 2.6271 4.5014 .40069 .32293 .58361 .34060 GAS 30.382 10.546 .81922 1.7142 2.8808 8.2989 FUEL OIL -2.3477 1.0523 .89964 -1.2321 -2.2311 4.9777 INCOME .40195E-02 .28719E-02 .73261 .75883- 1.3996 1.9589 DEGREE DAYS .16139E-02 .21329E-02 .12315 .48501 .75667 .57255 e. b
r I. I i !- [ s , 3 ; Table J-42 4 Appliance Saturation Time Series Electric Water Heating MACOMB , ( EQUATION WATER HEAT = 34.451 - 2.7034* ELECTRICITY + 8.1786* GAS .62846* FUEL OIL
.0034756* INCOME .0006987* DEGREE DAYS 4
R-SQUARED = .55816 , 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .44188 RESIDUAL SUM SQUARE = 27.819 STANDARD ERROR = 1.21 F-RATIO = 4.8004 DEPENDENT MEAN = 13.952 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN WATER HEAT = 8.6728 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -2.7034 2.0302 -1.1250 .52792 -1.3316 1.7731 GAS 8.1786 4.3481 .60631 .73237 1.8809 3.5379 FUEL OIL .62846 .44779 .68454 .52399 -1.4035 1.9697
-2.0902 INCOME .34756E-02 .16628E-02 -1.1256 .82831 4.3691 DEGREE DAYS .69870E-03 .90793E-03 .12364 .32143 .76955- .59220
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Table J-43 Appliance Saturation Time Series Electric Water Heating WASHTENAW EQUATION WATER HEAT = 63.334 - 6.4504* ELECTRICITY + 3.8157* GAS .54561* FUEL OIL ,003847* INCOME .001153* DEGREE DAYS , R-SQUARED = .48793 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .35317 RESIDUAL SUM SQUARE = 155.22 STANDARD ERROR = 2.8582 F-RATIO = 3.6208
- DEPENDENT MEAN = 24.448 DEGREES OF FREEDOM = 19
- STANDARD ERROR AS % MEAN WATER HEAT = 11.691
, STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F l ELECTRICITY -6.4504 7.1860 -1.2234 .71886 -.89763 .80574 1
GAS 3.8157 13.680 .19809 .20197 .27893 .77799E-01 FUEL OIL .54561 1.2762 .27085 .25961 .42753 .18278 INCOME .38470E-02 .41842E-02 .65941 .50865 .91940 .84530 DEGREE DAYS .11530E-02 .25802E-02 .10172 .30542 .44688 .19970
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4 Table J-44 I Appliance Saturation Time Series Electric Water Heating r
- LENAWEE EQUATION WATER HEAT = 74.851 - 12.029* ELECTRICITY + 6.5246* GAS + .067702* FUEL OIL .0049692* INCOME .0019758*0EGREE DAYS R-SQUARED = .90151 25 OBSERVATIONS, 5 VARIABLES
. CORRECTED R-SQUARED = .8756 RESIDUAL SUM SQUARE = 59.252 STANDARD ERROR
= 1.7659 F-RATIO = 34.784 DEPENDENT MEAN = 24.676 DEGREES OF FREEDOM = 19 i' STANDARD ERROR AS % MEAN WATER HEAT = 7.1565 STANDARD VARIABLE COEFFICIENT ERROR 8 ETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -12.029 3.1168 -1.6194 -1.3282 -3.8594 14.895 GAS 6.5246 6.3416 .15648 .33035 1.0289' 1.0586 l-
' ~ ~
- FUEL OIL .67702E-01 .66385 .23856E-01 .31916E-01 .10198 .10401E-01 INCOME .49692E-02 .24824E-02 .56619 .52049 -2.0018 4.0072
~
DEGREE DAYS .19758E-02 .12237E-02 .12976 .54696 -1.6146 2.6070
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I - [ ~f- f] l , , i . i . i3 i ; Table J-45 Appliance Saturation Time Series , Electric Water Heating LIVINGSTON EQUATION WATER HEAT = 21.92 - 2.9806* ELECTRICITY + 20.351* GAS - 1.1952* FUEL OIL + .00084154* INCOME .00048839* DEGREE DAYS R-SQUARED = .58949 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .48146 RESIDUAL SUM SQUARE = 124.43 STANDARD ERROR = 2.5591 F-RATIO = 5.4568 DEPENDENT MEAN = 24.448 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN WATER HEAT = 10.468 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -2.9806 3.4455 .56530 .33217 .86506 .74833 ' GAS 20.351 9.0786 .68761 1.0400 2.2417 5.0251 FUEL OIL -1.1952 .81604 .59332 .56869 -1.4646 2.1451 INCOME .84154E-03 .24834E-02 .14092 .99739E-01 .33887 .11483 DEGREE DAYS .48839E-03 .18531E-02 .46006E-01 .13550 .26355 .69459E-01 c .I -
l Table J-46 Appliance Saturation Time Series Electric Water Heating INGHAM EQUATION ji WATER HEAT = 61.448 - 8.834* ELECTRICITY + 16.33* GAS .53743* FUEL OIL .005012* INCOME .0017191* DEGREE DAYS R-SQUARED = .62869 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .53097 RESIDUAL SUM SQUARE = 112.55 STANDARD ERROR = 2.4339 F-RATIO = 6.4339 DEPENDENT MEAN = 24.448 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN WATER HEAT = 9.9554 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY -T-STATISTIC PARTIAL F ELECTRICITY -8.8340 4.2749 -1.6755 .98450 -2.0665 4.2704 GAS 16.330 8.8272 .55175 .83453 1.8500 3.4225 s. , FUEL OIL .53743 .89317 .26679 .25572 .60171 .36206 INCOME .50120E-02 .34336E-02 .81197 .62341 -1.4597 2.1308 DEGREE DAYS .17191E-02 .18253E-02 .15828 .48432 .94181 .88701 o to
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i , i Table J-47 Appliance Saturation Time Series Electric Water Heating MONR0E , EQUATION WATER HEAT = 63.006 - 4.2057* ELECTRICITY - 19.623* GAS + .88051* FUEL OIL .0025789* INCOME .00080854* DEGREE DAYS t , R-SQUARED = .91952 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .89835 RESIDUAL SUM SQUARE = 48.417 STANDARD ERROR = 1.5963 F-RATIO = 43.419 DEPENDENT MEAN = 24.676 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN WATER HEAT = 6.4691 STANDARD . VARIABLE COEFFICIENT ERROR BETA ELASTICITY FSTATISTIC PARTIAL F ELECTRICITY -4.2057 3.1051 .54828 .46167 -1.3545 1.8346 GAS -19.623 5.4065 -1.0060 -1.0076 -3.6296 13.174 FUEL OIL .88051 .73356 .28840 .41266 1.2003 1.4408 1 INCOME . 25789E-02 .21991E-02 .32042 .28369 -1.1727 1.3753 DEGREE DAYS .80854E-03 .12081E-02 .49523E-01 .21301 .66925 .44790
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g . l p-x-l p- g - N , Table J-48 Appliance Saturation Time Series Electric Water Heating WAYNE EQUATION WATER HEAT = 10.367 - 1.9386* ELECTRICITY + 1.3236* GAS .07428* FUEL OIL .0004027* INCOME .000072367* DEGREE DAYS R-SQUARED = .93908 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .92305 RESIDUAL SUM SQUARE = 1.5523 STANDARD ERROR = .28583 F-RATIO = 58.58 DEPENDENT MEAN = 3.952 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN WATER HEAT = 7.2326 STANDARD VARIABLE COEFFICIENT ERROR 8 ETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -1.9386 .71003 -1.2280' -1.3288 -2.7304 7.4550 GAS 1.3236 1.6556' .16736 .37002 .79944 .63910 FUEL OIL .74283E-01 .14365 .11822 .21737 .51710 .26739 INCOME .40270E-03 .33386E-03 .24052 .33078 -1.2062 1.4549 DEGREE DAYS .72367E-04 .27162E-03 .19135E-01 .11642 .26643 .70983E-01 e b
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Table J-49 2 Appliance Saturation Time Series Air Conditioning CENTRAL EQUATION AC = 13.007 - 6.1128* ELECTRICITY - 8.2712* GAS + .44376* FUEL OIL + .0037566* INCOME + .00023343* DEGREE DAYS R-SQUARED = .93704 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .92048 RESIDUAL SUM SQUARE = 22.271 STANDARD ERROR = 1.0827 F-RATIO = 56.56 DEPENDENT MEAN = 4.588 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 23.598 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -5.1128 2.9532 .53111 -2.8611 -2.0699 4.2846
- GAS -8.2712 3.8962 .25868 -2,2524 -2.1229 4.5067 FUEL OIL .44376 .32955 .20392 1.1252 1.3466 1.8132 INCOME .37566E-02 .18778E-02 .39330 1.8044 2.0005 4.0021 DEGREE DAYS .23343E-03 .80705E-03 .17531E-01 .34899 .28924 .83659E-01 4
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i i ; i~l t i ! t 'l 'b Table J-50 , Appliance Saturation Time Series
. Air Conditioning 9
BATTLE CREEK EQUATION
- AC = 2.8529 - 4.0503* ELECTRICITY - 13.377* GAS + .72292* FUEL OIL + .010008* INCOME .00087778* DEGREE DAYS R-SQUARED = .95578 25 OBSERVATIONS, 5 VARIABLES ,
CORRECTED R-SQUARED = .94414 RESIDUAL SUM SQUARE = 52.064 STANDARD ERROR = 1.6554 F-RATIO = 82.128 DEPENDENT MEAN = 7.176 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 23.068
. STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ,
i ELECTRICITY -4.0503 4.0946 .19291 -1.2121 .98920 .97852 GAS -13.377 6.2883 .22934 -2.3291 -2.1274 4.5256 . FUEL OIL .72292 .53366 .18210 1.1719 1.3547 1.8351 INCOME .10008E-01 .18921E-02 .73857 3.7919 5.2894 27.978 DEGREE DAYS .87778E-03 .12269E-02 .39156E-01 .82021 .71546 .51188 1
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Table J-51 Appliance Saturation Time Series Air Conditioning NORTHEAST , EQUATION AC = 6.2584 - 4.4874* ELECTRICITY - 10.155* GAS + .65726* FUEL OIL + .0058151* INCOME .000262* DEGREE DAYS 1 R-SQUARED = .93138
- 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .91333 RESIDUAL SUM SQUARE =^36.386 STANDARD ERROR = 1.3839 F-RATIO = 51.581
- DEPENDENT MEAN = 4.968 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 27.856 1
STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F
- ELECTRICITY -4.4874 3.8455 .31845 -1.9397 -1.1669 1.3618 GAS -10.155 5.1170 .25940 -2.5538 -1.9845 3.9384 FUEL OIL .65726 .46123 .24668 1.5390 1.4250 2.0307 INCOME .58151E-02 .19741E-02 .63975. 3.0567 2.9457 8.6773 DEGREE DAYS .26200E-03 .91017E-03 .24667E-01 .36197 .28786 .82863E-01 W
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Table J-52
- Appliance Saturation Time Series Air Conditioning FLINT EQUATION AC = 4.0191 - 3.9195* ELECTRICITY - 21.004* GAS + .79117* FUEL OIL + .010033* INCOME .00031761* DEGREE DAYS R-SQUARED = .93801 25 OBSERVATIONS, 5 VARIABLES 1
CORRECTED R-SQUARED = .9217 RESIDUAL SUM SQUARE = 89.457 STANDARD ERROR = 2.1699 F-RATIO = 57.499 DEPENDENT MEAN = 7.94 - DEGREES OF FREEDOM = 19 STANDARD ERROR AS % ME8?; AC = 27.328 STANDARD VARIABLE COEFFICIENT ERROR BETA ' ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -3.9195 5.3850 .16861 -1.0601 .72785 .52977 GAS -21.004 7.5197 .32525 -3.3051 -2.7932 7.8021 FUEL OIL .79117 .64299 .18001 1.1591 1.2304 '1.5140 INCOME .10033E-01 .26626E-02 .66450 3.9819 3.7683 14.200 DEGREE DAYS .31761E-03 .15528E-02 .13527E-01 28212 .20454 .41837E-01 s
- 8;
r 7, _ .- Table J-53 4 Appliance Saturation Time Series Air Conditioning GRAND RAPIDS I EQUATION AC = 16.029 + 8.5211* ELECTRICITY - 35.945* GAS .10693* FUEL OIL + .0070035* INCOME + .00017288* DEGREE DAYS j R-SQUARED = .98625 25 OBSERVATIONS, 5 VARIABLES , CORRECTED R-SQUARED = .98263 RESIDUAL SUM SQUARE-= 18.504 STANDARD ERROR = .98687 F-RATIO = 272.57 DEPENDENT MEAN = 8.056 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 12.250 i STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY 8.5211 2.7997 .37958 2.2714 3.0436 9.2635 GAS -35.945 4.0459 .88562 -5.7740 -8.8842 78.930 FUEL OIL .10693 .32087 .25192E-01 .15440 .33324 .11105 i
~
4 INCOME .70035E-02 .14275E-02 .44136 2.5218 4.9060 24.069 DEGREE DAYS .17288E-03 .61203E-03 .97041E-02 .14544 .28246 .79786E-01 { K 8 0
4 - : ; .., I . . . - - ? Table J-54 ', Appliance Saturation Time Series Air Conditioning JACKSON EQUATION AC = - 16.174 + .59427* ELECTRICITY - 12.928* GAS + .51687* FUEL OIL + .011013* INCOME + .00033282* DEGREE DAYS R-SQUARED = .95405 25 OBSERVATIONS, 5 VARIABLES l CORRECTED R-SQUARED = .94195 RESIDUAL SUM SQUARE = 56.716 STANDARD ERROR = 1.7277 F-RATIO = 78.894 DEPENDENT MEAN = 7.052 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 24.500 i STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .59427 4.2443 .27644E-01 .18097 .14002 .19605E-01 GAS -12.928 6.3871 .21646 -2.2904 -2.0240 4.0968 FUEL OIL .51687 .53960 .12716 .85262 .95788 .91754 INCOME .11013E-01 .17991E-02 .90942 4.2280 6.1218 37.476 DEGREE DAYS .33282E-03 .11680E-02 .15260E-01 .32239 .28494 .81191E-01 W
i m 7 , , Table J-55 Apr.liance Saturation Time Series Air Conditioning
- KALAMAZOO i
EQUATION AC = - 11.681 - 2.43* ELECTRICITY - 18.179* GAS + .77064* FUEL OIL + .012534* INCOME + .00064535* DEGREE DAYS. 1 R-SQUARED = .92925 25 OBSERVATIONS, 5 VARIABLES 4 CORRECTED R-SQUARED = .91063 RESIDUAL SUM SQUARE = 121.52 STANDARD ERROR = 2.529 F-RATIO = 49.912 DEPENDENT MEAN = 8.392 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 30.135 4 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -2.4300 6.5753 .95817E-01 .62180 .36956 .13657 GAS -18.179 9.8142 .25803 -2.7065 -1.8523 3.4312
- FUEL OIL .77064 .78210 .16071 1.0682 .98535 .97092 INCOME .12534E-01 .34667E-02 .77174 4.1716 3.6157 13.073 DEGREE DAYS .64535E-03 .20926E-02 .21544E-01 .48026 .30839 .95104E-01 is O 5
~m Table J-56 Appliance Saturation Time Series Air Conditioning LANSING EQUATION AC = - 5.7071 .93071* ELECTRICITY - 17.494* GAS + .81648* FUEL OIL + .0093405* INCOME + .00023866* DEGREE DAYS R-SQUARE 0 = .92309 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .90285 RESIDUAL SUM SQUARE = 85.575 STANDARD ERROR = 2.1222 F-RATIO = 45.608 DEPENDENT MEAN = 6.652 DEGREES OF FREEDOM =.19 STANDARD ERROR AS % MEAN AC = 31.904 STANDARD VARIABLE COEFFICIENT ERROR 8 ETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY .93071 5.7449 .45597E-01 .30046 .16201 .26246E-01 GAS -17.494 8.1139 .30850 -3.2856 -2.1560 4.6484 FUEL OIL .81648' .70409 .21156 1.4278 1.1596 1.3447 INCOME .93405E-02 .24625E-02 .80607 3.7671 3.7931 14.388 DEGREE DAYS .23866E-03 .15741E-02 .12998E-01 .24911 .15162 .22988E-01 W
u
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' Table J-57 Appliance Saturation Time Series Air Conditioning MUSKEGON EQUATION AC = 12.832 + 6.9738* ELECTRICITY - 20.932* GAS .24254* FUEL OIL + .0018199* INCOME + .000086122* DEGREE DAYS R-SQUARED = .97255 25 OBSERVATIONS, 5 VARIABLES .
CORRECTED R-SQUARED = .96532 . RESIDbAL SUM SQUARE = 5.4837 STANDARD ERROR = .53723 F-RATIO = 134.63 DEPENDENT MEAN = 3.04 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 17.672 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY 6.9738 1.6107 .80634 4.9263 4.3296 18.746 GAS -20.932 1.9450 -1.3387 -8.9107 -10.762 115.82 FUEL OIL .24254 .17442 .14832 .92810 -1.3905 1.9336 INCOME .18199E-02 .88118E-03 .25950 1.4993 2.0653 4.2655 DEGREE DAYS .86122E-04 .33348E-03 .12548E-01 .19200 .25825 .66696E-01 O
t
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3 >
- Table J-58 Appliance Saturation Time Series Air Conditioning SAGINAW EQUATION AC = - 14.236 - 7.9414* ELECTRICITY - 11.845* GAS + 1.5786* FUEL OIL + .010975* INCOME + .00078427* DEGREE DAYS R-SQUARED = .95884 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .94801 RESIDUAL SUM SQUARE = 65.279 STANDARD ERROR = 1.8536 F-RATIO = 88.522 DEPENDENT MEAN = 8.94 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 20.733 STANDARD .
VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -7.9414 4.3521 .32588 -1.9076 -1.8247 3.3296 GAS -11.845 6.7421 .17496 -1.6553 -1.7569 3.0866 i FUEL OIL 1.5786 .55771 .34260 2.0541 2.8305 8.0118 INCOME .10975E-01 .17212E-02 .79760 3.4756 6.3762 40.656 DEGREE DAYS .78427E-03 .12744E-02 .30099E-01 .62559 .61542 .37875 i 8-*
~'
l~ ~ 1 F
~
i ~~; 1 i - - x, I T4 i , _. . 1- i 4 9 Table J-59 Appliance Saturation Time Series . Air Conditioning NORTHWEST EQUATION AC = 6.9169 + 6.6584* ELECTRICITY - 14.143* GAS .3586* FUEL OIL + .0013137* INCOME + 1.0479E-06* DEGREE DAYS R-SQUARED = .94172 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .92638 RESIDUAL SUM SQUARE = 4.4615 STANDARD ERROR = .48458 F-RATIO , = 61.401 DEPENDENT MEAN = 1.572 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 30.826 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY 6.6584 1.5331 1.2437 9.0958 4.3432 18.863 GAS -14.143 2.0534 -1.4611 -11.643 -6.8875 47.437 FUEL OIL .35860 .16025 .35424 -2.6537 -2.2377 5.0075 INCOME .13037E-02 .94086E-03 .34838 1.7950 1.3856 1.9199 DEGREE DAYS .10479E-05 .30311E-03 .20025E-03 .53967E-02 .34572E-02 .11952E-04 c N
t . - i Table J-60 p
- l. Appliance Saturation Time Series e
Air Conditioning o HURON EQUATION AC = - 26.721 + .35436* ELECTRICITY + 29.098* GAS - 1.757* FUEL OIL .00034303* INCOME + .0033555* DEGREE DAYS R-SQUARED = .21303 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .0059319 RESIDUAL SUM SQUARE = 682.73 > STANDARD ERROR = 5.9944 F-RATIO = 1.0286 DEPENDENT MEAN = 12.48 DEGREES OF FREEDON = 19 STANDARD ERROR AS % MEAN AC = 48.032
- STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F 4
ELECTRICITY .35436 10.225 .39727E-01 .77363E-01 .34655E-01 .12010E-02 GAS 29.098 24.476 .58112 2.9130 1.1888 1.4133 FUEL OIL -1.7570 2.4140 .51558 -1.6378 .72787 .52979 i INCOME .34303E-03 .72575E-02 .38308E-01 56913E-01 .47265E-01 .22340E-02 DEGREE DAYS .33555E-02 .38859E-02 .24699 1.8454 .86351 .74565 1 4
~
. ,r , . -m Table J-61 Appliance Saturation' Time Series Air Conditioning LAPEER 3
EQUATION AC = - 74.338 + 6.4976* ELECTRICITY + 28.154* GAS - 2.5674* FUEL OIL + .00693* INCOME + .0065953* DEGREE DAYS R-SQUARED = .29168 25 OBSERVATIONS, 5 VARIABLES , CORRECTED R-SQUARED = .10528 RESIDUAL SUM SQUARE = 614.49 STANDARD ERROR = 5.687 F-RATIO = 1.5648 DEPENDENT MEAN = 12.48 DEGREES OF FREEDOM = 19 , STANDARD ERROR AS % MEAN AC = 45.569 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY Y-STATISTIC PARTIAL F ELECTRICITY 6.4976 9.6518 .72843 1.4185 .67319 .45319 GAS 28.154 19.325 .56227 2.8185 1.4568 2.1224 FUEL OIL -2.5674 1.9067 .75336 -2.3931 -1.3465 1.8130 . INCOME .69300E-02 .84155E-02 .59448 1.3855 .82348 .67811 DEGREE DAYS .65953E-02 .38241E-02 .36229 3.7271 1.7247 2.9745
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7- ; _ .. , ] j. Table J-62 Appliance Saturation Time Series Air Conditioning 4 SANILAC , EQUATION AC = 43.962 - 8.9645* ELECTRICITY + 15.555* GAS - 1.3616* FUEL OIL .010453* INCOME + .0013335* DEGREE DAYS R-SQUARED = .16103 25 OBSERVATIONS,.5 VARIABLES 4 4' CORRECTED R-SQUARED = .059747 RESIDUAL SUM SQUARE = 727.84 STANDARD ERROR = 6.1893 F-RATIO = .72938 DEPENDENT MEAN = 12.48 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 49.594 STANDARD
- VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -8.9645 15.593 -1.0050 -1.9571' .57492 .33053 GAS 15.555 26.765 .52059 1.8054 .58117 . 33775 FUEL OIL -1.3616 2.3348 .39953 -1.2691 .58315 .34006 INCOME .10453E-01 .11583E-01 88807 -1.8494 .90237 .81426 DEGREE DAYS . 13335E-02 .45840E-02 .74641E-01 .74770 .29090 .84623E-01
, S
j- ; ^ l Table J-63 Appliance Saturation Tirne Series Air Conditiening ST. CLAIR . EQUATION AC = 111.76 - 21.313* ELECTRICITY + 15.181* GAS + .092747* FUEL OIL .019628* INCOME .001971* DEGREE DAYS R-SQUARED = .32074 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .14198 RESIDUAL SUM SQUARE = 589.29 STANDARD ERROR = 5.5691 F-RATIO = 1.7943
, DEPENDENT MEAN = 12.48 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 44.624 -
STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -21.313 13.228 -2.3894 -4.6531 -1.6113 2.5961 GAS 15.181 25.034 .50808 1.7620 .60642 .36774 FUEL OIL .92747E-01 2.0773 .27215E-01 .86451E-01 .44648E-01 .19934E-02 INCOME .19628E-01 .79702E-02 -1.9079 -4.1371 -2.4626 6.0646 DEGREE DAYS .19710E-02 .44114I-02 .93964E-01 -1.0137 -
.44680 .19963 d4
7_m. ,
- r
=- T Table J-64 Appliance Saturation Tine Series Air Conditioning
~
TUSCOLA ! l EQUATION j AC = - 30.986 + 1.1678* ELECTRICITY + 30.09* GAS - 1.8783* FUEL OIL + .00037374* INCOME + .0034564* DEGREE DAYS R-SQUARED = .21301 25 OBSERVATIONS, 5 VARIABLE ' CORRECTED R-SQUARED = .0059072 RESIDUAL SUM SQUARE = 682.75 STANDARD ERROR = 5.9945 F-RATIO = 1.0285
. DEPENDENT MEAN = 12.48 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 48.033 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY 1.1678 11.736 .13092 .25495 .99502E-01 .99006E-02 i
GAS 30.090 22.141 .60095 3.0123 1.3590 1.8470 ! FUEL OIL -1.8783 2.4330 .55116 -1.7508 .77199 .59597 l INCOME .37374E-03 .89056E-02 .377790E-01 .65443E-01 .41967E-01 .17613E-02 i DEGREE DAYS .34564E-02 .39285E-02 .25442 1.9009 .87982 .77408 be j
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Table J-65 Appliance Saturation Time Series Air Conditioning
, OAKLAND EQUATION '
AC = 73.31 - 20.093* ELECTRICITY - 17.645* GAS + 1.9219* FUEL OIL + .0021836* INCOME .0013202* DEGREE DAYS R-SQUARED = .93675 25 0.BSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .92011 RESIDUAL SUM SQUARE = 298.69 STANDARD ERROR = 3.9649 F-RATIO = 56.283 DEPENDENT MEAN = 20.012 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 19.813 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -20.093 5.8805 .93494 -2.7197 -3.4169 11.675 GAS -17.645 13.777 .14515 -1.0963 -1.2807 1.6403 FUEL 0IL 1.9219 1.3746 .22468 1.1107 1.3981 1.9548
- . INCOME .21836E-02 .37517E-02 .12141 .45393 .58203 .33875 l
DEGREE DAYS '- .13202E-02 .27864E-02 .30730E-01 .43686 .47379 .22448
. . - )
t-1 8
4 - ! Table J-66 Appliance Saturation Time Series Air Conditioning MACOMB EQUATION AC = 48.449 - 13.852*E!.ECTRICITY - 16.082*oAS + 1.5379* FUEL OIL + .0049742* INCOME .0015059* DEGREE DAYS R-SQUARED = .96143 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .95128 RESIDUAL SUM SQUARE = 118.53 STANDARD ERROR = 2.4977 F-RATIO = 94.724 DEPENDENT MEAN = 15.38 DEGREES OF FREEDOM. = 19 STANDARD ERROR AS % MEAN AC = 16.240 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -13.852 4.1907 .82508 -2.4539 -3.3054 10.926 GAS -16.082 8.9752 .17065 -1.3064 -1.7918 3.2107 FUEL OIL 1.5379 .92431 .23977 1.1632 1.6639 2.7684 INCOME .49742E-02 .34322E-02 .23058 1.0754 1.4493 2.1004 DEGREE DAYS .15059E-02 .18741E-02 .38143E-01 .62844 .80351 .64563
Table J-67 Appliance Saturation Time Series Air Conditioning WASHTENAW EQUATION AC = 71.946 + 3.8069* ELECTRICITY - 48.756* GAS - 1.8884* FUEL OIL .0013455* INCOME + .0037885* DEGREE DAYS R-SQUARED = .89149 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .86294 RESIDUAL SUM SQUARE = 225.47 STAriDARD ERROR = 3.4448 F-RATIO = 31.22 DEPENDENT MEAN = 17.428 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 19.766 STANDARD . VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY 3.8069 8.6608 .27576 .59514 .43955 .19320 GAS -48.766 16.488 .96696 -3.6211 -2.9577 8.7482 FUEL OIL -1.8884 1.5381 .35805' -1.2605 -1.2277 1.5073 INCOME .13455E-02 .50430E-02 .88087E-01 .24956 .26681 .71186E-01 DEGREE DAYS .37885E-02 .31098E-02 .12765 1.4077 1.2183 1.4842 e
^'
- t l l~ i I - > ' '
Table J-68 Appliance Saturation Time Series . Air Conditioning a 9w LENAWEE 4 EQUATION AC = 101.41 - 20.988* ELECTRICITY - 7.8676* GAS + 1.6982* FUEL. OIL .0067731* INCOME .0028123* DEGREE DAYS i R-SQUARED = .85424 25 O8SERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .81589 RESIDLAL~ SUM SQUARE = 302.87 STANDARD ERROR = 3.9926 F-RATIO = 22.271 DEPENDENT.NEAN = 17.428 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 22.909 4 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -20.988 7.0467 -1.5204 - 3.2812 -2.9785 8.8714 GAS -7.8676 14.337 .10153 -.56401 .54874 .30112 FUEL OIL 1.6982 1.5009 .32198 1.1335 1.1314 1.2801 INCOME .67731E-02 .56123E-02 .41525 -1.0045 -1.2068 1.4564 DEGREE DAYS .28123E-02 .27666E-02 .99381E-01 - 1.1023 -1.0165 1.0333 ww - a mb C4
- i ~
l
- i Table J-69
' Appliance Saturation Time Series Air Conditioning LIVINGSTON EQUATION AC = 117.41 - 21.351* ELECTRICITY - 7.2147* GAS + 1.0476* FUEL OIL .0082601* INCOME .0030918* DEGREE DAYS R-SQUARED = .87718 25 OBSERVATIONS, 5 VARIABLES ,
i CORRECTED R-SQUARED = .84486 RESIDUAL SUM SQUARE = 255.21 STANDARD ERROR = 3.665 F-RATIO = 27.14 DEPENDENT MEAN = 17.428 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 21.029 STANDARD - VARIABLE COEFFICIENT ERROR , BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -21.351 4.9344 -1.5467 -3.3380 -4.3271 18.723 GAS -7.2747 13.002 .93877E-01 .52151 .55953 .31307 FUEL OIL 1.0476 1.1687 .19864 .69927 .89645 .80352 INCOME .82601E-02 .35565E-02 .52830 -1.3733 -2.3225 5.3941 DEGREE DAYS .30918E-02 .26539E-02 .11124 -1.2033 -1.1650 1.3572
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e O
m 7% Table J-70 Appliance Saturation Time Series Air Londitioning INGHAM EQUATION AC = 65.516 - 14.799* ELECTRICITY - 3.881* GAS + .76916* FUEL OIL .00088558* INCOME .0013318* DEGREE DAYS R-SQUARED = .84205 25 OBSERVATIONS, 5 Variables CORRECTED R-SQUARED =. 80048 RESIDUAL SUM SQUARE = 328.21 STANDARD ERROR = 4.1562 F-RATIO = 20.258 DEPENDENT MEAN = 17.428 DEGREES OF FREEDOM = 19 STANDARD ERROR AS'% MEAN AC = 23.848 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -14.799 7.3000 -1.0720 -2.3136 -2.0272 4.1097 GAS -3.8810 15.074 .50083E-01 -
.27822 .25747 .66290E-01 FUEL OIL .76916 1.5252 .14584 - 51340 .50430 .25432 INCOME
.88558E-03 .58633E-02 ~.547%E-01 .15452 .15104 .228125 01 DEGP.EE DAYS .13318E-02 .31170E-02 .46831E-01 .52631 .42726 .18255
i , ! _. : ,. Table J-71 - Appliance Saturation Time Series Air Conditioning
- -~
@NROE
~
EQUATION AC = - 2.756 - 2.8697* ELECTRICITY - 18.754* GAS + 1.4967* FUEL OIL + .0069007* INCOME + .002412* DEGREE DAYS R-SQUARED = .8543 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .81596 RESIDUAL SUM SQUARE = 302.75 STANDARD ERROR = 3.9918 F-RATIO = 22.281 DEPENDENT MEAN = 17.428 - DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 22.904 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -2.8597 7.7645 .20130 .44602 .36959 .13660 GAS -18.754 13.519 .51731 -1.3635 -1.3872 . 1.9242 FUEL OIL 1.4957 1.8343 .26377 .99313 .81592 .66573 INCOME .69007E-02 .54990E-02 .46134 1.0748 1.2549 1.5748 CEGREE DAYS .24120E-02 .30210E-02 .79494E-01 .89971 .79841 .63745 1 o
i - Table J-72 Appliance Saturation Time Series Air Conditioning WAYNE EQUATION AC = 20.204 - 9.5* ELECTRICITY - 1.9672* GAS .056349* FUEL OIL + .0044694* INCOME + .0013932* DEGREE DAYS i R-SQUARED = .95049 25 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .93746 RESIDUAL SUM SQUARE = 106.07 STANDARD ERROP. = 2.3627 F-RATIO = 72.948 DEPENDENT MEAN = 15.012 DEGREES OF FREEDOM = 19 STANDARD ERROR AS % MEAN AC = 15.739 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F ELECTRICITY -9.5000 5.8691 .65633 -1.7141 -1.6186 2.6200 GAS - -1.9672 13.686 .27129E-01 .14477 .14374 .20661E-01 FUEL OIL .56349E-01 1.1875 .97808E-02 .43409E-01 .47454E-01 .22518E-02 INCOME .44694E-02 .27597E-02 .29115 .96645 1.6195 2.6229 DEGREE DAYS .13932E-02 .22452E-02 .40178E-01 .59005 .62053 .38506 i
I'j , f'- F. i : 1 8 l Table J-73 Detroit Edison Individual Customer Apoliance Model Linear Specification EQUATION SPACE SAT = 1.1688 .049175* CENTS /KWH .005469* INCOME + .0031941* AGE HEAD + .00052043*R00MS
+ .0054121* TYPE HOUSE R-SQUARED = .042596 712 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .035816 RESIDUAL SUM SQUARE = F 6359' STANDARD ERROR = .09695 F-RATIO = 6.2822 DEPENDENT MEAN = 1.0098 DEGREES OF FREEDOM = 706 STANDARD ERROR AS % MEAN SPACE SAT = 9.6006 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH .4917EE-01 .91016E-02 .23491 .15164 -5.4029 29.191 INCOME .54691E-02 .22444E-02 .11069 .29057E-01 -2.4368 5.9378 AGE HEAD .31941E-02 .27539E-02 .47328E-01 .12381E-01 1.1598 1.3452 ROOMS .52043E-03 .28474E-03 .77483E-02 .30003E-02 .18278 .33408E-01 TYPE HOUSE .54121E-02 .35661E-02 .62276E-01 .79337E-02 1.5176 2.3032
,~ ! ! . .
Table J-74 Detroit Edison Individual Customer Appliance Model Linear Specification EQUATION WATER SAT = 2.7981 .43938* CENTS /KWH .028482* INCOME .026374* FAMILY .0097349*R00MS R-SQUARED = .28077 711 OBSERVATIONS, 4 VARIABLES CORRECTED R-SQUARED = .2767 RESIDUAL SUM SQUARE = 57.607 STANDARD ERROR = .28565 F-RATIO = 68.902 DEPENDENT MEAN = 1.1294 DEGREES OF FREEDOM = 706 STANDARD ERROR AS % MEAN WATER SAT = 25.292 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH .43938 .26632E-01 .61696 -1.2117 -16.498 272.19 INCOME .28482E-01 .63351E-02 .16936 .13521 -4.4959 20.213 FAMILY .26374E-01 .69927E-02 .14254 .80436E-01 -3.7717 14.225 ROOMS .97349E-02 .83655E-02 .42495E-01 .50142E-01 -1.1637 1.3542 N
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Table J-75 Detroit Edison Individual Customer Appliance Model Linear Specification EQUATION AC SAT = 1.8251 .19315* CENTS /KWH + .045684* INCOME .11013* RATE + .051047* TYPE HOUSE R-SQUARED = .094472 717 OBSERVATIONS, 4 VARIABLES i CORRECTED R-SQUARED = .089385 RESIDUAL SUM SQUARE = 157.06 STANDARD ERROR = .46967 F-RATIO = 18.57 . DEPENDENT MEAN = 1.41 DEGREES OF FREEDOM = 712 STANDARD ERROR AS % MEAN AC SAT = 33.309 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH .19315 .46592E-01 .18539 .42637 -4.1455 17.185 INCOME .45684E-01 .99442E-02 .18621 .17374 4.5940 21.105 RATE .11013 .29055E-01 .14670 .95425E-01 -3.1905 14.368 TYPE HOUSE .51047E-01 .16260E-01 .11827 .53673E-01 3.1394 9.8555
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4 Table J-76 - Detroit Edison Individual Customer Appliance Model ' Linear Specification EQUATION ST0VE = 1.6617 .23877* CENTS /KWH + .042592* INCOME .026705*FAVILY + .062865* AGE HEAD + .12054* RATE R-SQUARED = .15345 716 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .14749 RESIDUAL SUM SQUARE = 149.91 - STANDARD ERROR = .45951 F-RATIO = 25.739 DEPENDENT MEAN = 1.4483 DEGREES OF FREEDOM = 710 STANDARD ERROR AS % MEAN ST0VE = 31.727 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH .23877 .45686E-01 .22665 .51326 -5.2263 27.314 INCOME .42592E-01 .10458E-01 .17160 .15759 4.0726 16.586 FAMILY .26705E-01 .11329E-01 .97417E-01 .63454E-01 -2.3572 5.5565 AGE HEAD .62865E-01 .13755E-01 .18474 .17011 4.5704 20.888 RATE .12054 .28597E-01 .15889 .10171 4.2151 17.767 - p 3
i ~~ _ _ Table J-77 J Detroit Edison Individual Customer Appliance Model Linear Specification 1 EQUATION FREEZER = 1.5241 .21738* CENTS /KWH + .054102* TEENS + .042709* AGE HEAD + .050733* RATE + .031407*R00NS R-SQUARED = .13335 712 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .12721 RESIDUAL SUM SQUARE = 131.75 STANDARD ERROR = .43199 F-RATIO = 21.727 DEPENDENT MEAN = 1.309 DEGREES OF FREEDOM = 766 STANDARD ERROR AS % MEAN FREEZER = 33.002 STANDARD VARIABLE COEFFICIENT ERROR BETA ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH .21738 .40841E-01 .22173 .51714 -5.3227 28.331 TEENS .54102E-01 .13540E-01 .15667 .38138E-01 3.9957 15.965 AGE HEAD .42709E-01 .12014E-01 .13513 .12772 3.5550 12.638 RATE .50733E-01 .26896E-01 .71720E-01 .47249E-01 1.8862 3.5578 ROOMS .31407E-01 .12189E-01 .99843E-01 .13968 2.5766 6.6388 c
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7 ___ ,__ ,_. y _. y , t Table J-78 Detroit Edison Individual Customer Appliance Model Linear Specification EQUATION DRYER = 1.4243 .17803* CENTS /KWH + .01093* INCOME .019731* FAMILY + .0029947* AGE HEAD + .16018* RATE
+ .039104*R00MS .019864* TYPE HOUSE R-SQUARED = .17421 711 OBSERVATIONS, 7 VARIABLES -
CORRECTED R-SQUARED = .16598 RESIDUAL SUM SQUARE = 113.42 STANDARD ERROR = .40166 F-RATIO = 21.186 DEPENDENT MEAN = 1.2616 DEGREES OF FREEDOM = 703 STANDARD ERROR'AS % MEAN DRYER = 31.837 STANDARD VARIABLE COEFFICIENT ERROR BEIJL ELASTICITY T-STATISTIC PARTIAL F CENTS /KWH .17803 .41307E-01 .19091 .43953 -4.3100 18.576 INCOME .10193E-01 .938205-02 .46287E-01 .43318E-01 1.0865 1.1804 . FAMILY .19731E-01 .10685E-01 .81435E-01 .53869E-01 -1.8465 3.4097 AGE HEAD .29947E-02 .12389E-01 .99686E-02 .92914E-02 .24172 .58427E-01 RATE .16018 .25157E-01 .23822 .15482 6.3672 40.542 ROOMS .39104E-01 .12423E-01 .13036 .18031 3.1477 9.9080 TYPE HOUSE .19864E-01 .14900E-01 .51342E-01 .23319E-01 -1.3332 1.7774 _. . . _ . _ _ _ _ c.
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, Table J-79 Detroit Edison Individual Customer Appliance Model Logarithmic Specification a
EQUATION - - AC SAT = 1.978* CENTS /KWH *48671* INCOME *10039* RATE .18342* TYPE HOUSE *065978 R-SQUARED = .088553 717 OBSERVATIONS, 4 VARIABLES CORRECTED R-SQUARED = .083432 RESIDUAL SUM SQUARE = 75.954 STANDARD ERROR = .32661 F-RATIO = 17.294-DEPENDENT MEAN = .28422 DEGREES OF FREEDOM = 712 STANDARD ERROR AS % MEAN AC SAT = 114.92 . STANDARD VARIABLE COEFFICIENT ERROR BETA T-STA'JISTIC PARTIAL F CENTS /KWH .48671 .10856 .21076 -4.4833 20.100 INCOME .10039 .25381E-01 .16008 3.9552 15.644 RATE .18342 .41736E-01 .18004 -4.3947 19.313 TYPE HOUSE .65978E-01 .26002E-01 .96020E-01 2.5374 6.4386 I
. n
7- . Table J-80 Detroit Edison Individual Customer Appliance Model Logarithmic Specification } 1 SAT = 4.803* CENTS /KWH l.0897* INCOME'* FAMILY .07216*R00MS R-SQUARED = .3568 711 OBSERVATIONS, 4 VARIABLES CORRECTED R-SQUARED < .35315 RESIDUAL SUM SQUARE = 24.752 STANDARD ERROR = .18724 F-RATIO = 97.907 DEPENDENT MEAN = .08969 DECREES OF FREEDOM = 706 STANDARD ERROR AS % MEAN WATER SAT = 208.77 STANDARD VARIABLE . COEFFICIENT ERROR BETA T-STATISTIC PARTIAL F CENTS /KWH -1.0897 .55553E-01 .68945 -19.615 384.74 i INCOME .60057E-01 .15563E-01 .13958 -3.8589 14.891 FAMILY - .72160E-01 .15266E-01 .17746 -4.7269 22.343 ROOMS .46921E-01 .29686E-01 .54666E-01 -1.5806 2.4982
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Table J-81 Detroit Edison Individual Customer Appliance Model Logarithmic Specification EQUATION - SPACE SAT = 1.186* CENTS /KWH .12288* INCOME .017124* AGE HEAD.0025645*R00MS .0023088* TY R-SQUARED = .053167 712 O8SERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .046461 RESIDUAL SUM SQUARE = 3.1531 STANDARD ERROR = .066829 F-RATIO = 7.9287 DEPENDENT MEAN = .0068146 DEGREES OF FREEDOM = 706 STANDARD ERROR AS % MEAN SPACE SAT = 980.66 STANDARD VARIABLE COEFFICIENT ERROR Jugg( T-STATISTIC PARTIAL F CENTS /KWH .12288 .19912E-01 .26451 -6.1709 38.080 INCOME .17124E-01 .55431E-02 .13538 -3.0893 9.5437 AGE HEAD .25645E-02 .62067E-02 .16235E-01 .41318 .17072 ROOMS .23088E-02 .10769E-01 .91633E-02 .21439 .45964E-01 TYPE HOUSE .79160E-02 .57517E-02 .57283E-01 1.3763 1.8942 i - i C.
g .. N Table J-82 Detroit Edison Individual Customer Appliance Model Logarithmic Specification EQUATION .60799 .069404 ST0VE = 2.178* CENTS!KWH
- INCOME.070826* FAMILY
- AGE HEAD.12697* RATE.14308 R-SQUARED = .15137 716 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .14539 RESIDUAL SUM SQUARE = 72.204 STANDARD ERROR = .3189 F-RATIO +
= 25.328 DEPENDENT MEAN = .31075 DEGREES OF FREEDOM = 710 STANDARD ERROR AS % MEAN ST0VE = 102.62 STANDARD -
VARIABLE COEFFICIENT ERROR BETA T-STATISTIC PARTIAL F CENTS /KWH .60799 .10673 26035 -5.6964 32.449 INCOME .70826E-01 .26905E-01 .11170 2.6325 6.9299 FAMILY .69404E-01 .25773E-01 .11530 -2.6929 7.2518 AGE HEAD -
.12697 .30709E-01 .15932 4.1347 17.096 RATE .14308 .41167E-01 .13898 3.4757 12.081 8?
--m I _
i i Table J-83 Detroit Edison Individual Customer Appliance Model Logarithmic Specification ZER = 1.852* CENTS /KWH
- TEENS '
- AGE HEAD. 0373* RATE * *R00MS' R-SQUARED = .10422 .
298 OBSERVATIONS, 5 VARIABLES CORRECTED R-SQUARED = .088884 RESIDUAL SUM SQUARE = 30.931 STANDARD ERROR = .32547 F-RATIO = 6.7948 DEPENDENT MEAN .= .28145 DEGREES OF FREEDOM = 292 STANDARD ERROR AS % MEAN FREEZER = 115.64 STANDARD VARIABLE COEFFICIENT ERROR BETA T-STATISTIC PARTIAL F CENTS /KWH .73133 .25387 17523 -2.8808 8.2989 TEENS .77774E-01 .35709E-01 .12311 2.1780 4.7436 i AGE HEAD .20373 .63224E-01 .18044 3.2223 10.383
- RATE .53548E-01 .60155E-01 .53464E-01 .89017 .79240 ROOMS .89174E-01 .94141E-01 .54344E-01 .94724 .89727 c
6 0
' Table J-84 -
Detroit Edison Individual Customer Appliance Model Logarithmic Specification EQUATION - - DRYER = 1.436* CENTS /KWH *39137* INCOME.025569* FAMILY .044056* + AGE HEAD.0011362 RATE.211
- TYPE HOUSE .033283 R-SQUARED = .17454 711 OBSERVATIONS, 7 VARIABLES CORRECTED R-SQUARED = .16632 RESIDUAL SUM SQUARE = 54.469 STANDARD ERROR = .27835 F-RATIO = 21.235 DEPENDENT MEAN = .18133 DEGREES OF FREEDOM = 703
, STANDARD ERROR'AS % MEAN DRYER = 153.51 STANDARD VARIABLE COEFFICIENT ERROR BETA T-STATISTIC PARTIAL F CENTS /KWH .39137 .96342E-01 .18911 -4.0623 16.502 INCOME .25569E-01 .23868E-01 .45382E-01 1.0713 1.1477 FAMILY .44056E-01 .24491E-01 .82742E-01 -1.7989 3.2359
; AGE HEAD .11362E-02 .27661E-01 . 16158E-02 .41076E-01 .16872E-02 4
RATE .21107 .36253E-01 .23088 5.8220 33.896 ROOMS .14319 .47116E-01 . 12740 3.0392 9.2366 i TYPE HOUSE .33283E-01 .24295E-01 .54099E-01 -1.3700 1.8768
. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _}}