USE OF MATHEMATICAL PLANNING MODELS TO PREDICT INCINERATION REQUIREMENTS

Transcription

1 USE OF MATHEMATICAL PLANNING MODELS TO PREDICT INCINERATION REQUIREMENTS J. H. BACHER E. D. RANARD Cmbustin En g ineerin g, Inc. Windsr, Cnnecticut ABSTRACT This paper presents mathematical mdels (equatins) t predict incineratr requirements in Cnnecticut. The technique f stepwise curvilinear regressin analysis was used t generate these mathematical mdels. The input infrmatin necessary t execute these mdels was taken frm a "transprtatin" study cnducted by the State f Cnnecticut. A transprtatin study investigates the effects f land use, ppulatin, and manufacturing intensities n highway requirements. Since similar transprtatin studies are being, r have been, cnducted in many states, the cncepts presented in this reprt can be used by ther states t develp their wn mdels t predict incineratr requirements. Regressin Analysis Regressin Line R Technique f fitting a curve t data s that the square f the difference between the bserved and predicted value is minimized Curve fund as result f regressin analysis Crrelatin cefficient. Measure f hw well regressin line fits the data; it can have a maximum value f (perfect fit) and a minimum value f (n crrelatin) Standard errr f estimate. Measure f the spread f data abut the regressin line Standard deviatin. Measure f the spread f the data abut the mean Dependent Variable Independent Variables NOMENCLATURE Variable t be predicted. Dependent variables are lcated t the left f the equal sign in this reprt Variables t be used in predicting dependent variable. Independent variables are lcated t the right f the equal sign in this reprt Mathematical Equatin(s) using ne r mre independent Mdel variables t predict a dependent variable Multiplier f standard deviatin. When t =, the range described by ± to y abut the me y will include 68 percent f the pints. When t =, the range described by ±to y abut the mean y will include 9 percent f the pints INTRODUCTION Municipal, cunty, and state planning bdies require infrmatin in rder t plan fr waste reductin and dispsal facilities. The methds described in this reprt can be develped s that fairly gd estimates f future waste

2 reductin requirements can be made n the cunty and state level. The methds are less accurate when used n the municipal level. The basic methd f apprach was t develp a series f mdels fr the State f Cnnecticut which culd frm the basis fr similar planning mdels in ther states. Inputs fr the mdels are btained frm transprtatin studies. A transprtatin study investigates the effect f land use, ppulatin, and manufacturing intensities n highway requirements. The mdels develped in this reprt utilize regressin analysis, a well knwn mathematical technique fr expressing ne variable (tns per day f incineratr capacity) as a functin f several thers (ppulatin, ppulatin density, manufacturing emplyment, etc.). This reprt describes the mathematical techniques and the mdeling cncepts used, and frecasts incineratr capacity in Cnnecticut t 97. INTRODUCTION TO MATHEMATICAL MODELING Mathematical mdels are mathematical equatins which use ne r mre knwn variables t predict ne r mre unknwn variables. The equatins mathematically represent past trends and can be extraplated t the future assuming past trends cntinue. The mathematical mdels develped utilize linear regressin analysis which is a statistical technique used t determine the mathematical relatinship between a dependent variable ( ) and a set f independent variables (X, X, f the frm Xn). An equatin is btained when linear regressin analysis has been applied t a set f data. The numerical values f the cefficients are such that the sum f the squares f the vertical distances between the data pints and the straight line representing the equatin is minimized. The quantity ts y in the abve equatin is a measure f these vertical distances. The standard deviatin, u y, is a measure f the spread f the data abut the mean f the V's. There is a 68 percent chance that a randm value f will fall within ne u y f the mean f the V's. The standard errr f the estimate, S is a measure f the spread f the data abut the y ' linear regressin line. When t =, there is a 68 percent chance that a randm value f will fall within ± S y f the value predicted by the line. When t =, there is a 9 percent chance that a randm value f will fall within ± s y f the value predicted by the line. The crrelatin cefficient, R, is a measure f hw well the equatin represents the data. R is defined s that R equals the percent f the variability f that is accunted fr by the relatinship with the X's. In mathematical frm R = - S Y Uy In this study, a regressin analysis cmputer prgram prvided the ability t cnsider nnlinear as well as linear relatinships. This additinal capability allwed fr a mre exact analysis f capacity needs fr slid waste reductin. The cmputer prgram als selected the best cmbinatin f variables; all variables which had cefficients with a cnfidence f less than 9 percent were eliminated frm the equatin. In ther wrds, all regressin equatins predicted in this reprt are given with 9 percent cnfidence. While regressin analysis is a valuable tl fr mathematical mdel building, cnsideratin must be given t the pssible misuse f it. The use f regressin analysis can result in invalid predictins because f the assumptin f nnexisting cause-and-effect relatinships. Fr example, if we get an extremely high linear crrelatin by cnsidering the increase in alchl cnsumptin with the increase in teachers' salaries, it is recgriized that n cause-and-effect relatinship exists. The example illustrates tw changes in ur envirnment with n real relatinship. The abve example is t emphasize the need fr cmmn sense judgments in gathering input infrmatin fr any cmputer analysis f sets f interrelated variables. In additin, the use f regressin equatins t predict the future implies that the histrical relatinship between the variables will remain cnstant ver time; i.e., the cefficients a ' a etc., will remain cnstant. Any changes in these relatinships and, hence, in the cnstants, will intrduce errrs int the predicting equatin. MODEL CONCEPT The Cnnecticut waste reductin mdels are shwn in relatin t ther planning mdels in Fig.. The chrnlgical develpment f these mdels is als illustrated. Mdel can be any natinal prjectin f ecnmic activity. The ne shwn was develped by the Natinal Planning Assciatin. Mdels and were develped by Cnnecticut fr its planning needs. Similar mdels can be

3 MODEL Natinal Planning Assciatin Reprts n Industrial Emplym nt[ll Future emplyment by S.I.C. Cde Cnnecticut "Sci-Ecnmic Grwth Mdel" by Cnnecticut Interreginal Planning Prgram [ MODEL Regressin analysis n past trends and an ecnmic input - utput mdel fr Cnnecticut were used t predict ppulatin and emplyment levels and utputs t the industrial and service sectrs t the year. Emplyment and ppulatin fr Cnnecticut in 96, 97, 98, 99, and. "A Mdel fr Allcating Ecnmic Activities int Sub-Areas in a State"[, MODEL Prepared fr the Cnnecticut Interreginal Plannine Prgram (CIPP) by Alan M. Vrhees & Assciates, Inc. A mathematical mdel (Transprtatin Study) develped by linear regressin techniques allcated Cnnecticut's residential and industrial ppulatin int each f the 69 twns fr 96, 97, 98, 99, and. Vacant land, ppulatin and emplyment (manufacturing, retail, service and thers) by twns fr 96, 97, 98, 99, and. Cnnecticut Slid Waste Mdels[] MODEL The waste generatin per capita and per emplyee by S.I.C. Cde were determined frm the municipal and industrial slid waste inventries. By means f linear regressin, th waste eductin capacity f Cnnecticut twns was crrelated with the data f the CIPP study. The resulting mathematical mdel was used t prject installed waste reductin capacity by cunty t 97. Municipal and industrial waste prductin were als estimated. Municipal Waste, industrial aste and incineratin Capacity in 97. FIG. THE INFORMA TlON SOURCES OF THE CONNECTICUT REDUCTION CAPACITY MODEL

4 develped by ther states fr highway and ther municipal planning activities. This reprt discusses the develpment f a Cnnecticut slid waste mdel. Cnnecticut's land usage study (Mdel ) cmplied with the Federal regulatin that all twns f ver, peple in a state must undertake a land usage study in rder that the state be eligible fr the 9 percent Federal aid in rad building prjects. The Cnnecticut land usage study served as a basis fr develping the Cnnecticut waste reductin mdel. Mdel, Cnnecticut's land usage study, [] distributed the state ttal f several ecnmic variables such as ppulatin and manufacturing emplyment t each f the 69 Cnnecticut twns. This was dne thrugh the use f a methd called differential shift analysis. The change in an ecnmic variable f a sub-regin is assumed t cnsist f tw factrs. The first factr, called the prprtinal shift, allws fr the change f this variable as a percentage f the change f the entire state. The secnd factr allws fr the differential shift between the subregin and the state. That is, this secnd factr allws fr the difference in the grwth rates f the entire state and the individual twns. [] The Cnnecticut land use mdel was frmulated as a set f simultaneus equatins, each equatin describing ne sectr f the ecnmy. The equatins mathematically frmulated the interplay between transprtatin facilities in and leading t a twn and the presence f peple in the twn. The tendency f peple t settle near transprtatin facilities and the tendency f highways t be built near peple were described mathematically. These equatins TABLE I TYPICAL SUMMARY OF FAIRFIELD COUNTY DATA 966 OBTAINED FROM CONNECTICUT TRANSPORTATION STUDY [] Twn Ppulatin Ttal Pssible Ppulatin Mfg. Ppulatin Ttal Pssible Mfg. Ppulatin Tns/Day Installed Tns/Week Reduced Bethel Bridgeprt Brkfield Danbury Darien Eastern Fairfield Greenwich Mnre New Canaan New Fairfield Newtn Nrwalk Redding Ridgefield Sheltn Sherman Stamfrd Stratfrd Trumbull Westn Westprt Wiltn 9,7 7,68 6,66 6,,,78,8 7,88 9, 9,,78,69 7,86,,,,9,6,9 6,,7 7,66,8 8,7 8,9,89,9 7,9, 7,99 68,79,987,68 6,8 6, 96,68 6,,7 8,8 7,7,6 6,8 7,97,,6,89 87,68 9,6,8,7 6 6,, 7 6,9 7,8,66 9 7,79 6,87 7,9,9,9,7 89,9,6,68 8, 9,68 8,87,6 9, 6 6,66 7 7,,8 8 78,686,79, 9, 6,89,,9

5 were slved with a cmputer and the results were used in this reprt as inputs t the incineratr mdels. DESCRIPTION OF VARIABLES Tw mathematical mdels (equatins) are described in this reprt. The first uses incineratr capacity as a dependent variable and the secnd uses tns f waste incinerated as the dependent variable. The data fr tns f installed capacity per day per twn came frm a number f statistical surces described in []. The data fr tns f slid waste incinerated per week per twn was btained frm [6 and 7]. Cnnecticut's incineratrs are nt utilized Zne Ind. Spec Cm TABLE II [J ZONE CLASSES IN CONNECTICUT Industrial Residential lts up t,999 sq ft Residential lts, t 9,999 sq ft Residential lts, t 9,999 sq ft Residential lts, sq ft and ver Specially zned fr such purpses as recreatin and fld plain zning Cmmercial TABLE III (a) [6 J LAND CLASSES IN CONNECTICUT Sil Class N. Excellent fr building purpses Sil Class N. Gd - Fair fr building purpses Sil Class N. - Pr fr building purpses Sil Class N. Very Pr fr building purpses Sil Class N. A is a mdificatin f Sil Class N. Sil Class A TABLE III (b) % % % % % /+ Land Slpe t capacity. Fr example, the twn f Greenwich with a rated capacity f tns per day r, tns per week reduces nly 7 tns f slid waste per week. The data n the utilizatin f Cnnecticut incineratrs (tns per week reduced in incineratr) were incrprated int the Cnnecticut utilizatin mdel. Typical utilizatin data is prvided in Table. The chice f independent variables fr these mdels was based n the assumptin that slid waste reductin capacity was primarily dependent upn tw factrs: () amunt f refuse generated and, () amunt f land available fr landfill. The independent variables used in the Cnnecticut mdels are presented belw. Independent Variable. Ppulatin. Ttal pssible ppulatin (based n zning laws). Manufac. Ttal pssible turing Emplyment manufacturing emplyment. Vacant land Why Selected Mre peple means mre waste Measures residential land available Industry is a surce f slid waste and als indicates general ecnmic activity which is assciated with slid waste prductin Measures industrial land available Influences methd f waste dispsal The Variable is an Indicatin f the Fllwing Factr Municipal waste generatin Vacant land Industrial waste generatlon Vacant land Vacant land The data fr these independent variables was fund in [ and J Table I presents a typical summary f cunty data. Ttal pssible ppulatin was btained by the land allcatin mdel [] frm a cnsideratin f the twn zning laws and the suitability f this land t supprt ppulatin n the basis f slpe and sil characteristics. Ttal pssible manufacturing emplyment was similarly btained frm land zned fr industrial purpses.

6 In the develpment f the mdels, the variables mentined abve were cmbined t prvide a mre meaningful explanatin f slid waste reductin capacity. Fr example, the rati f ppulatin t ttal pssible ppulatin saturatin wuld indicate when waste reductin equipment shuld be installed. Hwever, it wuld nt indicate the size f the equipment necessary. Ppulatin, as a measure f the waste prduced, des indicate the size f equipment if it is necessary. A parameter which cmbines these tw factrs is a better factr than bth taken independently. Manufacturing emplyment and ttal pssible manufacturing were similarly cmbined. Since sme twns are cmpletely residential and ttal pssible manufacturing is zer, a "ne" was added in the denminatr t prevent the variable frm becming indeterminate. As shwn in Tables II and III, land in Cnnecticut is characterized by class and is described by land charac- TABLE IV NUMBER OF WASTE DISPOSAL SITES BY ZONE FOR CONNECTICUT IN 966 Zne Industrial Number f Sites teristics by the Cnnecticut Interreginal Planning Assciatin. Land zning is prescribed by twn gvernments. The land characteristics depend upn the sil and slpe f the terrain. It may be pssible t develp a relatinship between the number f slid waste dispsal sites and the type f land n which they are built. Hwever, the data summarized in Tables IV and V indicate that Cnnecticut twns have in the past used any type f land fr waste dispsal sites. Fr this reasn, the variable "vacant land" included all the unused land in a twn rather than land f specific sil, slpe, r zne characteristics. Data such as that shwn in Table VI was available fr all Cnnecticut twns fr 96, but nt fr 966 and 97. The vacant land fr these years was estimated by assuming the fllwing relatinship existed between vacant land and ppulatin. Vacant land66 - Vacant land6 + Ppulatin6 - Ppulatin66 Ttal Pssible Ppulatin Vacant land6 Subscripts indicate applicable year. Table VII shws the relatinship amng the dependent and independent variables f the Cnnecticut capacity mdel. Table VIII shws the relatinship amng the dependent and independent variables f the Cnnecticut utilizatin mdel Special 7 Cmmercial TABLE VI [] TYPICAL SUMMARY OF VACANT LAND DATA Bethel 96 - Vacant Land in Acres LAND CLASS TABLE V NUMBER OF WASTE DISPOSAL SITES BY LAND CLASS FOR CONNECTICUT Zne Residential Ttal Land Class Number f Sites Residential Residential , Residential,,8 68,7, 6,6 Cmmercial Industrial Other Ttal,6,7 697,6,8 8,9 6

7 Tables VII and VIII shw the crrelatin between dependent and independent variables. Fr example, the intersectin f rw and clumn cntains the crrelatin cefficient f variables and. Similarly, the number at the intersectin f rw and clumn is the same because it is a measure f the crrelatin f the same tw variables and. Therefre, the matrix shwn in Tables VII and VIII is symmetrical abut the diagnal dented by the unity cefficients. If a regressin line were fitted between variable and variable in Table VII, it wuld have a crrelatin cefficient f.8. Similarly when a regressin line is fitted between variable Y ' (tns f installed capacity per day) and variable, the crrelatin cefficient is.8. It can be seen frm Table VII that there is very pr crrelatin between Y ' and variables 6, 7, and 8 which are functins f vacant land, and very gd crrelatin between y' and variables,, and which are functins f ppulatin and ppulatin density. The data shwn in Table VII can be used t select thse variables which shuld yield high crrelatin when they are cmbined using multiple regressin analysis. This is discussed in the next sectin. PROJECTIONS OF INSTALLED WASTE REDUCTION CAPACITY TO 97 Equatins () and (), shwn in Table IX, mdel the slid waste reductin capacity f Cnnecticut by twn. One hundred sixty-nine bservatins, ne fr each f Cnnecticut's twns, were used t generate each equatin. The first equatin uses nine terms (three independent variables) and achieves a multiple crrelatin cefficient f.9 with a standard errr f. tns per day. Thus, TABLE VII CONNECTICUT MATHEMATICAL CAPACITY MODEL CORRELATION MATRIX Variable * y' Variable [.8] See Text [.8] See Text [.8].8 See Text y' y' *Numbers refer t the fllwing list f variables: Ppulatin X = x I - Ttal Pssible Ppulatin X X I X. I X I X = (Manufacturing Emplyment) Ttal Pssible Manufacturing Emplyment + 6 X - 7 X. 8 X y ' = Vacant land x (X Yz I ) Tns f installed capacity per hur day 7

8 9 percent (.9 x.9) f the variability f the installed capacities in all f Cnnecticut's twns is accunted fr by this mdel. Althugh the simplified mdel, equatin (), uses nly three terms (ne independent variable), it des almst as well as the cmplex mdel. A multiple crrelatin cefficient f.9 is achieved with a standard errr f 7.6 tns per day. Thus, this simple mdel accunts fr 88 perc en t (.9 x.9) f the variability f the installed capacities in all f Cnnecticut's twns. Equatin () is pltted in Fig.. Nte that the curve (equatin ) levels ff at 6 tns per day, because a Cnnecticut twn with a value f Xl that crrespnds t a Y equal t 6 tns per day is prbably saturated. That is, the ppulatin f the twn is abut equal t the ttal pssible ppulatin allwed by existing zning restrictins. Thus, the nly slid waste reductin increase will prbably be due t increased waste per capita r due t municipalities handling a larger share f the industrial slid waste stream. PROJECTIONS OF UTILIZED WASTE REDUCTION CAPACITY TO 97 Equatins () and () in Table XI relate the tns f slid waste incinerated per week with several independent variables fr each twn in Cnnecticut. One hundred sixty-nine bservatins (twns) were used t generate each equatin. The first equatin uses nine terms (fur independent variables) and achieves a multiple crrelatin cefficient f.97 with a standard errr f 7. tns per week. Thus, 9 percent (.97 x.97) f the variability TABLE VIII CONNECTICUT MATHEMATICAL UTILIZATION MODEL CORRELATION MATRIX Variable * y " Variable y " y " *Numbers refer t the fllwing list f variables: Ppulatin X l - (Ttal Pssible Ppulatin) x - 6 X = Vacant land x (Xl) \/ X l I.S X I (Manufacturing Ppulatin) X - (Ttal Pssible Mfg. Ppulatin) 7 X. 8 X (Manufacturing Ppulatin) x Ppulatin X = (Ttal Pssible Ppulatin) X. X 9 X. y" = Tns f slid waste reduced per week 8

9 f the tns incinerated is explained by these variables. The crrelatin cefficient and standard errr f the utilizatin mdel as cmpared t the crrelatin cefficient (.9) and standard errr (. tns per day) f the capacity mdel indicate that the utilizatin mdel is the better mdel. Fr example, the percentage errr at the maximum y ' fr the capacity mdel is./6 r apprximately.7 percent; the percentage errr in the utilizatin mdel at maximum y ' is 7./8 r. percent. The utilizatin mdel remves ne additinal surce f errr frm the capacity mdels previusly described, the time each incineratr is utilized. That is, a twn can have tns per day installed capacity and perate it 8 hurs t prvide the same quantity f refuse incinerated in a -tn-per-day plant perating apprximately 6 hurs a day. The simplified utilizatin mdel, equatin (), des almst as well as the cmplex mdel althugh nly three terms (ne independent variable) are used. A multiple crrelatin cefficient f.96 is achieved with a standard errr f 8.9 tns per week. Thus, this simple mdel accunts fr 9 percent (.96 x.96) f the variability f the utilized capacities f Cnnecticut twns. Table XII presents a cmpilatin f the Cnnecticut utilizatin mdel 97 prjectins in terms f tns f refuse incinerated per cunty. The cunty data was btained by summing the twn data fr each cunty. Typical cunty data (Fairfield) is shwn in Table. Equatin () is pltted in Fig.. TABLE IX COMPLEX CONNECTICUT CAPACITY MODEL Eq. () y ' X +.89Xl. S -.79X X - X -. X -7 X +. 6X X - X X -7 X Where: y ' tns installed capacity per day per twn ppulatin (twn) X - ttal pssible ppulatin (twn) manufacturing emplyment (twn) ttal pssible manufacturing emplyment (twn) + vacant land (acres - twn) ppulatin (twn) X - ttal pssible ppulatin (twn) Crrelatin Cefficient R =.9 Standard Errr f Estimate. tns/day Number f Observatins = 69 SIMPLIFIED CONNECTICUT CAPACITY MODEL Eq. () Where: y ' y ' X +.7Xl. _.66X tns installed capacity per day per twn ppulatin (twn) X - ttal pssible ppulatin (twn) Crrelatin Cefficient R =.9 Standard Errr f Estimate 7.6 tns/day Number f Observatins = 69 9

10 ACKNOWLEDGMENT The wrk which is described in this paper was accmplished under cntract frm the Slid Wastes Pr- TABLE X CONNECTICUT SOLID WASTE REDUCTION CAPACITY BY COUNTY TONS OF INSTALLED CAPACITY PER HOUR DAY Cunty Actual Eq. () Eq. () gram f the Public Health Service, Department f Health, Educatin and Welfare (Cntract N. ph ). The wrk frmed a prtin f a survey by Cmbustin Engineering, Inc. f municipal and industrial slid waste dispsal needs and practices in the United States. The cntract wrk is intended t prvide an initial imprvement t a situatin which has seen slid waste management effrts seriusly hampered by the lack f cnsistent and reliable infrmatin in the slid waste field. The authrs wish t acknwledge the valuable data prcessing assistance prvided by Messrs. M. Daversa and Fairfield,,, TABLE XII Hartfrd,,, CONNECTICUT SOLID WASTE INCINERATED Litchfield Middlesex New Haven New Lndn Tlland,8,9,87 7 Windham 7,96 6,8 6,6 Cunty Fairfield Hartfrd Litchfield Middlesex Tns f Utilized Capacity Per Week Actual Eq. (),9,6 6,9,76 97 Eq. () 7,,7 Nte: The mdel als assumes n increase in punds per capita. If % per year applies t all types f refuse in Cnnecticut, the values shwn abve fr 97 wuld be increased by apprximately % assuming all equipment runs at same - New Haven New Lndn Tlland,7,97, 8 utilizatin factr. In additin, if a larger prtin f the industrial slid waste stream was handled in municipal Windham facilities, installed capacity wuld increase even further. Ttal,87 7,76 8,66 7, ' -, ;Ju.. : "c It".... Cc OC ''Ii g-... ) ZOO "fjfnrs OF zelia t"le/weiiar" CAPACirr 'ALL" TO THIS Olllr r 6 I * _ ( POftULATION J. J POII'ULATION J( TOTAL.. u: fiicni'ulat" " '" '",.. z..., '"..... " U z - '"..... ;!! 8 8 e POfIi'ULATtON X ( '"' FIG. TONS PER DA Y OF INSTALLED INCINERA TOR CAPACITY DETERMINED FROM CONNECTICUT MODEL FIG. TONS PER WEEK OF SOLID WASTE INCINERATED DETERMINED FROM CONNECTICUT UTlLlZA TION MODEL

11 G. W. Tuite f Cmbustin Engineering, Inc. and the assistance in btaining data prvided by Mr. B. Chase, Mr. C. Kurker, and Mr. F. Cleman f the Cnnecticut Develpment Cmmissin, State Department f Health, and the State Highway Department, respectively. REFERENCES [] Vrhees, A. M. and Assciates, Inc., "A Mdel fr Allcating Ecnmic Activities int Sub-Areas in a State," prepared fr the Cnnecticut Interreginal Planning Prgram, 966. [ ] "Study Prcedure Manual III-A t," Cnnecticut Interreginal Planning Prgram, July 96. [] Cmbustin Engineering, Inc., "Technical-Ecnmic Study f Slid Waste Dispsal Needs and Practices," prepared fr the Department f Health, Educatin and Welfare, Nvember 967. [ ] American Industry in 976 and 98. Reprt N. 6-. [6] Kurker, C., Cnnecticut State Health Department, Natinal Planning Assciatin Center fr Ecnmic Prjectins_ private crrespndence, May 967. [] "The Sci-Ecnmic Grwth Mdel," Staff Paper [7] Weekly Health Bulletin, Cnnecticut State Department N. D, Cnnecticut Interreginal Planning Prgram, p.. f Health, March 96. TABLE XI COMPLEX CONNECTICUT UTILIZATION MODEL Eq. () y " Xl Xl. -.99Xl +.86 X - X Where: y " X - X +.6X -.8 X - X. +.7 X -6 X X - X. tns f slid waste reduced per week per twn ppulatin (twn) X ttal pssible ppulatin (twn) manufacturing emplyment (twn) ttal pssible manufacturing emplyment (twn) + vacant land (acres - twn) ppulatin (twn) X - ttal pssible ppulatin (twn).. ppulatin (twn) manufactunng ppulatlon (twn) X tt al POSS l 'bl e ppu I atlon ' (twn) Crrelatin Cefficient =.97 Standard Errr f Estimate 7. tns/week Number f Observatins = 69 SIMPLIFIED CONNECTICUT UTILIZATION MODEL Eq. () y " X XlI. -.9Xl Where: y " tns f slid waste reduced per week per twn ppulatin (twn) ttal pssible ppulatin (twn) Crrelatin Cefficient =.96 Standard Errr f Estimate 8.9 tns/week Number f Observatins = 69