marshall ce 254 trip-distribution

CE 254Transportation EngineeringWes Marshall, P.E. University of Connecticut February 2008The Four-Step Model:

II. Trip Distribution

The Basic Transportation ModelStudy Area Zones Attributes of ZonesSocioeconomic DataLand Use DataCost of Travel btw. ZonesThe Road Network Traffic Volume by Road Link Mode Splits EmissionsInputsOutputs

Whats in the Black Box?The Four-Step Model

The Four-Step Modeling Process Trip Generation

Trip Distribution

Mode Choice

Trip AssignmentWHY?

The Four-Step ModelThe main reason we use the four-step model is:To predict roadway traffic volumes & traffic problems such as congestion and pollution emissions In turn, we typically use the models to compare several transportation alternatives

The Four-Step ModelOriginally developed in the 1950s with the interstate highway movement Since the 1950s, researchers have developed a multitude of advanced modeling techniques

Nevertheless, most agencies still use the good ol four-step model

Overview of the Four-Step Model

Model residential trip productions and non-residential trip attractions w/ - Regression Models- Trip-Rate Analysis- Cross-Classification Models - i.e. traffic flows on network, ridership on transit lines - A matrix of trips between each TAZ also called a trip table - i.e. columns of trip productions and trip attractions

- No. of Housing Units - Office, Industrial SF - HH Size- Income- No. of CarsIterative Process

Land Use DataInput:Household Socioeconomic Data}Examples of HH socioeconomic data}Examples of land use dataOutput:Trip Ends by purpose Input:Trip Ends by purpose Output:Trip Interchanges Input:Trip Interchanges Output:Trip Table by ModeInput:Trip Table by Mode Output:Daily Link Traffic Volumes TRIP GENERATIONTRIP DISTRIBUTIONMODE CHOICETRIP ASSIGNMENTProcess:Survey DataGrowth Factor ModelsNot as accurate as Gravity ModelUsed for external trips or short-term planningGravity ModelUsed for regional or long-term planning Process:

- i.e. traffic flows on network, ridership on transit linesIterative ProcessInput:Trip Interchanges Output:Trip Table by ModeInput:Trip Table by Mode Output:Daily Link Traffic Volumes MODE CHOICETRIP ASSIGNMENTFinds trip interchanges between i & j for each mode- Function of Trip Maker, Journey, and Transport FacilityTrip End ModelMode plays role in trip endsTypically used for small cities with little traffic and little transitNo accounting for the role that policy decisions play in mode choiceTrip Interchance ModelUse when LOS is important, transit is a true choice, highways are congested, and parking is limited Process:Allocate trips to links between nodes i & j- Function of Path to Destination and Minimum Cost (time & money)Identify Attractive Routes via Tree BuildingShortest Path Algorithm or Dijkstras AlgorithmAssign Portions of Matrix to Routes / TreeUser Equilibrium, Heuristic Methods, Stochastic Effects w/ LogitSearch for ConvergenceProcess:

Some General Problems with the Conventional MethodologyHuge focus on vehicular traffic A transit component is typical in better modelsTypically forecasts huge increases in trafficLeads to engineers building bigger roads to accommodate forecast traffic Which leads to induced traffic and congestion right back where we started when we needed the bigger roads in the first place

Some General Problems with the Conventional MethodologyPedestrians and bicyclists are rarely includedLevel of geography is difficult for non-motorized modesNetwork scale is insignificantInput variables are too limited

Preparing for a Four-Step ModelBefore jumping into trip generation, we first have to set up our project

Define study area and boundariesEstablish the transportation networkCreate the zones

Defining the Study Area3 Basic TypesRegionalStatewide or a large metro areaUsed to predict larger patterns of traffic distribution, growth, and emissionsCorridorMajor facility such as a freeway, arterial, or transit lineUsed to evaluate trafficSite or ProjectProposed development or small scale change (i.e. intersection improvement)Used to evaluate traffic impact

Establish the NetworkRoads are represented by a series of links & nodes

Links are defined by speed and capacityTurns are allowed at nodesLinkNode

Establish the NetworkTypically only main roads and intersections are included Even collector roads are often excludedThis practice is becoming less common as the processing power of computers has increased

Creating ZonesCreate Traffic Analysis Zones (TAZ)Uniform land useBounded by major roadsTypically small in size (about the size of a few neighborhood blocks) The State of Connecticut model has ~2,000 zones that cover 5,500 square miles and over 3.4 million people

Creating ZonesAll modeled trips begin in a zone and are destined for a zoneZones are usually large enough that most pedestrian and bicycle trips start and end in the same zone (and thus not modeled)Also, the typical data we collect about zones in terms of population and employment information is not enough to predict levels of walking and biking

Trip Generation

Trip GenerationUsing socioeconomic data, we try to estimate how many trips are produced by each TAZFor example, we might use linear regression to estimate that a 2-person, 2-car household with a total income of $90,000 makes 2 home-based work trips per day Using land use data, we estimate how many trips are attracted to each TAZFor example, an 3,000 SF office might bring in 12 work trips per day

Trip GenerationThe process considers the total number of tripsThus, walking and biking trips have not been officially excluded (although most models ignore them completely)The trips are generated by trip purpose such as work or shoppingRecreational or discretionary trips are difficult to include

Trip GenerationSocioeconomic DataLand Use DataInput:Output:Trip Ends by purpose (i.e. work) in columns of productions & attractions

Sheet1

TAZProductionsTAZAttractions

11219

219212

33534

44438

55545

61066

71374

82282

120120

Sheet2

Sheet3

Sheet1


11219

219212

33534

44438

55545

61066

71374

82282

120120

Sheet2

Sheet3

Sheet1


11219

219212

33534

44438

55545

61066

71374

82282

120120

Sheet2

Sheet3

Sheet1


11219

219212

33534

44438

55545

61066

71374

82282

120120

Sheet2

Sheet3

Sheet1


11219

219212

33534

44438

55545

61066

71374

82282

120120

Sheet2

Sheet3

Sheet1


11219

219212

33534

44438

55545

61066

71374

82282

120120

Sheet2

Sheet3

Trip Generation Trip DistributionThe question is how do we allocate all the productions among all the attractions?Zone 1Trip Matrix or Trip Table

Sheet1


11219

219212

33534

44438

55545

61066

71374

82282

120120

Sheet2

Sheet3

Sheet1


11219

219212

33534

44438

55545

61066

71374

82282

120120

Sheet2

Sheet3

Sheet1

TAZProductionsTAZAttractionsTAZ12345678

112191

2192122

335343

444384

555455

610666

713747

822828

120120

TAZ12345678

1

2

3

4

5

6

7

8

Sheet2

Sheet3

Trip Distribution

Trip DistributionWe link production or origin zones to attraction destination zonesA trip matrix is produced

The cells within the trip matrix are the trip interchanges between zones

Trip InterchangesDecrease with distance between zonesIn addition to the distance between zones, total trip cost can include things such as tolls and parking costsIncrease with zone attractivenessTypically includes square footage of retail or office space but can get much more complicated

Trip DistributionSimilar to Trip Generation, all the modes are still lumped together by purpose (i.e. work, shopping)This creates a problem for non-vehicular trips because distance affects these trips very differentlyAdditionally, many walking and biking trips are intra-zonal & difficult to model

Criteria for allocating all the productions among all the attractionsCost of tripTravel TimeActual CostsAttractivenessQuantity of OpportunityDesirability of OpportunityBasic Criteria for TD

How to Distribute the Trips?Growth Factor ModelsGravity Model

Growth Factor ModelsGrowth Factor Models assume that we already have a basic trip matrix

Usually obtained from a previous study or recent survey data

Sheet1


112191550100200

2192122505100300

335343501005100

44438410020025020

555455

610666

713747

822828

120120

TAZ12345678

1

2

3

4

5

6

7

8

Sheet2

Sheet3

Growth Factor ModelsThe goal is then to estimate the matrix at some point in the future For example, what would the trip matrix look like in 10 years time?Trip Matrix, t (2008)Trip Matrix, T (2018)

Sheet1


112191550100200

2192122505100300

335343501005100

44438410020025020

555455

610666

713747

822828

120120

TAZ12345678

1

2

3

4

5

6

7

8

Sheet2

Sheet3

Sheet1


112191550100200

2192122505100300

335343501005100

44438410020025020

555455

610666

713747

822828

120120

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

TAZ12345678

1????

2????

3????

4????

5

6

7

8

Sheet2

TAZ123478

1550100200355400

2505100300455460

3501005100255400

410020025020570702

20535545562016351962

6

7

8

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

TAZ123478

15.656.3112.7225.4400400

250.55.1101.1303.3460460

378.4156.97.8156.9400400

4123.2246.3307.924.6702702

257.7464.6529.5710.219621962

6

7

8

Sheet3

TAZ123478

1550100200355400

2505100300455460

3501005100255400

410020025020570702

20535545562016351962

1804063807401706

7

8

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

TAZ123478

15.656.3112.7225.4400400

250.55.1101.1303.3460460

378.4156.97.8156.9400400

4123.2246.3307.924.6702702

257.7464.6529.5710.219621962

6

7

8

Avg Factor

TAZ123478

1060100200360400

2505100300455460

3501005100255400

410020025020570702

20036545562016401962

1804063807401706

7

8

TAZ12345678

1060120240

2606120360

3601206120

412024030024

5

6

7

8

TAZ123478

15.656.3112.7225.4400400

250.55.1101.1303.3460460

378.4156.97.8156.9400400

4123.2246.3307.924.6702702

257.7464.6529.5710.219621962

6

7

8

Some of the More Popular Growth Factor ModelsUniform Growth FactorSingly-Constrained Growth FactorAverage FactorDetroit FactorFratar Method

Uniform Growth Factor Model

Uniform Growth FactorTij = tij for each pair i and jTij = Future Trip Matrix tij = Base-year Trip Matrix = General Growth Rate i= I = Production Zone j= J = Attraction Zone

Uniform Growth FactorTrip Matrix, t (2008)Trip Matrix, T (2018)If we assume = 1.2, then Tij = tij= (1.2)(5)= 6Tij = tij for each pair i and j Tij = Future Trip Matrix tij = Base-year Trip Matrix = General Growth Rate

Sheet1


112191550100200

2192122505100300

335343501005100

44438410020025020

555455

610666

713747

822828

120120

TAZ12345678

1

2

3

4

5

6

7

8

Sheet2

Sheet3

Sheet1


112191550100200

2192122505100300

335343501005100

44438410020025020

555455

610666

713747

822828

120120

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

Sheet2

Sheet3

Uniform Growth FactorThe Uniform Growth Factor is typically used for 1 or 2 year horizonsHowever, assuming that trips grow at a standard uniform rate is a fundamentally flawed concept

Singly-Constrained Growth Factor Model

Singly-Constrained Growth Factor MethodSimilar to the Uniform Growth Factor Method but constrained in one directionFor example, lets start with our base matrix, tattractions, jproductions, izones

Sheet1


112191550100200

2192122505100300

335343501005100

44438410020025020

555455

610666

713747

822828

120120

TAZ12345678

1

2

3

4

5

6

7

8

Sheet2

Sheet3

Singly-Constrained Growth Factor MethodInstead of one uniform growth factor, assume that we have estimated how many more or less trips will start from our origins

Now all we have to do is multiply each row by the ratio of (Target Pi) / (j)

Sheet1


112191550100200

2192122505100300

335343501005100

44438410020025020

555455

610666

713747

822828

120120

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

Sheet2

TAZ1234jTarget Pi78

1550100200355400

2505100300455460

3501005100255400

410020025020570702

i20535545562016351962

6

7

8

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

Sheet3

Sheet1


112191550100200

2192122505100300

335343501005100

44438410020025020

555455

610666

713747

822828

120120

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

Sheet2

TAZ1234jTarget Oi78

1550100200355400

2505100300455460

3501005100255400

410020025020570702

i20535545562016351962

6

7

8

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

Sheet3

Sheet1


112191550100200

2192122505100300

335343501005100

44438410020025020

555455

610666

713747

822828

120120

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

Sheet2

TAZ1234jTarget Oi78

1550100200355400

2505100300455460

3501005100255400

410020025020570702

i20535545562016351962

6

7

8

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

Sheet3

Sheet1


112191550100200

2192122505100300

335343501005100

44438410020025020

555455

610666

713747

822828

120120

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

Sheet2

TAZ1234jTarget Oi78

1550100200355400

2505100300455460

3501005100255400

410020025020570702

i20535545562016351962

6

7

8

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

Sheet3

Singly-Constrained Growth Factor Method Tij = tij (Target Pi) / (j) = 5 (400 / 355)= 5.6

Sheet1


112191550100200

2192122505100300

335343501005100

44438410020025020

555455

610666

713747

822828

120120

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

Sheet2

TAZ1234jTarget Pi78

1550100200355400

2505100300455460

3501005100255400

410020025020570702

i20535545562016351962

6

7

8

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

Sheet3

Singly-Constrained Growth Factor MethodCan also perform the singly-constrained growth factor method for a destination specific future trip tableBy multiplying each column by the ratio of (Target Aj) / (i)

Sheet1


112191550100200

2192122505100300

335343501005100

44438410020025020

555455

610666

713747

822828

120120

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

Sheet2

TAZ1234jTarget Oi78

1550100200355400

2505100300455460

3501005100255400

410020025020570702

i20535545562016351962

6

7

8

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

TAZ1234jTarget Oi78

15.656.3112.7225.4400400

250.55.1101.1303.3460460

378.4156.97.8156.9400400

4123.2246.3307.924.6702702

i257.7464.6529.5710.219621962

6

7

8

Sheet3

TAZ1234jTarget Oi78

1550100200355400

2505100300455460

3501005100255400

410020025020570702

i20535545562016351962

Target Aj1804063807401706

7

8

TAZ12345678

1660120240

2606120360

3601206120

412024030024

5

6

7

8

TAZ1234jTarget Oi78

15.656.3112.7225.4400400

250.55.1101.1303.3460460

378.4156.97.8156.9400400

4123.2246.3307.924.6702702

i257.7464.6529.5710.219621962

6

7

8

Overview of the Singly-Constrained Growth Factor MethodologyOne of the simplest trip distribution techniquesUsed with existing trip table & future trip endsTypically, we balance flows after processingThis means that the total number of productions equals the total number of attractions (or in terms of origins & destinations)Tij = TjiBut there are more advanced growth factor models

Average Growth Factor Model

Average Growth Factor Function F = Growth Factor =Ratio of Target Trips toPrevious Iteration Trips k =Iteration Numberg ( )=Fik FjkF.kg ( )=Fik + Fjk2

The Basic StepsCollect InputsMatrix of Existing Trips, {tij}Vector of Future Trips Ends, {Ti}Compute Growth Factor for each zone

Compute Inter-zonal Flows

Compute Trips Ends

If tik = Ti for each zone i, then stop otherwise, go back to Step 1>Fik=Titik-1=Target Trip EndPrevious Iteration Trip End>tijk = tijk-1 [g(Fik, Fjk, )] for each ij pairtik = tijk for each zone i

Growth Factor Models: Average Factor Example

SC Growth Model HW

Singly-constrained by Originating

1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

3783867601061

1234

10793637541196

25804765141047

3203101078381

42893741060768

550553.5944.351345.15

Singly-constrained by Destined

1234T(i)0T(i)^

10602755719061200

25004104439031050

312361047231380

4205265750545770

T(i)03783867601061

T(i)^670730950995

F(i)1 = T(i)^ / T(i)01.771.891.250.94

1234

10113344537994

28905134161017

3218115044377

4363501940957

669730950997

&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A

Average Factors HW

Observed Trips Tij(0)

1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

Tj(0)3783867601061

Tj^670730950995

Fj(1) = Tj^ / Tj(0)1.771.891.250.94

Iteration 1: Fij(1) = [Fi(1) + Fj(1)] / 2

1234

11.5461.6061.2851.129

21.4661.5261.2051.049

31.7111.7711.4501.294

41.5911.6511.3301.174

tij(1) = tij(0) * Fij(1)

1234ti(1)TiFi(2) = Ti / ti(1)

10.0096.34353.38644.60109412001.10

273.310.00494.05464.66103210501.02

3210.48108.010.0060.813793801.00

4326.20437.4199.750.008637700.89

tj(1)6106429471170

Tj670730950995

Fj(2) = Tj / tj(1)1.101.141.000.85


1234

11.0991.1191.0510.975

21.0591.0791.0110.935

31.0491.0691.0010.925

40.9941.0140.9460.870

Tij(2) = Tij(1) * Fij(2)

1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)

10.00107.78371.57628.61110812001.08

277.650.00499.73434.55101210501.04

3220.83115.430.0056.263933800.97

4324.31443.4394.410.008627700.89

Tj(2)6236679661119

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.081.100.980.89


1234

11.0781.0881.0320.984

21.0581.0681.0120.964

31.0231.0330.9770.929

40.9830.9930.9370.889

Tij(3) = Tij(2) * Fij(3)

1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)

10.00117.21383.41618.82111912001.07

282.150.00505.66419.09100710501.04

3225.89119.190.0052.293973800.96

4318.76440.1188.450.008477700.91

Tj(3)6276779781090

Tj^670730950995

Fj(4) = Tj^ / Tj(3)1.071.080.970.91


1234

11.0691.0751.0210.991

21.0541.0601.0060.976

31.0141.0200.9660.936

40.9890.9950.9410.911

Tij(4) = Tij(3) * Fij(4)

1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)

10.00125.95391.43613.46113112001.06

286.620.00508.65409.17100410501.05

3229.16121.520.0048.964003800.95

4315.40437.7183.230.008367700.92

Tj(4)6316859831072

Tj^670730950995

Fj(5) = Tj^ / Tj(4)1.061.070.970.93


DETROIT FACTORS HW

Observed Trips T(ij)0

1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

10251020551152.09

225060301151501.30

31060015851351.59

4203015065951.46

sum =3204951.55= F(.)1

Iteration 1: F(ij)1 = [F(i)1 * F(j)1] / F(.)1

1234

12.8181.7532.1441.969

21.7531.0901.3341.225

32.1441.3341.6311.498

41.9691.2251.4981.375

T(ij)1 = T(ij)0 * F(ij)1

1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1

104421391051151.10

244080371611500.93

321800221241351.09

4393722099950.96

sum =4884951.01= F(.)2


1234

11.1981.0131.1871.046

21.0130.8561.0040.884

31.1871.0041.1761.036

41.0460.8841.0360.912

T(ij)2 = T(ij)1 * F(ij)2

1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2

104425411111151.04

244080321571500.95

325800231291351.05

4413223097950.98

sum =4944951.00= F(.)3


1234

11.0820.9881.0921.019

20.9880.9030.9980.931

31.0920.9981.1031.029

41.0190.9311.0290.960

T(ij)3 = T(ij)2 * F(ij)3

1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3

104428421141151.01

244080301541500.97

328800241321351.02

4423024096950.99

sum =4964951.00= F(.)4


1234

11.0200.9801.0301.000

20.9800.9410.9890.960

31.0300.9891.0401.010

41.0000.9601.0100.980

T(ij)4 = T(ij)3 * F(ij)4

1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4

104329421141151.01

243079291511500.99

329790241321351.02

4422924095951.00

sum =492495


FRATAR METHOD HW


1234T(i)0T(i)^F(i)1Sum(z) T(iz)0 F(z)1

10251020551152.0978

225060301151501.30191

31060015851351.59121

4203015065951.46105

Iteration 1: t(ij)1 = T(ij)0 T(i)^ F(j)1 / Sum(z) {T(iz)0 F(z)1]

1234

10482443

24107534

32387024

43835220

T(ij)1 = [t(ij)1 + t(ji)1] / 2


104523411091151.06106

245081351601500.94167

323810231271351.06123

4413523099950.96100


1234

10462742

24307730

32783024

44131230

T(ij)2 = [t(ij)2 + t(ji)2] / 2


104427421131151.02112

244080311551500.97158

327800241311351.03129

4423124096950.9997


1234

10442942

24307929

32981025

44229240

T(ij)3 = [t(ij)3 + t(ji)3] / 2

1234T(i)3T(i)^F(i)4

104329421141151.01

243080291521500.98

329800241331351.01

4422924095951.00


SC Growth Model HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

3783867601061

1234

10793637541196

25804765141047

3203101078381

42893741060768

550553.5944.351345.15


1234T(i)0T(i)^

10602755719061200

25004104439031050

312361047231380

4205265750545770

T(i)03783867601061

T(i)^670730950995

F(i)1 = T(i)^ / T(i)01.771.891.250.94

1234

10113344537994

28905134161017

3218115044377

4363501940957

669730950997


Average Factors HW


1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

Tj(0)3783867601061

Tj^670730950995

Fj(1) = Tj^ / Tj(0)1.771.891.250.94


1234

11.5461.6061.2851.129

21.4661.5261.2051.049

31.7111.7711.4501.294

41.5911.6511.3301.174

tij(1) = tij(0) * Fij(1)

1234ti(1)TiFi(2) = Ti / ti(1)

10.0096.34353.38644.60109412001.10

273.310.00494.05464.66103210501.02

3210.48108.010.0060.813793801.00

4326.20437.4199.750.008637700.89

tj(1)6106429471170

Tj670730950995

Fj(2) = Tj / tj(1)1.101.141.000.85


1234

11.0991.1191.0510.975

21.0591.0791.0110.935

31.0491.0691.0010.925

40.9941.0140.9460.870

Tij(2) = Tij(1) * Fij(2)

1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)

10.00107.78371.57628.61110812001.08

277.650.00499.73434.55101210501.04

3220.83115.430.0056.263933800.97

4324.31443.4394.410.008627700.89

Tj(2)6236679661119

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.081.100.980.89


1234

11.0781.0881.0320.984

21.0581.0681.0120.964

31.0231.0330.9770.929

40.9830.9930.9370.889

Tij(3) = Tij(2) * Fij(3)

1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)

10.00117.21383.41618.82111912001.07

282.150.00505.66419.09100710501.04

3225.89119.190.0052.293973800.96

4318.76440.1188.450.008477700.91

Tj(3)6276779781090

Tj^670730950995

Fj(4) = Tj^ / Tj(3)1.071.080.970.91


1234

11.0691.0751.0210.991

21.0541.0601.0060.976

31.0141.0200.9660.936

40.9890.9950.9410.911

Tij(4) = Tij(3) * Fij(4)

1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)

10.00125.95391.43613.46113112001.06

286.620.00508.65409.17100410501.05

3229.16121.520.0048.964003800.95

4315.40437.7183.230.008367700.92

Tj(4)6316859831072

Tj^670730950995

Fj(5) = Tj^ / Tj(4)1.061.070.970.93


DETROIT FACTORS HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

10251020551152.09

225060301151501.30

31060015851351.59

4203015065951.46

sum =3204951.55= F(.)1


1234

12.8181.7532.1441.969

21.7531.0901.3341.225

32.1441.3341.6311.498

41.9691.2251.4981.375

T(ij)1 = T(ij)0 * F(ij)1

1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1

104421391051151.10

244080371611500.93

321800221241351.09

4393722099950.96

sum =4884951.01= F(.)2


1234

11.1981.0131.1871.046

21.0130.8561.0040.884

31.1871.0041.1761.036

41.0460.8841.0360.912

T(ij)2 = T(ij)1 * F(ij)2

1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2

104425411111151.04

244080321571500.95

325800231291351.05

4413223097950.98

sum =4944951.00= F(.)3


1234

11.0820.9881.0921.019

20.9880.9030.9980.931

31.0920.9981.1031.029

41.0190.9311.0290.960

T(ij)3 = T(ij)2 * F(ij)3

1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3

104428421141151.01

244080301541500.97

328800241321351.02

4423024096950.99

sum =4964951.00= F(.)4


1234

11.0200.9801.0301.000

20.9800.9410.9890.960

31.0300.9891.0401.010

41.0000.9601.0100.980

T(ij)4 = T(ij)3 * F(ij)4

1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4

104329421141151.01

243079291511500.99

329790241321351.02

4422924095951.00

sum =492495


FRATAR METHOD HW



10251020551152.0978

225060301151501.30191

31060015851351.59121

4203015065951.46105


1234

10482443

24107534

32387024

43835220

T(ij)1 = [t(ij)1 + t(ji)1] / 2


104523411091151.06106

245081351601500.94167

323810231271351.06123

4413523099950.96100


1234

10462742

24307730

32783024

44131230

T(ij)2 = [t(ij)2 + t(ji)2] / 2


104427421131151.02112

244080311551500.97158

327800241311351.03129

4423124096950.9997


1234

10442942

24307929

32981025

44229240

T(ij)3 = [t(ij)3 + t(ji)3] / 2

1234T(i)3T(i)^F(i)4

104329421141151.01

243080291521500.98

329800241331351.01

4422924095951.00


SC Growth Model HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

3783867601061

1234

10793637541196

25804765141047

3203101078381

42893741060768

550553.5944.351345.15


1234T(i)0T(i)^

10602755719061200

25004104439031050

312361047231380

4205265750545770

T(i)03783867601061

T(i)^670730950995

F(i)1 = T(i)^ / T(i)01.771.891.250.94

1234

10113344537994

28905134161017

3218115044377

4363501940957

669730950997


Average Factors HW


1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

Tj(0)3783867601061

Tj^670730950995

Fj(1) = Tj^ / Tj(0)1.771.891.250.94


1234

11.5461.6061.2851.129

21.4661.5261.2051.049

31.7111.7711.4501.294

41.5911.6511.3301.174

Tij(1) = Tij(0) * Fij(1)

1234ti(1)TiFi(2) = Ti / ti(1)

10.0096.34353.38644.60109412001.10

273.310.00494.05464.66103210501.02

3210.48108.010.0060.813793801.00

4326.20437.4199.750.008637700.89

tj(1)6106429471170

Tj670730950995

Fj(2) = Tj / tj(1)1.101.141.000.85


1234

11.0991.1191.0510.975

21.0591.0791.0110.935

31.0491.0691.0010.925

40.9941.0140.9460.870

Tij(2) = Tij(1) * Fij(2)

1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)

10.00107.78371.57628.61110812001.08

277.650.00499.73434.55101210501.04

3220.83115.430.0056.263933800.97

4324.31443.4394.410.008627700.89

Tj(2)6236679661119

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.081.100.980.89


1234

11.0781.0881.0320.984

21.0581.0681.0120.964

31.0231.0330.9770.929

40.9830.9930.9370.889

Tij(3) = Tij(2) * Fij(3)

1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)

10.00117.21383.41618.82111912001.07

282.150.00505.66419.09100710501.04

3225.89119.190.0052.293973800.96

4318.76440.1188.450.008477700.91

Tj(3)6276779781090

Tj^670730950995

Fj(4) = Tj^ / Tj(3)1.071.080.970.91


1234

11.0691.0751.0210.991

21.0541.0601.0060.976

31.0141.0200.9660.936

40.9890.9950.9410.911

Tij(4) = Tij(3) * Fij(4)

1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)

10.00125.95391.43613.46113112001.06

286.620.00508.65409.17100410501.05

3229.16121.520.0048.964003800.95

4315.40437.7183.230.008367700.92

Tj(4)6316859831072

Tj^670730950995

Fj(5) = Tj^ / Tj(4)1.061.070.970.93


DETROIT FACTORS HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

10251020551152.09

225060301151501.30

31060015851351.59

4203015065951.46

sum =3204951.55= F(.)1


1234

12.8181.7532.1441.969

21.7531.0901.3341.225

32.1441.3341.6311.498

41.9691.2251.4981.375

T(ij)1 = T(ij)0 * F(ij)1

1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1

104421391051151.10

244080371611500.93

321800221241351.09

4393722099950.96

sum =4884951.01= F(.)2


1234

11.1981.0131.1871.046

21.0130.8561.0040.884

31.1871.0041.1761.036

41.0460.8841.0360.912

T(ij)2 = T(ij)1 * F(ij)2

1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2

104425411111151.04

244080321571500.95

325800231291351.05

4413223097950.98

sum =4944951.00= F(.)3


1234

11.0820.9881.0921.019

20.9880.9030.9980.931

31.0920.9981.1031.029

41.0190.9311.0290.960

T(ij)3 = T(ij)2 * F(ij)3

1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3

104428421141151.01

244080301541500.97

328800241321351.02

4423024096950.99

sum =4964951.00= F(.)4


1234

11.0200.9801.0301.000

20.9800.9410.9890.960

31.0300.9891.0401.010

41.0000.9601.0100.980

T(ij)4 = T(ij)3 * F(ij)4

1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4

104329421141151.01

243079291511500.99

329790241321351.02

4422924095951.00

sum =492495


FRATAR METHOD HW



10251020551152.0978

225060301151501.30191

31060015851351.59121

4203015065951.46105


1234

10482443

24107534

32387024

43835220

T(ij)1 = [t(ij)1 + t(ji)1] / 2


104523411091151.06106

245081351601500.94167

323810231271351.06123

4413523099950.96100


1234

10462742

24307730

32783024

44131230

T(ij)2 = [t(ij)2 + t(ji)2] / 2


104427421131151.02112

244080311551500.97158

327800241311351.03129

4423124096950.9997


1234

10442942

24307929

32981025

44229240

T(ij)3 = [t(ij)3 + t(ji)3] / 2

1234T(i)3T(i)^F(i)4

104329421141151.01

243080291521500.98

329800241331351.01

4422924095951.00


SC Growth Model HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

3783867601061

1234

10793637541196

25804765141047

3203101078381

42893741060768

550553.5944.351345.15


1234T(i)0T(i)^

10602755719061200

25004104439031050

312361047231380

4205265750545770

T(i)03783867601061

T(i)^670730950995

F(i)1 = T(i)^ / T(i)01.771.891.250.94

1234

10113344537994

28905134161017

3218115044377

4363501940957

669730950997


Average Factors HW


1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

Tj(0)3783867601061

Tj^670730950995

Fj(1) = Tj^ / Tj(0)1.771.891.250.94


1234

11.5461.6061.2851.129

21.4661.5261.2051.049

31.7111.7711.4501.294

41.5911.6511.3301.174

tij(1) = tij(0) * Fij(1)

1234ti(1)TiFi(2) = Ti / ti(1)

10.0096.34353.38644.60109412001.10

273.310.00494.05464.66103210501.02

3210.48108.010.0060.813793801.00

4326.20437.4199.750.008637700.89

tj(1)6106429471170

Tj670730950995

Fj(2) = Tj / tj(1)1.101.141.000.85


1234

11.0991.1191.0510.975

21.0591.0791.0110.935

31.0491.0691.0010.925

40.9941.0140.9460.870

Tij(2) = Tij(1) * Fij(2)

1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)

10.00107.78371.57628.61110812001.08

277.650.00499.73434.55101210501.04

3220.83115.430.0056.263933800.97

4324.31443.4394.410.008627700.89

Tj(2)6236679661119

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.081.100.980.89


1234

11.0781.0881.0320.984

21.0581.0681.0120.964

31.0231.0330.9770.929

40.9830.9930.9370.889

Tij(3) = Tij(2) * Fij(3)

1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)

10.00117.21383.41618.82111912001.07

282.150.00505.66419.09100710501.04

3225.89119.190.0052.293973800.96

4318.76440.1188.450.008477700.91

Tj(3)6276779781090

Tj^670730950995

Fj(4) = Tj^ / Tj(3)1.071.080.970.91


1234

11.0691.0751.0210.991

21.0541.0601.0060.976

31.0141.0200.9660.936

40.9890.9950.9410.911

Tij(4) = Tij(3) * Fij(4)

1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)

10.00125.95391.43613.46113112001.06

286.620.00508.65409.17100410501.05

3229.16121.520.0048.964003800.95

4315.40437.7183.230.008367700.92

Tj(4)6316859831072

Tj^670730950995

Fj(5) = Tj^ / Tj(4)1.061.070.970.93


DETROIT FACTORS HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

10251020551152.09

225060301151501.30

31060015851351.59

4203015065951.46

sum =3204951.55= F(.)1


1234

12.8181.7532.1441.969

21.7531.0901.3341.225

32.1441.3341.6311.498

41.9691.2251.4981.375

T(ij)1 = T(ij)0 * F(ij)1

1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1

104421391051151.10

244080371611500.93

321800221241351.09

4393722099950.96

sum =4884951.01= F(.)2


1234

11.1981.0131.1871.046

21.0130.8561.0040.884

31.1871.0041.1761.036

41.0460.8841.0360.912

T(ij)2 = T(ij)1 * F(ij)2

1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2

104425411111151.04

244080321571500.95

325800231291351.05

4413223097950.98

sum =4944951.00= F(.)3


1234

11.0820.9881.0921.019

20.9880.9030.9980.931

31.0920.9981.1031.029

41.0190.9311.0290.960

T(ij)3 = T(ij)2 * F(ij)3

1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3

104428421141151.01

244080301541500.97

328800241321351.02

4423024096950.99

sum =4964951.00= F(.)4


1234

11.0200.9801.0301.000

20.9800.9410.9890.960

31.0300.9891.0401.010

41.0000.9601.0100.980

T(ij)4 = T(ij)3 * F(ij)4

1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4

104329421141151.01

243079291511500.99

329790241321351.02

4422924095951.00

sum =492495


FRATAR METHOD HW



10251020551152.0978

225060301151501.30191

31060015851351.59121

4203015065951.46105


1234

10482443

24107534

32387024

43835220

T(ij)1 = [t(ij)1 + t(ji)1] / 2


104523411091151.06106

245081351601500.94167

323810231271351.06123

4413523099950.96100


1234

10462742

24307730

32783024

44131230

T(ij)2 = [t(ij)2 + t(ji)2] / 2


104427421131151.02112

244080311551500.97158

327800241311351.03129

4423124096950.9997


1234

10442942

24307929

32981025

44229240

T(ij)3 = [t(ij)3 + t(ji)3] / 2

1234T(i)3T(i)^F(i)4

104329421141151.01

243080291521500.98

329800241331351.01

4422924095951.00


SC Growth Model HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

3783867601061

1234

10793637541196

25804765141047

3203101078381

42893741060768

550553.5944.351345.15


1234T(i)0T(i)^

10602755719061200

25004104439031050

312361047231380

4205265750545770

T(i)03783867601061

T(i)^670730950995

F(i)1 = T(i)^ / T(i)01.771.891.250.94

1234

10113344537994

28905134161017

3218115044377

4363501940957

669730950997


Average Factors HW


1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

Tj(0)3783867601061

Tj^670730950995

Fj(1) = Tj^ / Tj(0)1.771.891.250.94


1234

11.5461.6061.2851.129

21.4661.5261.2051.049

31.7111.7711.4501.294

41.5911.6511.3301.174

tij(1) = tij(0) * Fij(1)

1234ti(1)TiFi(2) = Ti / ti(1)

10.0096.34353.38644.60109412001.10

273.310.00494.05464.66103210501.02

3210.48108.010.0060.813793801.00

4326.20437.4199.750.008637700.89

tj(1)6106429471170

Tj670730950995

Fj(2) = Tj / tj(1)1.101.141.000.85


1234

11.0991.1191.0510.975

21.0591.0791.0110.935

31.0491.0691.0010.925

40.9941.0140.9460.870

Tij(2) = Tij(1) * Fij(2)

1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)

10.00107.78371.57628.61110812001.08

277.650.00499.73434.55101210501.04

3220.83115.430.0056.263933800.97

4324.31443.4394.410.008627700.89

Tj(2)6236679661119

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.081.100.980.89


1234

11.0781.0881.0320.984

21.0581.0681.0120.964

31.0231.0330.9770.929

40.9830.9930.9370.889

Tij(3) = Tij(2) * Fij(3)

1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)

10.00117.21383.41618.82111912001.07

282.150.00505.66419.09100710501.04

3225.89119.190.0052.293973800.96

4318.76440.1188.450.008477700.91

Tj(3)6276779781090

Tj^670730950995

Fj(4) = Tj^ / Tj(3)1.071.080.970.91


1234

11.0691.0751.0210.991

21.0541.0601.0060.976

31.0141.0200.9660.936

40.9890.9950.9410.911

Tij(4) = Tij(3) * Fij(4)

1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)

10.00125.95391.43613.46113112001.06

286.620.00508.65409.17100410501.05

3229.16121.520.0048.964003800.95

4315.40437.7183.230.008367700.92

Tj(4)6316859831072

Tj^670730950995

Fj(5) = Tj^ / Tj(4)1.061.070.970.93


DETROIT FACTORS HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

10251020551152.09

225060301151501.30

31060015851351.59

4203015065951.46

sum =3204951.55= F(.)1


1234

12.8181.7532.1441.969

21.7531.0901.3341.225

32.1441.3341.6311.498

41.9691.2251.4981.375

T(ij)1 = T(ij)0 * F(ij)1

1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1

104421391051151.10

244080371611500.93

321800221241351.09

4393722099950.96

sum =4884951.01= F(.)2


1234

11.1981.0131.1871.046

21.0130.8561.0040.884

31.1871.0041.1761.036

41.0460.8841.0360.912

T(ij)2 = T(ij)1 * F(ij)2

1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2

104425411111151.04

244080321571500.95

325800231291351.05

4413223097950.98

sum =4944951.00= F(.)3


1234

11.0820.9881.0921.019

20.9880.9030.9980.931

31.0920.9981.1031.029

41.0190.9311.0290.960

T(ij)3 = T(ij)2 * F(ij)3

1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3

104428421141151.01

244080301541500.97

328800241321351.02

4423024096950.99

sum =4964951.00= F(.)4


1234

11.0200.9801.0301.000

20.9800.9410.9890.960

31.0300.9891.0401.010

41.0000.9601.0100.980

T(ij)4 = T(ij)3 * F(ij)4

1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4

104329421141151.01

243079291511500.99

329790241321351.02

4422924095951.00

sum =492495


FRATAR METHOD HW



10251020551152.0978

225060301151501.30191

31060015851351.59121

4203015065951.46105


1234

10482443

24107534

32387024

43835220

T(ij)1 = [t(ij)1 + t(ji)1] / 2


104523411091151.06106

245081351601500.94167

323810231271351.06123

4413523099950.96100


1234

10462742

24307730

32783024

44131230

T(ij)2 = [t(ij)2 + t(ji)2] / 2


104427421131151.02112

244080311551500.97158

327800241311351.03129

4423124096950.9997


1234

10442942

24307929

32981025

44229240

T(ij)3 = [t(ij)3 + t(ji)3] / 2

1234T(i)3T(i)^F(i)4

104329421141151.01

243080291521500.98

329800241331351.01

4422924095951.00


SC Growth Model HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

3783867601061

1234

10793637541196

25804765141047

3203101078381

42893741060768

550553.5944.351345.15


1234T(i)0T(i)^

10602755719061200

25004104439031050

312361047231380

4205265750545770

T(i)03783867601061

T(i)^670730950995

F(i)1 = T(i)^ / T(i)01.771.891.250.94

1234

10113344537994

28905134161017

3218115044377

4363501940957

669730950997


Average Factors HW


1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

Tj(0)3783867601061

Tj^670730950995

Fj(1) = Tj^ / Tj(0)1.771.891.250.94


1234

11.5461.6061.2851.129

21.4661.5261.2051.049

31.7111.7711.4501.294

41.5911.6511.3301.174

tij(1) = tij(0) * Fij(1)

1234ti(1)TiFi(2) = Ti^ / Ti(1)

10.0096.34353.38644.60109412001.10

273.310.00494.05464.66103210501.02

3210.48108.010.0060.813793801.00

4326.20437.4199.750.008637700.89

tj(1)6106429471170

Tj670730950995

Fj(2) = Tj / tj(1)1.101.141.000.85


1234

11.0991.1191.0510.975

21.0591.0791.0110.935

31.0491.0691.0010.925

40.9941.0140.9460.870

Tij(2) = Tij(1) * Fij(2)

1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)

10.00107.78371.57628.61110812001.08

277.650.00499.73434.55101210501.04

3220.83115.430.0056.263933800.97

4324.31443.4394.410.008627700.89

Tj(2)6236679661119

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.081.100.980.89


1234

11.0781.0881.0320.984

21.0581.0681.0120.964

31.0231.0330.9770.929

40.9830.9930.9370.889

Tij(3) = Tij(2) * Fij(3)

1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)

10.00117.21383.41618.82111912001.07

282.150.00505.66419.09100710501.04

3225.89119.190.0052.293973800.96

4318.76440.1188.450.008477700.91

Tj(3)6276779781090

Tj^670730950995

Fj(4) = Tj^ / Tj(3)1.071.080.970.91


1234

11.0691.0751.0210.991

21.0541.0601.0060.976

31.0141.0200.9660.936

40.9890.9950.9410.911

Tij(4) = Tij(3) * Fij(4)

1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)

10.00125.95391.43613.46113112001.06

286.620.00508.65409.17100410501.05

3229.16121.520.0048.964003800.95

4315.40437.7183.230.008367700.92

Tj(4)6316859831072

Tj^670730950995

Fj(5) = Tj^ / Tj(4)1.061.070.970.93


DETROIT FACTORS HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

10251020551152.09

225060301151501.30

31060015851351.59

4203015065951.46

sum =3204951.55= F(.)1


1234

12.8181.7532.1441.969

21.7531.0901.3341.225

32.1441.3341.6311.498

41.9691.2251.4981.375

T(ij)1 = T(ij)0 * F(ij)1

1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1

104421391051151.10

244080371611500.93

321800221241351.09

4393722099950.96

sum =4884951.01= F(.)2


1234

11.1981.0131.1871.046

21.0130.8561.0040.884

31.1871.0041.1761.036

41.0460.8841.0360.912

T(ij)2 = T(ij)1 * F(ij)2

1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2

104425411111151.04

244080321571500.95

325800231291351.05

4413223097950.98

sum =4944951.00= F(.)3


1234

11.0820.9881.0921.019

20.9880.9030.9980.931

31.0920.9981.1031.029

41.0190.9311.0290.960

T(ij)3 = T(ij)2 * F(ij)3

1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3

104428421141151.01

244080301541500.97

328800241321351.02

4423024096950.99

sum =4964951.00= F(.)4


1234

11.0200.9801.0301.000

20.9800.9410.9890.960

31.0300.9891.0401.010

41.0000.9601.0100.980

T(ij)4 = T(ij)3 * F(ij)4

1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4

104329421141151.01

243079291511500.99

329790241321351.02

4422924095951.00

sum =492495


FRATAR METHOD HW



10251020551152.0978

225060301151501.30191

31060015851351.59121

4203015065951.46105


1234

10482443

24107534

32387024

43835220

T(ij)1 = [t(ij)1 + t(ji)1] / 2


104523411091151.06106

245081351601500.94167

323810231271351.06123

4413523099950.96100


1234

10462742

24307730

32783024

44131230

T(ij)2 = [t(ij)2 + t(ji)2] / 2


104427421131151.02112

244080311551500.97158

327800241311351.03129

4423124096950.9997


1234

10442942

24307929

32981025

44229240

T(ij)3 = [t(ij)3 + t(ji)3] / 2

1234T(i)3T(i)^F(i)4

104329421141151.01

243080291521500.98

329800241331351.01

4422924095951.00


SC Growth Model HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

3783867601061

1234

10793637541196

25804765141047

3203101078381

42893741060768

550553.5944.351345.15


1234T(i)0T(i)^

10602755719061200

25004104439031050

312361047231380

4205265750545770

T(i)03783867601061

T(i)^670730950995

F(i)1 = T(i)^ / T(i)01.771.891.250.94

1234

10113344537994

28905134161017

3218115044377

4363501940957

669730950997


Average Factors HW

1234

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

3783867601061

670730950995

1.771.891.250.94

1234

11.5461.6061.2851.129

21.4661.5261.2051.049

31.7111.7711.4501.294

41.5911.6511.3301.174

1234

10.0096.34353.38644.60109412001.10

273.310.00494.05464.66103210501.02

3210.48108.010.0060.813793801.00

4326.20437.4199.750.008637700.89

6106429471170

670730950995

1.101.141.000.85

1234

11.0991.1191.0510.975

21.0591.0791.0110.935

31.0491.0691.0010.925

40.9941.0140.9460.870

1234

10.00107.78371.57628.61110812001.08

277.650.00499.73434.55101210501.04

3220.83115.430.0056.263933800.97

4324.31443.4394.410.008627700.89

6236679661119

670730950995

1.081.100.980.89

1234

11.0781.0881.0320.984

21.0581.0681.0120.964

31.0231.0330.9770.929

40.9830.9930.9370.889

1234

10.00117.21383.41618.82111912001.07

282.150.00505.66419.09100710501.04

3225.89119.190.0052.293973800.96

4318.76440.1188.450.008477700.91

6276779781090

670730950995

1.071.080.970.91

1234

11.0691.0751.0210.991

21.0541.0601.0060.976

31.0141.0200.9660.936

40.9890.9950.9410.911

1234

10.00125.95391.43613.46113112001.06

286.620.00508.65409.17100410501.05

3229.16121.520.0048.964003800.95

4315.40437.7183.230.008367700.92

6316859831072

670730950995

1.061.070.970.93


DETROIT FACTORS HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

10251020551152.09

225060301151501.30

31060015851351.59

4203015065951.46

sum =3204951.55= F(.)1


1234

12.8181.7532.1441.969

21.7531.0901.3341.225

32.1441.3341.6311.498

41.9691.2251.4981.375

T(ij)1 = T(ij)0 * F(ij)1

1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1

104421391051151.10

244080371611500.93

321800221241351.09

4393722099950.96

sum =4884951.01= F(.)2


1234

11.1981.0131.1871.046

21.0130.8561.0040.884

31.1871.0041.1761.036

41.0460.8841.0360.912

T(ij)2 = T(ij)1 * F(ij)2

1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2

104425411111151.04

244080321571500.95

325800231291351.05

4413223097950.98

sum =4944951.00= F(.)3


1234

11.0820.9881.0921.019

20.9880.9030.9980.931

31.0920.9981.1031.029

41.0190.9311.0290.960

T(ij)3 = T(ij)2 * F(ij)3

1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3

104428421141151.01

244080301541500.97

328800241321351.02

4423024096950.99

sum =4964951.00= F(.)4


1234

11.0200.9801.0301.000

20.9800.9410.9890.960

31.0300.9891.0401.010

41.0000.9601.0100.980

T(ij)4 = T(ij)3 * F(ij)4

1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4

104329421141151.01

243079291511500.99

329790241321351.02

4422924095951.00

sum =492495


FRATAR METHOD HW



10251020551152.0978

225060301151501.30191

31060015851351.59121

4203015065951.46105


1234

10482443

24107534

32387024

43835220

T(ij)1 = [t(ij)1 + t(ji)1] / 2


104523411091151.06106

245081351601500.94167

323810231271351.06123

4413523099950.96100


1234

10462742

24307730

32783024

44131230

T(ij)2 = [t(ij)2 + t(ji)2] / 2


104427421131151.02112

244080311551500.97158

327800241311351.03129

4423124096950.9997


1234

10442942

24307929

32981025

44229240

T(ij)3 = [t(ij)3 + t(ji)3] / 2

1234T(i)3T(i)^F(i)4

104329421141151.01

243080291521500.98

329800241331351.01

4422924095951.00


SC Growth Model HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

3783867601061

1234

10793637541196

25804765141047

3203101078381

42893741060768

550553.5944.351345.15


1234T(i)0T(i)^

10602755719061200

25004104439031050

312361047231380

4205265750545770

T(i)03783867601061

T(i)^670730950995

F(i)1 = T(i)^ / T(i)01.771.891.250.94

1234

10113344537994

28905134161017

3218115044377

4363501940957

669730950997


Average Factors HW

Observed Trips tij(0)

1234ti(0)TiFi(1) = Ti / ti(0)

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

Tj(0)3783867601061

Tj^670730950995

Fj(1) = Tj^ / Tj(0)1.771.891.250.94


1234

11.5461.6061.2851.129

21.4661.5261.2051.049

31.7111.7711.4501.294

41.5911.6511.3301.174

Tij(1) = Tij(0) * Fij(1)

1234Ti(1)Ti^Fi(2) = Ti^ / Ti(1)

10.0096.34353.38644.60109412001.10

273.310.00494.05464.66103210501.02

3210.48108.010.0060.813793801.00

4326.20437.4199.750.008637700.89

Tj(1)6106429471170

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.101.141.000.85


1234

11.0991.1191.0510.975

21.0591.0791.0110.935

31.0491.0691.0010.925

40.9941.0140.9460.870

Tij(2) = Tij(1) * Fij(2)

1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)

10.00107.78371.57628.61110812001.08

277.650.00499.73434.55101210501.04

3220.83115.430.0056.263933800.97

4324.31443.4394.410.008627700.89

Tj(2)6236679661119

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.081.100.980.89


1234

11.0781.0881.0320.984

21.0581.0681.0120.964

31.0231.0330.9770.929

40.9830.9930.9370.889

Tij(3) = Tij(2) * Fij(3)

1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)

10.00117.21383.41618.82111912001.07

282.150.00505.66419.09100710501.04

3225.89119.190.0052.293973800.96

4318.76440.1188.450.008477700.91

Tj(3)6276779781090

Tj^670730950995

Fj(4) = Tj^ / Tj(3)1.071.080.970.91


1234

11.0691.0751.0210.991

21.0541.0601.0060.976

31.0141.0200.9660.936

40.9890.9950.9410.911

Tij(4) = Tij(3) * Fij(4)

1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)

10.00125.95391.43613.46113112001.06

286.620.00508.65409.17100410501.05

3229.16121.520.0048.964003800.95

4315.40437.7183.230.008367700.92

Tj(4)6316859831072

Tj^670730950995

Fj(5) = Tj^ / Tj(4)1.061.070.970.93


DETROIT FACTORS HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

10251020551152.09

225060301151501.30

31060015851351.59

4203015065951.46

sum =3204951.55= F(.)1


1234

12.8181.7532.1441.969

21.7531.0901.3341.225

32.1441.3341.6311.498

41.9691.2251.4981.375

T(ij)1 = T(ij)0 * F(ij)1

1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1

104421391051151.10

244080371611500.93

321800221241351.09

4393722099950.96

sum =4884951.01= F(.)2


1234

11.1981.0131.1871.046

21.0130.8561.0040.884

31.1871.0041.1761.036

41.0460.8841.0360.912

T(ij)2 = T(ij)1 * F(ij)2

1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2

104425411111151.04

244080321571500.95

325800231291351.05

4413223097950.98

sum =4944951.00= F(.)3


1234

11.0820.9881.0921.019

20.9880.9030.9980.931

31.0920.9981.1031.029

41.0190.9311.0290.960

T(ij)3 = T(ij)2 * F(ij)3

1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3

104428421141151.01

244080301541500.97

328800241321351.02

4423024096950.99

sum =4964951.00= F(.)4


1234

11.0200.9801.0301.000

20.9800.9410.9890.960

31.0300.9891.0401.010

41.0000.9601.0100.980

T(ij)4 = T(ij)3 * F(ij)4

1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4

104329421141151.01

243079291511500.99

329790241321351.02

4422924095951.00

sum =492495


FRATAR METHOD HW



10251020551152.0978

225060301151501.30191

31060015851351.59121

4203015065951.46105


1234

10482443

24107534

32387024

43835220

T(ij)1 = [t(ij)1 + t(ji)1] / 2


104523411091151.06106

245081351601500.94167

323810231271351.06123

4413523099950.96100


1234

10462742

24307730

32783024

44131230

T(ij)2 = [t(ij)2 + t(ji)2] / 2


104427421131151.02112

244080311551500.97158

327800241311351.03129

4423124096950.9997


1234

10442942

24307929

32981025

44229240

T(ij)3 = [t(ij)3 + t(ji)3] / 2

1234T(i)3T(i)^F(i)4

104329421141151.01

243080291521500.98

329800241331351.01

4422924095951.00


SC Growth Model HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

3783867601061

1234

10793637541196

25804765141047

3203101078381

42893741060768

550553.5944.351345.15


1234T(i)0T(i)^

10602755719061200

25004104439031050

312361047231380

4205265750545770

T(i)03783867601061

T(i)^670730950995

F(i)1 = T(i)^ / T(i)01.771.891.250.94

1234

10113344537994

28905134161017

3218115044377

4363501940957

669730950997


Average Factors HW


1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

tj(0)3783867601061

Tj^670730950995

Fj(1) = Tj^ / Tj(0)1.771.891.250.94


1234

11.5461.6061.2851.129

21.4661.5261.2051.049

31.7111.7711.4501.294

41.5911.6511.3301.174

Tij(1) = Tij(0) * Fij(1)

1234Ti(1)Ti^Fi(2) = Ti^ / Ti(1)

10.0096.34353.38644.60109412001.10

273.310.00494.05464.66103210501.02

3210.48108.010.0060.813793801.00

4326.20437.4199.750.008637700.89

Tj(1)6106429471170

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.101.141.000.85


1234

11.0991.1191.0510.975

21.0591.0791.0110.935

31.0491.0691.0010.925

40.9941.0140.9460.870

Tij(2) = Tij(1) * Fij(2)

1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)

10.00107.78371.57628.61110812001.08

277.650.00499.73434.55101210501.04

3220.83115.430.0056.263933800.97

4324.31443.4394.410.008627700.89

Tj(2)6236679661119

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.081.100.980.89


1234

11.0781.0881.0320.984

21.0581.0681.0120.964

31.0231.0330.9770.929

40.9830.9930.9370.889

Tij(3) = Tij(2) * Fij(3)

1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)

10.00117.21383.41618.82111912001.07

282.150.00505.66419.09100710501.04

3225.89119.190.0052.293973800.96

4318.76440.1188.450.008477700.91

Tj(3)6276779781090

Tj^670730950995

Fj(4) = Tj^ / Tj(3)1.071.080.970.91


1234

11.0691.0751.0210.991

21.0541.0601.0060.976

31.0141.0200.9660.936

40.9890.9950.9410.911

Tij(4) = Tij(3) * Fij(4)

1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)

10.00125.95391.43613.46113112001.06

286.620.00508.65409.17100410501.05

3229.16121.520.0048.964003800.95

4315.40437.7183.230.008367700.92

Tj(4)6316859831072

Tj^670730950995

Fj(5) = Tj^ / Tj(4)1.061.070.970.93


DETROIT FACTORS HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

10251020551152.09

225060301151501.30

31060015851351.59

4203015065951.46

sum =3204951.55= F(.)1


1234

12.8181.7532.1441.969

21.7531.0901.3341.225

32.1441.3341.6311.498

41.9691.2251.4981.375

T(ij)1 = T(ij)0 * F(ij)1

1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1

104421391051151.10

244080371611500.93

321800221241351.09

4393722099950.96

sum =4884951.01= F(.)2


1234

11.1981.0131.1871.046

21.0130.8561.0040.884

31.1871.0041.1761.036

41.0460.8841.0360.912

T(ij)2 = T(ij)1 * F(ij)2

1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2

104425411111151.04

244080321571500.95

325800231291351.05

4413223097950.98

sum =4944951.00= F(.)3


1234

11.0820.9881.0921.019

20.9880.9030.9980.931

31.0920.9981.1031.029

41.0190.9311.0290.960

T(ij)3 = T(ij)2 * F(ij)3

1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3

104428421141151.01

244080301541500.97

328800241321351.02

4423024096950.99

sum =4964951.00= F(.)4


1234

11.0200.9801.0301.000

20.9800.9410.9890.960

31.0300.9891.0401.010

41.0000.9601.0100.980

T(ij)4 = T(ij)3 * F(ij)4

1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4

104329421141151.01

243079291511500.99

329790241321351.02

4422924095951.00

sum =492495


FRATAR METHOD HW



10251020551152.0978

225060301151501.30191

31060015851351.59121

4203015065951.46105


1234

10482443

24107534

32387024

43835220

T(ij)1 = [t(ij)1 + t(ji)1] / 2


104523411091151.06106

245081351601500.94167

323810231271351.06123

4413523099950.96100


1234

10462742

24307730

32783024

44131230

T(ij)2 = [t(ij)2 + t(ji)2] / 2


104427421131151.02112

244080311551500.97158

327800241311351.03129

4423124096950.9997


1234

10442942

24307929

32981025

44229240

T(ij)3 = [t(ij)3 + t(ji)3] / 2

1234T(i)3T(i)^F(i)4

104329421141151.01

243080291521500.98

329800241331351.01

4422924095951.00


SC Growth Model HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

3783867601061

1234

10793637541196

25804765141047

3203101078381

42893741060768

550553.5944.351345.15


1234T(i)0T(i)^

10602755719061200

25004104439031050

312361047231380

4205265750545770

T(i)03783867601061

T(i)^670730950995

F(i)1 = T(i)^ / T(i)01.771.891.250.94

1234

10113344537994

28905134161017

3218115044377

4363501940957

669730950997


Average Factors HW


1234ti(0)TiFi(1) = Ti / ti(0)

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

tj(0)3783867601061

Tj670730950995

Fj(1) = Tj / tj(0)1.771.891.250.94


1234

11.5461.6061.2851.129

21.4661.5261.2051.049

31.7111.7711.4501.294

41.5911.6511.3301.174

Tij(1) = Tij(0) * Fij(1)

1234Ti(1)Ti^Fi(2) = Ti^ / Ti(1)

10.0096.34353.38644.60109412001.10

273.310.00494.05464.66103210501.02

3210.48108.010.0060.813793801.00

4326.20437.4199.750.008637700.89

Tj(1)6106429471170

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.101.141.000.85


1234

11.0991.1191.0510.975

21.0591.0791.0110.935

31.0491.0691.0010.925

40.9941.0140.9460.870

Tij(2) = Tij(1) * Fij(2)

1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)

10.00107.78371.57628.61110812001.08

277.650.00499.73434.55101210501.04

3220.83115.430.0056.263933800.97

4324.31443.4394.410.008627700.89

Tj(2)6236679661119

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.081.100.980.89


1234

11.0781.0881.0320.984

21.0581.0681.0120.964

31.0231.0330.9770.929

40.9830.9930.9370.889

Tij(3) = Tij(2) * Fij(3)

1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)

10.00117.21383.41618.82111912001.07

282.150.00505.66419.09100710501.04

3225.89119.190.0052.293973800.96

4318.76440.1188.450.008477700.91

Tj(3)6276779781090

Tj^670730950995

Fj(4) = Tj^ / Tj(3)1.071.080.970.91


1234

11.0691.0751.0210.991

21.0541.0601.0060.976

31.0141.0200.9660.936

40.9890.9950.9410.911

Tij(4) = Tij(3) * Fij(4)

1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)

10.00125.95391.43613.46113112001.06

286.620.00508.65409.17100410501.05

3229.16121.520.0048.964003800.95

4315.40437.7183.230.008367700.92

Tj(4)6316859831072

Tj^670730950995

Fj(5) = Tj^ / Tj(4)1.061.070.970.93


DETROIT FACTORS HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

10251020551152.09

225060301151501.30

31060015851351.59

4203015065951.46

sum =3204951.55= F(.)1


1234

12.8181.7532.1441.969

21.7531.0901.3341.225

32.1441.3341.6311.498

41.9691.2251.4981.375

T(ij)1 = T(ij)0 * F(ij)1

1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1

104421391051151.10

244080371611500.93

321800221241351.09

4393722099950.96

sum =4884951.01= F(.)2


1234

11.1981.0131.1871.046

21.0130.8561.0040.884

31.1871.0041.1761.036

41.0460.8841.0360.912

T(ij)2 = T(ij)1 * F(ij)2

1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2

104425411111151.04

244080321571500.95

325800231291351.05

4413223097950.98

sum =4944951.00= F(.)3


1234

11.0820.9881.0921.019

20.9880.9030.9980.931

31.0920.9981.1031.029

41.0190.9311.0290.960

T(ij)3 = T(ij)2 * F(ij)3

1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3

104428421141151.01

244080301541500.97

328800241321351.02

4423024096950.99

sum =4964951.00= F(.)4


1234

11.0200.9801.0301.000

20.9800.9410.9890.960

31.0300.9891.0401.010

41.0000.9601.0100.980

T(ij)4 = T(ij)3 * F(ij)4

1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4

104329421141151.01

243079291511500.99

329790241321351.02

4422924095951.00

sum =492495


FRATAR METHOD HW



10251020551152.0978

225060301151501.30191

31060015851351.59121

4203015065951.46105


1234

10482443

24107534

32387024

43835220

T(ij)1 = [t(ij)1 + t(ji)1] / 2


104523411091151.06106

245081351601500.94167

323810231271351.06123

4413523099950.96100


1234

10462742

24307730

32783024

44131230

T(ij)2 = [t(ij)2 + t(ji)2] / 2


104427421131151.02112

244080311551500.97158

327800241311351.03129

4423124096950.9997


1234

10442942

24307929

32981025

44229240

T(ij)3 = [t(ij)3 + t(ji)3] / 2

1234T(i)3T(i)^F(i)4

104329421141151.01

243080291521500.98

329800241331351.01

4422924095951.00


SC Growth Model HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

3783867601061

1234

10793637541196

25804765141047

3203101078381

42893741060768

550553.5944.351345.15


1234T(i)0T(i)^

10602755719061200

25004104439031050

312361047231380

4205265750545770

T(i)03783867601061

T(i)^670730950995

F(i)1 = T(i)^ / T(i)01.771.891.250.94

1234

10113344537994

28905134161017

3218115044377

4363501940957

669730950997


Average Factors HW

Observed Trips tij(0)

1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

tj(0)3783867601061

Tj670730950995

Fj(1) = Tj / tj(0)1.771.891.250.94


1234

11.5461.6061.2851.129

21.4661.5261.2051.049

31.7111.7711.4501.294

41.5911.6511.3301.174

Tij(1) = Tij(0) * Fij(1)

1234Ti(1)Ti^Fi(2) = Ti^ / Ti(1)

10.0096.34353.38644.60109412001.10

273.310.00494.05464.66103210501.02

3210.48108.010.0060.813793801.00

4326.20437.4199.750.008637700.89

Tj(1)6106429471170

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.101.141.000.85


1234

11.0991.1191.0510.975

21.0591.0791.0110.935

31.0491.0691.0010.925

40.9941.0140.9460.870

Tij(2) = Tij(1) * Fij(2)

1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)

10.00107.78371.57628.61110812001.08

277.650.00499.73434.55101210501.04

3220.83115.430.0056.263933800.97

4324.31443.4394.410.008627700.89

Tj(2)6236679661119

Tj^670730950995

Fj(2) = Tj^ / Tj(1)1.081.100.980.89


1234

11.0781.0881.0320.984

21.0581.0681.0120.964

31.0231.0330.9770.929

40.9830.9930.9370.889

Tij(3) = Tij(2) * Fij(3)

1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)

10.00117.21383.41618.82111912001.07

282.150.00505.66419.09100710501.04

3225.89119.190.0052.293973800.96

4318.76440.1188.450.008477700.91

Tj(3)6276779781090

Tj^670730950995

Fj(4) = Tj^ / Tj(3)1.071.080.970.91


1234

11.0691.0751.0210.991

21.0541.0601.0060.976

31.0141.0200.9660.936

40.9890.9950.9410.911

Tij(4) = Tij(3) * Fij(4)

1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)

10.00125.95391.43613.46113112001.06

286.620.00508.65409.17100410501.05

3229.16121.520.0048.964003800.95

4315.40437.7183.230.008367700.92

Tj(4)6316859831072

Tj^670730950995

Fj(5) = Tj^ / Tj(4)1.061.070.970.93


DETROIT FACTORS HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

10251020551152.09

225060301151501.30

31060015851351.59

4203015065951.46

sum =3204951.55= F(.)1


1234

12.8181.7532.1441.969

21.7531.0901.3341.225

32.1441.3341.6311.498

41.9691.2251.4981.375

T(ij)1 = T(ij)0 * F(ij)1

1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1

104421391051151.10

244080371611500.93

321800221241351.09

4393722099950.96

sum =4884951.01= F(.)2


1234

11.1981.0131.1871.046

21.0130.8561.0040.884

31.1871.0041.1761.036

41.0460.8841.0360.912

T(ij)2 = T(ij)1 * F(ij)2

1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2

104425411111151.04

244080321571500.95

325800231291351.05

4413223097950.98

sum =4944951.00= F(.)3


1234

11.0820.9881.0921.019

20.9880.9030.9980.931

31.0920.9981.1031.029

41.0190.9311.0290.960

T(ij)3 = T(ij)2 * F(ij)3

1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3

104428421141151.01

244080301541500.97

328800241321351.02

4423024096950.99

sum =4964951.00= F(.)4


1234

11.0200.9801.0301.000

20.9800.9410.9890.960

31.0300.9891.0401.010

41.0000.9601.0100.980

T(ij)4 = T(ij)3 * F(ij)4

1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4

104329421141151.01

243079291511500.99

329790241321351.02

4422924095951.00

sum =492495


FRATAR METHOD HW



10251020551152.0978

225060301151501.30191

31060015851351.59121

4203015065951.46105


1234

10482443

24107534

32387024

43835220

T(ij)1 = [t(ij)1 + t(ji)1] / 2


104523411091151.06106

245081351601500.94167

323810231271351.06123

4413523099950.96100


1234

10462742

24307730

32783024

44131230

T(ij)2 = [t(ij)2 + t(ji)2] / 2


104427421131151.02112

244080311551500.97158

327800241311351.03129

4423124096950.9997


1234

10442942

24307929

32981025

44229240

T(ij)3 = [t(ij)3 + t(ji)3] / 2

1234T(i)3T(i)^F(i)4

104329421141151.01

243080291521500.98

329800241331351.01

4422924095951.00


SC Growth Model HW


1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

3783867601061

1234

10793637541196

25804765141047

3203101078381

42893741060768

550553.5944.351345.15


1234T(i)0T(i)^

10602755719061200

25004104439031050

312361047231380

4205265750545770

T(i)03783867601061

T(i)^670730950995

F(i)1 = T(i)^ / T(i)01.771.891.250.94

1234

10113344537994

28905134161017

3218115044377

4363501940957

669730950997


Average Factors HW


1234Ti(0)Ti^Fi(1) = Ti / ti(0)

106027557190612001.32

250041044390310501.16

3123610472313801.65

42052657505457701.41

tj(0)3783867601061

Tj670730950995

Fj(1) = Tj / tj(0)1.771.891.250.94


1234

11.5461.6061.2851.129

21.4661.5261.2051.049

31.7111.7711.4501.294

41.5911.6511.3301.174

Tij(1) = Tij(0) * Fij(1)

1234Ti(1)Ti^Fi(2) = Ti^ / Ti(1)

10.0096.34353.38644.60109412001.10

273.310.004

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