extrapolation technique summarized

Extrapolation Technique Summarized The extrapolation technique (aka curve fitting) is a simplistic model that uses past gross population trends to project future population levels. The defining characteristics of trend extrapolation is that future values of any variable are determined solely by its historical values. (SLPP, p. 161 emphasis added) Basic Procedure: 1) Identify overall past trend and fit proper curve 2) Project future populations based upon your chosen curve We use a linear equation for most of these equations. A linear transformation is required to make projections for all but the Parabolic Curve. Advantages: 1) Low data requirements 2) Very easy methodology 3) 1+2 = Low resource requirements (money, skills, etc.) Disadvantages: 1) Uses only aggregate data 2) Assumes that past trends will predict the future

Visualizing the Technique

Chart3

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192493

Year

Population

Leon County Population, 1940-1990

Florida County Pop Figures

POPULATION OF COUNTIES -- FLORIDA: 1890-1990

County19901980197019601950194019301920191019001890188018701860185018401830Notes

FLORIDA12,937,9269,746,3246,789,4434,951,5602,771,3051,897,4141,468,211968,470752,619528,542391,422269,493187,748140,42487,44554,47734,730

Alachua181,596151,348104,76474,07457,02638,60734,36531,68934,30532,24522,93416,46217,3288,2322,5242,2822,204

Baker18,48615,2899,2427,3636,3136,5106,2735,6224,8054,5163,3332,3031,325------------*New River (Bradford)

Bay126,99497,74075,28367,13142,68920,68612,09111,407---------------------------*Washington, Calhoun

Bradford22,51520,02314,62512,44611,4578,7179,40512,50314,09010,2957,5166,1123,6713,820---------*Columbia, Alachua; 1860: New River

Brevard398,978272,959230,006111,43523,65316,14213,2838,5054,7175,1583,4011,4781,216246139------See note 1

Broward1,255,4881,018,200620,100333,94683,93339,79420,0945,135---------------------------*Palm Beach, Dade

Calhoun11,0119,2947,6247,4227,9228,2187,2988,7757,4655,1321,6811,5809981,4461,3771,142---*Washington

Charlotte110,97558,46027,55912,5944,2863,6634,013------------------------------*DeSoto

Citrus93,51554,70319,1969,2686,1115,8465,5165,2206,7315,3912,394------------------*Hernando

Clay105,98667,05232,05919,53514,3236,4686,8595,6216,1165,6355,1542,8382,0981,914---------*Duval; Alachua, Columbia

Collier152,09985,97138,04015,7536,4885,1022,883------------------------------*Lee

Columbia42,61335,39925,25020,07718,21616,85914,63814,29017,68917,09412,8779,5897,3354,6464,8082,102---*Alachua

Dade1,937,0941,625,7811,267,792935,047495,084267,739142,95542,75311,9334,9558612578583159446---Monroe

DeSoto23,86519,03913,06011,6839,2427,7927,74525,43414,2008,0474,944------------------*Manatee; see note 2

Dixie10,5857,7515,4804,4793,9287,0186,419------------------------------*Lafayette

Duval672,971571,003528,865455,411304,029210,143155,503113,54075,16339,73326,80019,43111,9215,0744,5394,1561,970

Escambia262,798233,794205,334173,829112,70674,66753,59449,38638,02928,31320,18812,1567,8175,7684,3513,9933,386See note 3

Flagler28,70110,9134,4544,5663,3673,0082,4662,442---------------------------*St. Johns, Volusia

Franklin8,9677,6617,0656,5765,8145,9916,2835,3185,2014,8903,3081,7911,2561,9041,5611,030---*Gadsden, Washington

Gadsden41,10541,56539,18441,98936,45731,45029,89023,53922,19815,29411,89412,1699,8029,3968,7845,9924,895

Gilchrist9,6675,7673,5512,8683,4994,2504,137------------------------------*Alachua

Glades7,5915,9923,6692,9502,1992,7452,762------------------------------*DeSoto

Gulf11,50410,65810,0969,9377,4606,9513,182------------------------------*Calhoun

Hamilton10,9308,7617,7877,7058,9819,7789,4549,87311,82511,8818,5076,7905,7494,1542,5111,464553

Hardee19,49919,37914,88912,37010,07310,15810,348------------------------------*DeSoto

Hendry25,77318,59911,8598,1196,0515,2373,492------------------------------*Lee

Hernando101,11544,46917,00411,2056,6935,6414,9484,5484,9973,6382,4764,2482,9381,200926------See note 4

Highlands68,43247,52629,50721,33813,6369,2469,192------------------------------*DeSoto

Hillsborough834,054646,960490,265397,788249,894180,148153,51988,25778,37436,01314,9415,8143,2162,9812,377452---*Alachua

Holmes15,77814,72310,72010,84413,98815,44712,92412,85011,5577,7624,3362,1701,5721,3861,205------*Jackson, Walton

Indian River90,20859,89635,99225,30911,8728,9576,724------------------------------*St. Lucie

Jackson41,37539,15434,43436,20834,64534,42831,96931,22429,82123,37717,54414,3729,52810,2096,6394,6813,907See note 5

Jefferson11,29610,7038,7789,54310,41312,03213,40814,50217,21016,19515,75716,06513,3989,8767,7185,7133,312

Lafayette5,5784,0352,8922,8893,4404,4054,3616,2426,7104,9873,6862,4411,7832,068---------*Madison

Lake152,104104,87069,30557,38336,34027,25523,16112,7449,5097,4678,034------------------*Sumter, Orange

Lee335,113205,266105,21654,53923,40417,48814,9909,5406,2943,0711,414------------------*Monroe

Leon192,493148,655103,04774,22551,59031,64623,47618,05919,42719,88717,75219,66215,23612,34311,44210,7136,494

Levy25,92319,87012,75610,36410,63712,55012,4569,92110,3618,6036,5865,7672,0181,781465------*Alachua

Liberty5,5694,2603,3793,1383,1823,7524,0675,0064,7002,9561,4521,3621,0501,457---------*Gadsden; Franklin

Madison16,56914,89413,48114,15414,19716,19015,61416,51616,91915,44614,31614,79811,1217,7795,4902,644525

Manatee211,707148,44297,11569,16834,70426,09822,50218,7129,5504,6632,8953,5441,931854---------*Hillsborough, Brevard; Monroe; see note 2

Marion194,833122,48869,03051,61638,18731,24329,57823,96826,94124,40320,79613,04610,8048,6093,338------*Mosquito (Orange), Alachua

Martin100,90064,01428,03516,9327,8076,2955,111------------------------------*Palm Beach

Monroe78,02463,18852,58647,92129,95714,07813,62419,55021,56318,00618,78610,9405,6572,9132,645688517

Nassau43,94132,89420,62617,18912,81110,8269,37511,34010,5259,6548,2946,6354,2473,6442,1641,8921,511

Okaloosa143,776109,92088,18761,17527,53312,9009,8979,360---------------------------*Santa Rosa, Walton, Washington

Okeechobee29,62720,26411,2336,4243,4543,0004,1292,132---------------------------*Osceola, St. Lucie, Palm Beach

Orange677,491471,016344,311263,540114,95070,07449,73719,89019,10711,37412,5846,6182,195987466737331830-40: Mosquito

Osceola107,72849,28725,26719,02911,40610,11910,6997,1955,5073,4443,133------------------*Brevard, Orange

Palm Beach863,518576,863348,753228,106114,68879,98951,78118,6545,577------------------------*Dade

Pasco281,131193,64375,95536,78520,52913,98110,5748,8027,5026,0544,249------------------*Hernando

Pinellas851,659728,531522,329374,665159,24991,85262,14928,265---------------------------*Hillsborough

Polk405,382321,652227,222195,139123,99786,66572,29138,66124,14812,4727,9053,1813,169------------*Hillsborough, Brevard

Putnam65,07050,54936,29032,21223,61518,69818,09614,56813,09611,64111,1866,2613,8212,712687------*St. Johns, Alachua

St. Johns83,82951,30330,72730,03424,99820,01218,67613,06113,2089,1658,7124,5352,6183,0382,5252,6942,538

St. Lucie150,17187,18250,83639,29420,18011,8717,0577,8864,075------------------------*Brevard; see also note 1

Santa Rosa81,60855,98837,74129,54718,55416,08514,08313,67014,89710,2937,9616,6453,3125,4802,883------*Escambia

Sarasota277,776202,251120,41376,89528,82716,10612,440------------------------------*Manatee; see note 2

Seminole287,529179,75283,69254,94726,88322,30418,73510,986---------------------------*Orange

Sumter31,57724,27214,83911,86911,33011,04110,6447,8516,6966,1875,3634,6862,9521,549---------*Marion

Suwannee26,78022,28715,55914,96116,98617,07315,73119,78918,60314,55410,5247,1613,5562,303---------*Columbia

Taylor17,11116,53213,64113,16810,41611,56513,13611,2197,1033,9992,1222,2791,4531,384---------*Madison

Union10,25210,1668,1126,0438,9067,0947,428------------------------------*Bradford

Volusia370,712258,762169,487125,31974,22953,71042,75723,37416,51010,0038,4673,2941,7231,158---------*Orange

Wakulla14,20210,8876,3085,2575,2585,4635,4685,1294,8025,1493,1172,7232,5062,8391,955------*Leon

Walton27,76021,30016,08715,57614,72514,24614,57612,11916,4609,3464,8164,2013,0413,0371,8171,4611,207See notes 3 and 6

Washington16,91914,50911,45311,24911,88812,30212,18011,82816,40310,1546,4264,0892,3022,1541,950859978See notes 5 and 6

FLORIDA NOTES

Florida was a Spanish possession until transferred to the United States by treaty, concluded in 1819 but not in full effect until 1821. Florida was made a territory in 1822 with essentially its present boundaries, and was admitted as a State on March 3,

From 1830 on, all parts of Florida have had census coverage.

County Notes:

Note 1: Brevard: *Mosquito (Orange), Monroe. Originally named St. Lucie; renamed Brevard in 1855. The current St. Lucie County was created in 1905.

Note 2: DeSoto, Manatee, Sarasota: After 1950 some sparsely settled portions of Manatee and Sarasota were annexed to DeSoto, but these changes were reversed after 1960.

Note 3: Escambia, Walton: Escambia's 1830 population comprises 2,518 "west of Escambia River, including St. Rosa Island" and 868 "between Yellow and Escambia Rivers"; part of this area was in Walton County.

Note 4: Hernando: *Mosquito (Orange), Alachua, Hillsborough; 1850: Benton. Population for 1860 is estimated; the 1860 census did not enumerate the county.

Note 5: Jackson, Washington: Jackson's 1830 population excludes the portion west of Holmes Creek, which was reported with Washington, and includes the portion of Washington on the Chipola and Apalachicola Rivers.

Note 6: Walton, Washington: Walton's 1830 population is for the territory between the Choctowatchee and Yellow Rivers, including the isthmus south of the Choctowatchee; part of this area was in Washington County.

County Data Corrected


18301840185018601870188018901900191019201930194019501960197019801990

FLORIDA34,73054,47787,445140,424187,748269,493391,422528,542752,619968,4701,468,2111,897,4142,771,3054,951,5606,789,4439,746,32412,937,926

Alachua2,2042,2822,5248,23217,32816,46222,93432,24534,30531,68934,36538,60757,02674,074104,764151,348181,596

Baker------------1,3252,3033,3334,5164,8055,6226,2736,5106,3137,3639,24215,28918,486

Bay---------------------------11,40712,09120,68642,68967,13175,28397,740126,994

Bradford---------3,8203,6716,1127,51610,29514,09012,5039,4058,71711,45712,44614,62520,02322,515

Brevard------1392461,2161,4783,4015,1584,7178,50513,28316,14223,653111,435230,006272,959398,978

Broward---------------------------5,13520,09439,79483,933333,946620,1001,018,2001,255,488

Calhoun---1,1421,3771,4469981,5801,6815,1327,4658,7757,2988,2187,9227,4227,6249,29411,011

Charlotte------------------------------4,0133,6634,28612,59427,55958,460110,975

Citrus------------------2,3945,3916,7315,2205,5165,8466,1119,26819,19654,70393,515

Clay---------1,9142,0982,8385,1545,6356,1165,6216,8596,46814,32319,53532,05967,052105,986

Collier------------------------------2,8835,1026,48815,75338,04085,971152,099

Columbia---2,1024,8084,6467,3359,58912,87717,09417,68914,29014,63816,85918,21620,07725,25035,39942,613

Dade---44615983852578614,95511,93342,753142,955267,739495,084935,0471,267,7921,625,7811,937,094

DeSoto------------------4,9448,04714,20025,4347,7457,7929,24211,68313,06019,03923,865

Dixie------------------------------6,4197,0183,9284,4795,4807,75110,585

Duval1,9704,1564,5395,07411,92119,43126,80039,73375,163113,540155,503210,143304,029455,411528,865571,003672,971

Escambia3,3863,9934,3515,7687,81712,15620,18828,31338,02949,38653,59474,667112,706173,829205,334233,794262,798

Flagler---------------------------2,4422,4663,0083,3674,5664,45410,91328,701

Franklin---1,0301,5611,9041,2561,7913,3084,8905,2015,3186,2835,9915,8146,5767,0657,6618,967

Gadsden4,8955,9928,7849,3969,80212,16911,89415,29422,19823,53929,89031,45036,45741,98939,18441,56541,105

Gilchrist------------------------------4,1374,2503,4992,8683,5515,7679,667

Glades------------------------------2,7622,7452,1992,9503,6695,9927,591

Gulf------------------------------3,1826,9517,4609,93710,09610,65811,504

Hamilton5531,4642,5114,1545,7496,7908,50711,88111,8259,8739,4549,7788,9817,7057,7878,76110,930

Hardee------------------------------10,34810,15810,07312,37014,88919,37919,499

Hendry------------------------------3,4925,2376,0518,11911,85918,59925,773

Hernando------9261,2002,9384,2482,4763,6384,9974,5484,9485,6416,69311,20517,00444,469101,115

Highlands------------------------------9,1929,24613,63621,33829,50747,52668,432

Hillsborough---4522,3772,9813,2165,81414,94136,01378,37488,257153,519180,148249,894397,788490,265646,960834,054

Holmes------1,2051,3861,5722,1704,3367,76211,55712,85012,92415,44713,98810,84410,72014,72315,778

Indian River------------------------------6,7248,95711,87225,30935,99259,89690,208

Jackson3,9074,6816,63910,2099,52814,37217,54423,37729,82131,22431,96934,42834,64536,20834,43439,15441,375

Jefferson3,3125,7137,7189,87613,39816,06515,75716,19517,21014,50213,40812,03210,4139,5438,77810,70311,296

Lafayette---------2,0681,7832,4413,6864,9876,7106,2424,3614,4053,4402,8892,8924,0355,578

Lake------------------8,0347,4679,50912,74423,16127,25536,34057,38369,305104,870152,104

Lee------------------1,4143,0716,2949,54014,99017,48823,40454,539105,216205,266335,113

Leon6,49410,71311,44212,34315,23619,66217,75219,88719,42718,05923,47631,64651,59074,225103,047148,655192,493

Levy------4651,7812,0185,7676,5868,60310,3619,92112,45612,55010,63710,36412,75619,87025,923

Liberty---------1,4571,0501,3621,4522,9564,7005,0064,0673,7523,1823,1383,3794,2605,569

Madison5252,6445,4907,77911,12114,79814,31615,44616,91916,51615,61416,19014,19714,15413,48114,89416,569

Manatee---------8541,9313,5442,8954,6639,55018,71222,50226,09834,70469,16897,115148,442211,707

Marion------3,3388,60910,80413,04620,79624,40326,94123,96829,57831,24338,18751,61669,030122,488194,833

Martin------------------------------5,1116,2957,80716,93228,03564,014100,900

Monroe5176882,6452,9135,65710,94018,78618,00621,56319,55013,62414,07829,95747,92152,58663,18878,024

Nassau1,5111,8922,1643,6444,2476,6358,2949,65410,52511,3409,37510,82612,81117,18920,62632,89443,941

Okaloosa---------------------------9,3609,89712,90027,53361,17588,187109,920143,776

Okeechobee---------------------------2,1324,1293,0003,4546,42411,23320,26429,627

Orange733734669872,1956,61812,58411,37419,10719,89049,73770,074114,950263,540344,311471,016677,491

Osceola------------------3,1333,4445,5077,19510,69910,11911,40619,02925,26749,287107,728

Palm Beach------------------------5,57718,65451,78179,989114,688228,106348,753576,863863,518

Pasco------------------4,2496,0547,5028,80210,57413,98120,52936,78575,955193,643281,131

Pinellas---------------------------28,26562,14991,852159,249374,665522,329728,531851,659

Polk------------3,1693,1817,90512,47224,14838,66172,29186,665123,997195,139227,222321,652405,382

Putnam------6872,7123,8216,26111,18611,64113,09614,56818,09618,69823,61532,21236,29050,54965,070

St. Johns2,5382,6942,5253,0382,6184,5358,7129,16513,20813,06118,67620,01224,99830,03430,72751,30383,829

St. Lucie------------------------4,0757,8867,05711,87120,18039,29450,83687,182150,171

Santa Rosa------2,8835,4803,3126,6457,96110,29314,89713,67014,08316,08518,55429,54737,74155,98881,608

Sarasota------------------------------12,44016,10628,82776,895120,413202,251277,776

Seminole---------------------------10,98618,73522,30426,88354,94783,692179,752287,529

Sumter---------1,5492,9524,6865,3636,1876,6967,85110,64411,04111,33011,86914,83924,27231,577

Suwannee---------2,3033,5567,16110,52414,55418,60319,78915,73117,07316,98614,96115,55922,28726,780

Taylor---------1,3841,4532,2792,1223,9997,10311,21913,13611,56510,41613,16813,64116,53217,111

Union------------------------------7,4287,0948,9066,0438,11210,16610,252

Volusia---------1,1581,7233,2948,46710,00316,51023,37442,75753,71074,229125,319169,487258,762370,712

Wakulla------1,9552,8392,5062,7233,1175,1494,8025,1295,4685,4635,2585,2576,30810,88714,202

Walton1,2071,4611,8173,0373,0414,2014,8169,34616,46012,11914,57614,24614,72515,57616,08721,30027,760

Washington9788591,9502,1542,3024,0896,42610,15416,40311,82812,18012,30211,88811,24911,45314,50916,919

Selected Counties


18301840185018601870188018901900191019201930194019501960197019801990

FLORIDA34,73054,47787,445140,424187,748269,493391,422528,542752,619968,4701,468,2111,897,4142,771,3054,951,5606,789,4439,746,32412,937,926

Alachua2,2042,2822,5248,23217,32816,46222,93432,24534,30531,68934,36538,60757,02674,074104,764151,348181,596

Brevard------1392461,2161,4783,4015,1584,7178,50513,28316,14223,653111,435230,006272,959398,978

Broward---------------------------5,13520,09439,79483,933333,946620,1001,018,2001,255,488

Calhoun---1,1421,3771,4469981,5801,6815,1327,4658,7757,2988,2187,9227,4227,6249,29411,011

Dade---44615983852578614,95511,93342,753142,955267,739495,084935,0471,267,7921,625,7811,937,094

Escambia3,3863,9934,3515,7687,81712,15620,18828,31338,02949,38653,59474,667112,706173,829205,334233,794262,798

Flagler---------------------------2,4422,4663,0083,3674,5664,45410,91328,701

Hernando------9261,2002,9384,2482,4763,6384,9974,5484,9485,6416,69311,20517,00444,469101,115

Hillsborough---4522,3772,9813,2165,81414,94136,01378,37488,257153,519180,148249,894397,788490,265646,960834,054

Jefferson3,3125,7137,7189,87613,39816,06515,75716,19517,21014,50213,40812,03210,4139,5438,77810,70311,296

Leon6,49410,71311,44212,34315,23619,66217,75219,88719,42718,05923,47631,64651,59074,225103,047148,655192,493

Liberty---------1,4571,0501,3621,4522,9564,7005,0064,0673,7523,1823,1383,3794,2605,569

Madison5252,6445,4907,77911,12114,79814,31615,44616,91916,51615,61416,19014,19714,15413,48114,89416,569

Manatee---------8541,9313,5442,8954,6639,55018,71222,50226,09834,70469,16897,115148,442211,707

Okaloosa---------------------------9,3609,89712,90027,53361,17588,187109,920143,776

Orange733734669872,1956,61812,58411,37419,10719,89049,73770,074114,950263,540344,311471,016677,491

Pinellas---------------------------28,26562,14991,852159,249374,665522,329728,531851,659

Sarasota------------------------------12,44016,10628,82776,895120,413202,251277,776

Seminole---------------------------10,98618,73522,30426,88354,94783,692179,752287,529

Sumter---------1,5492,9524,6865,3636,1876,6967,85110,64411,04111,33011,86914,83924,27231,577

Taylor---------1,3841,4532,2792,1223,9997,10311,21913,13611,56510,41613,16813,64116,53217,111

Wakulla------1,9552,8392,5062,7233,1175,1494,8025,1295,4685,4635,2585,2576,30810,88714,202

Washington9788591,9502,1542,3024,0896,42610,15416,40311,82812,18012,30211,88811,24911,45314,50916,919

Selected Counties

34730

54477

87445

140424

187748

269493

391422

528542

752619

968470

1468211

1897414

2771305

4951560

6789443

9746324

12937926

FLORIDA

Year

Population

Florida Population, 1830-1990

Leon County

6494

10713

11442

12343

15236

19662

17752

19887

19427

18059

23476

31646

51590

74225

103047

148655

192493

Leon

Year

Population


Selected No. FL Counties

POPULATION OF LEON COUNTY 1890-1990

18301840185018601870188018901900191019201930194019501960197019801990

Leon6,49410,71311,44212,34315,23619,66217,75219,88719,42718,05923,47631,64651,59074,225103,047148,655192,493

-1594516.53431373

1900191019201930194019501960197019801990

Leon19,88719,42718,05923,47631,64651,59074,225103,047148,655192,493

194019501960197019801990

Leon31,64651,59074,225103,047148,655192,493

1960197019801990

Leon74,225103,047148,655192,493

Selected No. FL Counties

0

0

0

0

0

0

0

0

0

0

Leon

Year

Population


0

0

0

0

0

0

Leon

Year

Population


0

0

0

0

Leon

Year

Population


0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Leon

Year

Population


0

0

0

0

0

0

0

0

0

0

Year

Population


0

0

0

0

0

0

Year

Population


POPULATION OF SELECTED COUNTIES -- FLORIDA: 1890-1990

18301840185018601870188018901900191019201930194019501960197019801990

Calhoun---1,1421,3771,4469981,5801,6815,1327,4658,7757,2988,2187,9227,4227,6249,29411,011

Jefferson3,3125,7137,7189,87613,39816,06515,75716,19517,21014,50213,40812,03210,4139,5438,77810,70311,296

Liberty---------1,4571,0501,3621,4522,9564,7005,0064,0673,7523,1823,1383,3794,2605,569

Madison5252,6445,4907,77911,12114,79814,31615,44616,91916,51615,61416,19014,19714,15413,48114,89416,569

Taylor---------1,3841,4532,2792,1223,9997,10311,21913,13611,56510,41613,16813,64116,53217,111

Wakulla------1,9552,8392,5062,7233,1175,1494,8025,1295,4685,4635,2585,2576,30810,88714,202

000000

000000

000000

000000

000000

000000

000000

000000

000000

000000

Calhoun

Jefferson

Liberty

Madison

Taylor

Wakulla

Year

Population

Population for Selected North Florida Counties, 1990-1990

The Curves to Be Fit Linear Curve: Plots a straight line based on the formula: Y = a + bX Geometric Curve: Plots a curve based upon a rate of compounding growth over discrete intervals via the formula: Y = aebX Parabolic (Polynomial) Curve: A curve with one bend and a constantly changing slope. Formula: Y = a + bX + cX2 Modified Exponential Curve*: An asymptotic growth curve that recognizes that a region will reach an upper limit of growth. It takes the form: Y = c + abX Gompertz Curve*: Describes a growth pattern that is quite slow, increases for a time, and then tapers off as the population approaches a growth limit. Form: Y = c(a) exp (bX) Logistic Curve*: Similar to the Gompertz Curve, this is useful for describing phenomena that grow slowly at first, increase rapidly, and then slow with approach to a growth limit. Y = (c + abX)-1* = Asymptotic Curves

The Linear Curve (Y = a + bX) Fits a straight line to population data. The growth rate is assumed to be constant, with non-compounding incremental growth. Calculated exactly the same as using linear regression (least-squares criterion). Advantages: --Simplest curve --Most widely used --Useful for slow or non-growth areas Disadvantages: --Rarely appropriate to demographic data Example:Y = 55,000 + 6,000(X)In plain language, this equation tells us that for each year that passes, we can project an additional 6,000 people will be added to the population. So, in 10 years we would project 60,000 more people using this equation (6,000 * 10). Evaluation: Generally used as a staring point for curve fitting.

Manatee County Linear Curve

YearActual DataProjection195034,704 21,421 196069,168 67,862 197097,115 114,303 1980148,442 160,743 1990211,707 207,184 2000264,002 253,625 2010 300,066 2020 346,507 2030 392,948

Y Int-9034568.9Slope4644.09714

Chart1

3470421420.5714285728

6916867861.542857144

97115114302.514285715

148442160743.485714287

211707207184.457142858

264002253625.428571429

2010300066.4

2020346507.371428572

2030392948.342857143

Actual Data

Projection

Year

Population

Manatee County Linear Regression Projections

Chapin Lin Reg

MANATEE COUNTY BY 1950

LINEAR REGRESSION

Even Number of Observations

YearActual DataProjection

195034,70421,421

196069,16867,862

197097,115114,303

1980148,442160,743

1990211,707207,184

2000264,002253,625

2010300,066

2020346,507

2030392,948

Y Int-9034568.85714286

Slope4644.0971428571

Chapin Lin Reg

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


LR Eval


LINEAR REGRESSION (See Pages 207-213)

CURVE EVALUATION

FirstAbsolute

YearActual DataDifferenceProjectionsDeviationPercentage Error

195034,70421,42113,28338.28%

196069,16834,46467,8621,3061.89%

197097,11527,947114,303(17,188)17.70%

1980148,44251,327160,743(12,301)8.29%

1990211,70763,265207,1844,5232.14%

2000264,00252,295253,62510,3773.93%

2010300,066

2020346,507

2030392,948

Mean Error-0

MAPE12.04%

Calculating the Coefficient of Relative Variation

St Dev of 1st Diffs14,361

Mean of 1st Diffs45,860

CRV31.32

Chapin Geometric


GEOMETRIC CURVE (See Pages 213-217)

YearActual DataLog of PopLog ProjProjection

195034,7044.54044.615841,281

196069,1684.83994.788561,454

197097,1154.98734.961391,484

1980148,4425.17165.1341136,189

1990211,7075.32575.3069202,741

2000264,0025.42165.4797301,813

20105.6525449,298

20205.8253668,855

20305.9981995,702

Y Int(29.080)

Slope0.0173

Chapin Geometric

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population

Manatee County Geometric Curve Projections

Geo Eval



CURVE EVALUATION

Log ofDiff ofAbsolute

YearActual DataObservedLogsProjectionsDeviationPercentage Error

195034,7044.54041,281(6,577)18.95%

196069,1684.8400.30061,4547,71411.15%

197097,1154.9870.14791,4845,6315.80%

1980148,4425.1720.184136,18912,2538.25%

1990211,7075.3260.154202,7418,9664.24%

2000264,0025.4220.096301,813(37,811)14.32%

2010449,298

2020668,855

2030995,702

Mean Error(1,637)

MAPE10.45%


St Dev of Diff of Logs0.076

Mean of Diff of Logs0.176

CRV43.1

Parabolic


PARABOLIC CURVE (See Pages 217-221)

Even Number of ObservationsProduct of IndexColumn F

YearActual DataIndex ValueIndex SquaredIndex ^4and ObservedSquaredProjections

195034,704-525625-17352086760035,136

196069,168-3981-20750462251265,118

197097,115-111-9711597115103,330

1980148,442111148442148442149,771

1990211,70739816351211905363204,441

2000264,00252562513200106600050267,341

20107492401338,471

20209816561417,830

20301112114641505,419

Totals82513827701414162543410241082

(SUM Y)(SUM X^2)(SUM X^4)(SUM X*Y)(SUM X^2*Y)

N=6(Number of Observations)Denotes different formulas due to Even

(XY)=1625434number of observations

(X^2*Y)10241082

CALCULATING PARAMETER c:

c = (N*SumX^2*Y - SumX^2*SumY)/(N*SumX^4 - (SumX^2)^2) =

where:

N*SumX^2*Y =61446492

SumX^2*SumY =57759660

N*SumX^4 =8484

(SumX^2)^2)=4900

c =1028.692

CALCULATING PARAMETER a:

a = (SumY - c*SumX^2)/N =

where:

SumY =825138

c*SumX^2 =72008.438

N =6

a =125521.59

CALCULATING PARAMETER b:

b = SumXY/SumX^2 =

where:

SumXY =1625434

SumX^2 =70

b =23220.49

EQUATION

Yc =a+b* X +c* X^2

Odd Number of ObservationsProduct of IndexColumn F


193023,476-3981-7042821128423,381

194031,646-2416-6329212658432,696

195051,590-111-515905159049,606

196074,2250000074,112

1970103,047111103047103047106,215

1980148,6552416297310594620145,914

1990192,49339815774791732437193,208

2000416256248,099

2010525625310,586

20206361296380,668

Totals625,1320.028196792,5262,819,562


N=7(Number of Observations)

(XY)=792526

(X^2*Y)2819562



where:

N*SumX^2*Y =19736934

SumX^2*SumY =17503696

N*SumX^4 =1372

(SumX^2)^2)=784

c =3798.024



where:

SumY =625132

c*SumX^2 =106344.667

N =7

a =74112.48


b = SumXY/SumX^2 =

where:

SumXY =792526

SumX^2 =28

b =28304.50

EQUATION

Yc =a+b* X +c* X^2

Parabolic

00

00

00

00

00

00

00

00

00

Actual Data

Projections

Year

Pop

Manatee County Parablic Curve

Par Eval

11

#REF!

#REF!

Year

Pop (in 000's)

Klosterman Parabolic Curve (Even)

Mod Exponential



CURVE EVALUATION

FirstSecondAbsolute

YearActual DataDifferenceDifferenceProjectionsDeviationPercentage Error

195034,70435,136(432)1.25%

196069,16834,46465,1184,0505.85%

197097,11527,947(6,517)103,330(6,215)6.40%

1980148,44251,32723,380149,771(1,329)0.90%

1990211,70763,26511,938204,4417,2663.43%

2000264,00252,295(10,970)267,341(3,339)1.26%

2010338,471

2020417,830

2030505,419

Mean Error0

MAPE3.18%


St Dev of 2nd Diffs16,046.46

Mean of 2nd Diffs4,458

CRV360.0

ME Eval


MODIFIED EXPONENTIAL CURVE (See Pages 221-228)

Calculating the Upper Limit

Number of Observation Divisible by ThreeError of

YearIndexActual DataProjectionEstimate

1950034,70438,2423,538

1960169,16865,630(3,538)

1970297,115100,5353,420

19803148,442145,022(3,420)

19904211,707201,722(9,985)

20005264,002273,9879,985

20106366,090

20207483,476

20308633,087

Total825,138

Partial Sum 1-3103,872



Total for All825,138

n2N/3

b^n1.624(Sum 7-9) - (Sum 4-6) / (Sum 4-6) - (Sum 1-3)

b1.275

a99,765(Sum 4-6) - (Sum 1-3) X ((b-1)/(b^n-1)^2))

c(61,522.35)(1/n) X ((Sum1-3)X(Sum7-9) - Sum4-6^2)/((Sum1-3) +(Sum7-9) - 2(Sum 4-6))

ME Eval

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population

Manatee County Pop ProjectionsBest Fitting Mod Exp Curve

Gompertz



CURVE EVALUATION

FirstRatio ofAbsolute

YearActual DataDifference1st DiffProjectionsDeviationPercentage Error

195034,70438,242(3,538)10.20%

196069,16834,46465,6303,5385.12%

197097,11527,9470.811100,535(3,420)3.52%

1980148,44251,3271.837145,0223,4202.30%

1990211,70763,2651.233201,7229,9854.72%

2000264,00252,2950.827273,987(9,985)3.78%

2010366,090

2020483,476

2030633,087

Mean Error-0

MAPE4.94%


St Dev of Ratio of 1st Diffs0.48

Mean of Ratio of 1st Diffs1.18

CRV40.9

Gomp Eval


GOMPERTZ CURVE (See Pages 228-235)


Number of Observation Divisible by Three

Log ofLog ofError of

YearIndexActual DataObs ValueProjectionProjectionEstimate

1950034,7044.54044.578837,9103205.8

1960169,1684.83994.801563,319-5849.1

1970297,1154.98734.995298,9061791.1

19803148,4425.17165.1636145,754-2688.1

19904211,7075.32575.3100204,186-7520.5

20005264,0025.42165.4373273,7269723.6

201065.5480353,169

202075.6442440,755

203085.7278534,378

Total825,138

Partial Sum 1-39.3803




n2

b^n0.756(Sum 7-9) - (Sum 4-6) / (Sum 4-6) - (Sum 1-3)

b0.869

a(2)(Sum 4-6) - (Sum 1-3) X ((b-1)/(b^n-1)^2))

c6.28(1/n) X ((Sum1-3)X(Sum7-9) - Sum4-6^2)/((Sum1-3) +(Sum7-9) - 2(Sum 4-6))

Gomp Eval

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population

Leon County ProjectionsGompertz Curve (UL = 500,000)

Logistic

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population

Manatee County Pop Projections Best Fitting Gompertz Curve

Log Eval



CURVE EVALUATION

Log ofDiff ofRatio ofAbsolute

YearActual DataObservedLogsLog DiffsProjectionsDeviationPercentage Error

195034,7044.5437,910(3,206)9.24%

196069,1684.840.299563,3195,8498.46%

197097,1154.990.14740.49298,906(1,791)1.84%

1980148,4425.170.18431.250145,7542,6881.81%

1990211,7075.330.15420.837204,1867,5213.55%

2000264,0025.420.09590.622273,726(9,724)3.68%

2010353,169

2020440,755

2030534,378

Mean Error223

MAPE4.76%


St Dev of Ratio of Log Diffs0.33

Mean of Ratio of Log Diffs0.80

CRV41.5

Summary


LOGISTIC CURVE (See Pages 236-242)



ReciprocalLog ofError of

YearIndexActual Dataof ObservedProjectionProjectionEstimate

1950034,7040.000028820.00002695937,0932388.7

1960169,1680.000014460.00001631361,300-7868.0

1970297,1150.000010300.00001024697,601486.0

19803148,4420.000006740.000006788147,321-1121.4

19904211,7070.000004720.000004817207,588-4119.0

20005264,0020.000003790.000003694270,7006698.1

201060.000003054327,434

202070.000002689371,848

203080.000002481403,002

Total




Total for All

n2

b^n0.325(Sum 7-9) - (Sum 4-6) / (Sum 4-6) - (Sum 1-3)

b0.570

a0.00002475(Sum 4-6) - (Sum 1-3) X ((b-1)/(b^n-1)^2))


Summary

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population

Manatee County Pop ProjectionsBest Fitting Logistic Curve

Best Fitting



CURVE EVALUATION

ReciprocalDiff ofRatio ofAbsolute

YearActual Dataof ObservedReciprocalsRec. DiffsProjectionsDeviationPercentage Error

195034,7040.000028837,093(2,389)6.88%

196069,1680.0000145(0.0000144)61,3007,86811.38%

197097,1150.0000103(0.0000042)0.29097,601(486)0.50%

1980148,4420.0000067(0.0000036)0.856147,3211,1210.76%

1990211,7070.0000047(0.0000020)0.565207,5884,1191.95%

2000264,0020.0000038(0.0000009)0.465270,700(6,698)2.54%

2010327,434

2020371,848

2030403,002

Mean Error589

MAPE4.00%


St Dev of Ratio of Rec Diffs0.24

Mean of Ratio of Rec Diffs0.54

CRV43.6

All Curves


CURVE EVALUATIONS


Evaluating the Various Curves

CRVMEMAPE

Linear31.3-0.012.04%

Geometric43.1-1637.410.45%

Parabolic360.00.03.18%

Mod Exp*40.9-0.04.94%

Gompertz*41.5222.94.76%

Logistic*43.6589.24.00%

*Used "Best Fitting Curve"

MANATEE COUNTY POPULATION PROJECTIONS, 2000-2020

USING THE EXTRAPOLATION TECHNIQUE (BASE PERIOD 1950-2000)

YearObservedLinearGeometricParabolicMod Exp*Gompertz*Logistic*

195034,70421,42141,28135,13638,24237,91037,093

196069,16867,86261,45465,11865,63063,31961,300

197097,115114,30391,484103,330100,53598,90697,601

1980148,442160,743136,189149,771145,022145,754147,321

1990211,707207,184202,741204,441201,722204,186207,588

2000264,002253,625301,813267,341273,987273,726270,700

2010300,066449,298338,471366,090353,169327,434

2020346,507668,855417,830483,476440,755371,848

2030392,948995,702505,419633,087534,378403,002


LEON COUNTY POPULATION PROJECTIONS, 2000-2020


YearObservedCen 2000LinearGeometricParabolicMod Exp*Gompertz*Logistic*

194031,646

195051,590

196074,225

1970103,047

1980148,655

1990192,493

2000239,452212,701294,911247,928267,138260,974248,287

2010244,823421,863310,244359,595338,489299,504

2020276,944603,465380,109481,649430,470344,748


316461940194019401940194019401940

515901950195019501950195019501950

742251960196019601960196019601960

1030471970197019701970197019701970

1486551980198019801980198019801980

1924931990199019901990199019901990

2000239452212701.2294911.358774184247928.2267138.355667061260973.538154462248286.77724716

20102010244822.685714286421863.275628557310244.257142857359595.413357568338488.682706828299503.897770785

20202020276944.171428571603464.797231922380108.957142857481649.03548955430469.572388299344748.009890723

Observed

Cen 2000

Linear

Geometric

Parabolic

Mod Exp*

Gompertz*

Logistic*

Year

Population

Leon County Projections, 2000-2020All Curve Types Base Year 1940-1990

The Geometric Curve (Y = aebX) In this curve, a growth rate is assumed to be compounded at set intervals using a constant growth rate. To transform this equation into a linear equation, we use logarithms. Advantages: --Assumes a constant rate of growth --Still simple to use Disadvantage: --Does not take into account a growth limit Example:Y = 55,000 * (1.00 + 0.06)XIn plain language, this equation tells us that we have a 6% growth rate. After one year we project a population of 58,300. After 10 years we would project a population of 98,497. Evaluation: Pretty good for short term fast-growing areas. However, over the long-run, this curve usually generates unrealistically high numbers.

Manatee County Geometric Curve

YearActual DataLog of PopLog ProjProjection195034,7044.5404 4.6158 41,281 196069,1684.8399 4.7885 61,454 197097,1154.9873 4.9613 91,484 1980148,4425.1716 5.1341 136,189 1990211,7075.3257 5.3069 202,741 2000264,0025.4216 5.4797 301,813 2010 5.6525 449,298 2020 5.8253 668,855 2030 5.9981 995,702

Y Int (29.080)Slope 0.0173

Chart2

3470441281.1960571193

6916861453.8906121702

9711591484.2841798252

148442136189.493757415

211707202740.595023328

264002301812.920632692

2010449298.469555908

2020668855.111709936

2030995701.500836835

Actual Data

Projection

Year

Population


Chapin Lin Reg


LINEAR REGRESSION



195034,70421,421

196069,16867,862

197097,115114,303

1980148,442160,743

1990211,707207,184

2000264,002253,625

2010300,066

2020346,507

2030392,948

Y Int-9034568.85714286

Slope4644.0971428571

Chapin Lin Reg

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


LR Eval



CURVE EVALUATION

FirstAbsolute


195034,70421,42113,28338.28%

196069,16834,46467,8621,3061.89%

197097,11527,947114,303(17,188)17.70%

1980148,44251,327160,743(12,301)8.29%

1990211,70763,265207,1844,5232.14%

2000264,00252,295253,62510,3773.93%

2010300,066

2020346,507

2030392,948

Mean Error-0

MAPE12.04%




CRV31.32

Chapin Geometric




195034,7044.54044.615841,281

196069,1684.83994.788561,454

197097,1154.98734.961391,484

1980148,4425.17165.1341136,189

1990211,7075.32575.3069202,741

2000264,0025.42165.4797301,813

20105.6525449,298

20205.8253668,855

20305.9981995,702

Y Int(29.080)

Slope0.0173

Chapin Geometric

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Geo Eval



CURVE EVALUATION



195034,7044.54041,281(6,577)18.95%

196069,1684.8400.30061,4547,71411.15%

197097,1154.9870.14791,4845,6315.80%

1980148,4425.1720.184136,18912,2538.25%

1990211,7075.3260.154202,7418,9664.24%

2000264,0025.4220.096301,813(37,811)14.32%

2010449,298

2020668,855

2030995,702

Mean Error(1,637)

MAPE10.45%




CRV43.1

Parabolic





195034,704-525625-17352086760035,136

196069,168-3981-20750462251265,118

197097,115-111-9711597115103,330

1980148,442111148442148442149,771

1990211,70739816351211905363204,441

2000264,00252562513200106600050267,341

20107492401338,471

20209816561417,830

20301112114641505,419

Totals82513827701414162543410241082




(X^2*Y)10241082



where:

N*SumX^2*Y =61446492

SumX^2*SumY =57759660

N*SumX^4 =8484

(SumX^2)^2)=4900

c =1028.692



where:

SumY =825138

c*SumX^2 =72008.438

N =6

a =125521.59


b = SumXY/SumX^2 =

where:

SumXY =1625434

SumX^2 =70

b =23220.49

EQUATION

Yc =a+b* X +c* X^2



193023,476-3981-7042821128423,381

194031,646-2416-6329212658432,696

195051,590-111-515905159049,606

196074,2250000074,112

1970103,047111103047103047106,215

1980148,6552416297310594620145,914

1990192,49339815774791732437193,208

2000416256248,099

2010525625310,586

20206361296380,668

Totals625,1320.028196792,5262,819,562



(XY)=792526

(X^2*Y)2819562



where:

N*SumX^2*Y =19736934

SumX^2*SumY =17503696

N*SumX^4 =1372

(SumX^2)^2)=784

c =3798.024



where:

SumY =625132

c*SumX^2 =106344.667

N =7

a =74112.48


b = SumXY/SumX^2 =

where:

SumXY =792526

SumX^2 =28

b =28304.50

EQUATION

Yc =a+b* X +c* X^2

Parabolic

00

00

00

00

00

00

00

00

00

Actual Data

Projections

Year

Pop


Par Eval

11

#REF!

#REF!

Year

Pop (in 000's)


Mod Exponential



CURVE EVALUATION

FirstSecondAbsolute


195034,70435,136(432)1.25%

196069,16834,46465,1184,0505.85%

197097,11527,947(6,517)103,330(6,215)6.40%

1980148,44251,32723,380149,771(1,329)0.90%

1990211,70763,26511,938204,4417,2663.43%

2000264,00252,295(10,970)267,341(3,339)1.26%

2010338,471

2020417,830

2030505,419

Mean Error0

MAPE3.18%




CRV360.0

ME Eval






1950034,70438,2423,538

1960169,16865,630(3,538)

1970297,115100,5353,420

19803148,442145,022(3,420)

19904211,707201,722(9,985)

20005264,002273,9879,985

20106366,090

20207483,476

20308633,087

Total825,138





n2N/3

b^n1.624(Sum 7-9) - (Sum 4-6) / (Sum 4-6) - (Sum 1-3)

b1.275

a99,765(Sum 4-6) - (Sum 1-3) X ((b-1)/(b^n-1)^2))


ME Eval

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Gompertz



CURVE EVALUATION



195034,70438,242(3,538)10.20%

196069,16834,46465,6303,5385.12%

197097,11527,9470.811100,535(3,420)3.52%

1980148,44251,3271.837145,0223,4202.30%

1990211,70763,2651.233201,7229,9854.72%

2000264,00252,2950.827273,987(9,985)3.78%

2010366,090

2020483,476

2030633,087

Mean Error-0

MAPE4.94%




CRV40.9

Gomp Eval







1950034,7044.54044.578837,9103205.8

1960169,1684.83994.801563,319-5849.1

1970297,1154.98734.995298,9061791.1

19803148,4425.17165.1636145,754-2688.1

19904211,7075.32575.3100204,186-7520.5

20005264,0025.42165.4373273,7269723.6

201065.5480353,169

202075.6442440,755

203085.7278534,378

Total825,138





n2

b^n0.756(Sum 7-9) - (Sum 4-6) / (Sum 4-6) - (Sum 1-3)

b0.869

a(2)(Sum 4-6) - (Sum 1-3) X ((b-1)/(b^n-1)^2))


Gomp Eval

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Logistic

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Log Eval



CURVE EVALUATION



195034,7044.5437,910(3,206)9.24%

196069,1684.840.299563,3195,8498.46%

197097,1154.990.14740.49298,906(1,791)1.84%

1980148,4425.170.18431.250145,7542,6881.81%

1990211,7075.330.15420.837204,1867,5213.55%

2000264,0025.420.09590.622273,726(9,724)3.68%

2010353,169

2020440,755

2030534,378

Mean Error223

MAPE4.76%




CRV41.5

Summary







1950034,7040.000028820.00002695937,0932388.7

1960169,1680.000014460.00001631361,300-7868.0

1970297,1150.000010300.00001024697,601486.0

19803148,4420.000006740.000006788147,321-1121.4

19904211,7070.000004720.000004817207,588-4119.0

20005264,0020.000003790.000003694270,7006698.1

201060.000003054327,434

202070.000002689371,848

203080.000002481403,002

Total




Total for All

n2

b^n0.325(Sum 7-9) - (Sum 4-6) / (Sum 4-6) - (Sum 1-3)

b0.570

a0.00002475(Sum 4-6) - (Sum 1-3) X ((b-1)/(b^n-1)^2))


Summary

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Best Fitting



CURVE EVALUATION



195034,7040.000028837,093(2,389)6.88%

196069,1680.0000145(0.0000144)61,3007,86811.38%

197097,1150.0000103(0.0000042)0.29097,601(486)0.50%

1980148,4420.0000067(0.0000036)0.856147,3211,1210.76%

1990211,7070.0000047(0.0000020)0.565207,5884,1191.95%

2000264,0020.0000038(0.0000009)0.465270,700(6,698)2.54%

2010327,434

2020371,848

2030403,002

Mean Error589

MAPE4.00%




CRV43.6

All Curves


CURVE EVALUATIONS



CRVMEMAPE

Linear31.3-0.012.04%

Geometric43.1-1637.410.45%


Mod Exp*40.9-0.04.94%

Gompertz*41.5222.94.76%

Logistic*43.6589.24.00%





195034,70421,42141,28135,13638,24237,91037,093

196069,16867,86261,45465,11865,63063,31961,300

197097,115114,30391,484103,330100,53598,90697,601

1980148,442160,743136,189149,771145,022145,754147,321

1990211,707207,184202,741204,441201,722204,186207,588

2000264,002253,625301,813267,341273,987273,726270,700

2010300,066449,298338,471366,090353,169327,434

2020346,507668,855417,830483,476440,755371,848

2030392,948995,702505,419633,087534,378403,002





194031,646

195051,590

196074,225

1970103,047

1980148,655

1990192,493

2000239,452212,701294,911247,928267,138260,974248,287

2010244,823421,863310,244359,595338,489299,504

2020276,944603,465380,109481,649430,470344,748


316461940194019401940194019401940

515901950195019501950195019501950

742251960196019601960196019601960

1030471970197019701970197019701970

1486551980198019801980198019801980

1924931990199019901990199019901990

2000239452212701.2294911.358774184247928.2267138.355667061260973.538154462248286.77724716

20102010244822.685714286421863.275628557310244.257142857359595.413357568338488.682706828299503.897770785

20202020276944.171428571603464.797231922380108.957142857481649.03548955430469.572388299344748.009890723

Observed

Cen 2000

Linear

Geometric

Parabolic

Mod Exp*

Gompertz*

Logistic*

Year

Population


The Parabolic Curve (Y = a + bX + cX2) Generally has a constantly changing slope and one bend. Very similar to the Linear Curve except for the additional parameter (c). Growing very quickly when c > 0, declining quickly when c < 0. Advantage: --Models fast growing areas Disadvantages: --Poor for long range projections (familiar refrain?) --No Growth Limit --More complex Example:Y = 43.46 + 8.78(X) + 0.581(X2) When X=0, Y =43.46. When X = 6, Y = 117.1 Evaluation: Exactly the same as the Geometric Curve; good for fast growing areas, but poor over the long run.

Manatee County Parabolic Curve

Even Number of ObservationsProduct ofColumn FYearActual DataIndex ValueIndex SquaredIndex ^4Index and ObservedSquaredProjection195034,704-525625-173520867600 35,136 196069,168-3981-207504622512 65,118 197097,115-111-9711597115 103,330 1980148,442111148442148442 149,771 1990211,70739816351211905363 204,441 2000264,00252562513200106600050 267,341 20107492401 338,471 20209816561 417,830 20301112114641 505,419

Chart3

3470435136.4642857143

6916865118.3642857143

97115103329.8

148442149770.771428571

211707204441.278571429

264002267341.321428571

2010338470.9

2020417830.014285714

2030505418.664285714

Actual Data

Projections

Year

Pop

Manatee County Parabolic Curve

Chapin Lin Reg


LINEAR REGRESSION



195034,70421,421

196069,16867,862

197097,115114,303

1980148,442160,743

1990211,707207,184

2000264,002253,625

2010300,066

2020346,507

2030392,948

Y Int-9034568.85714286

Slope4644.0971428571

Chapin Lin Reg

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


LR Eval



CURVE EVALUATION

FirstAbsolute


195034,70421,42113,28338.28%

196069,16834,46467,8621,3061.89%

197097,11527,947114,303(17,188)17.70%

1980148,44251,327160,743(12,301)8.29%

1990211,70763,265207,1844,5232.14%

2000264,00252,295253,62510,3773.93%

2010300,066

2020346,507

2030392,948

Mean Error-0

MAPE12.04%




CRV31.32

Chapin Geometric




195034,7044.54044.615841,281

196069,1684.83994.788561,454

197097,1154.98734.961391,484

1980148,4425.17165.1341136,189

1990211,7075.32575.3069202,741

2000264,0025.42165.4797301,813

20105.6525449,298

20205.8253668,855

20305.9981995,702

Y Int(29.080)

Slope0.0173

Chapin Geometric

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Geo Eval



CURVE EVALUATION



195034,7044.54041,281(6,577)18.95%

196069,1684.8400.30061,4547,71411.15%

197097,1154.9870.14791,4845,6315.80%

1980148,4425.1720.184136,18912,2538.25%

1990211,7075.3260.154202,7418,9664.24%

2000264,0025.4220.096301,813(37,811)14.32%

2010449,298

2020668,855

2030995,702

Mean Error(1,637)

MAPE10.45%




CRV43.1

Parabolic





195034,704-525625-17352086760035,136

196069,168-3981-20750462251265,118

197097,115-111-9711597115103,330

1980148,442111148442148442149,771

1990211,70739816351211905363204,441

2000264,00252562513200106600050267,341

20107492401338,471

20209816561417,830

20301112114641505,419

Totals82513827701414162543410241082




(X^2*Y)10241082



where:

N*SumX^2*Y =61446492

SumX^2*SumY =57759660

N*SumX^4 =8484

(SumX^2)^2)=4900

c =1028.692



where:

SumY =825138

c*SumX^2 =72008.438

N =6

a =125521.59


b = SumXY/SumX^2 =

where:

SumXY =1625434

SumX^2 =70

b =23220.49

EQUATION

Yc =a+b* X +c* X^2



193023,476-3981-7042821128423,381

194031,646-2416-6329212658432,696

195051,590-111-515905159049,606

196074,2250000074,112

1970103,047111103047103047106,215

1980148,6552416297310594620145,914

1990192,49339815774791732437193,208

2000416256248,099

2010525625310,586

20206361296380,668

Totals625,1320.028196792,5262,819,562



(XY)=792526

(X^2*Y)2819562



where:

N*SumX^2*Y =19736934

SumX^2*SumY =17503696

N*SumX^4 =1372

(SumX^2)^2)=784

c =3798.024



where:

SumY =625132

c*SumX^2 =106344.667

N =7

a =74112.48


b = SumXY/SumX^2 =

where:

SumXY =792526

SumX^2 =28

b =28304.50

EQUATION

Yc =a+b* X +c* X^2

Parabolic

00

00

00

00

00

00

00

00

00

Actual Data

Projections

Year

Pop


Par Eval

11

#REF!

#REF!

Year

Pop (in 000's)


Mod Exponential



CURVE EVALUATION

FirstSecondAbsolute


195034,70435,136(432)1.25%

196069,16834,46465,1184,0505.85%

197097,11527,947(6,517)103,330(6,215)6.40%

1980148,44251,32723,380149,771(1,329)0.90%

1990211,70763,26511,938204,4417,2663.43%

2000264,00252,295(10,970)267,341(3,339)1.26%

2010338,471

2020417,830

2030505,419

Mean Error0

MAPE3.18%




CRV360.0

ME Eval






1950034,70438,2423,538

1960169,16865,630(3,538)

1970297,115100,5353,420

19803148,442145,022(3,420)

19904211,707201,722(9,985)

20005264,002273,9879,985

20106366,090

20207483,476

20308633,087

Total825,138





n2N/3

b^n1.624(Sum 7-9) - (Sum 4-6) / (Sum 4-6) - (Sum 1-3)

b1.275

a99,765(Sum 4-6) - (Sum 1-3) X ((b-1)/(b^n-1)^2))


ME Eval

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Gompertz



CURVE EVALUATION



195034,70438,242(3,538)10.20%

196069,16834,46465,6303,5385.12%

197097,11527,9470.811100,535(3,420)3.52%

1980148,44251,3271.837145,0223,4202.30%

1990211,70763,2651.233201,7229,9854.72%

2000264,00252,2950.827273,987(9,985)3.78%

2010366,090

2020483,476

2030633,087

Mean Error-0

MAPE4.94%




CRV40.9

Gomp Eval







1950034,7044.54044.578837,9103205.8

1960169,1684.83994.801563,319-5849.1

1970297,1154.98734.995298,9061791.1

19803148,4425.17165.1636145,754-2688.1

19904211,7075.32575.3100204,186-7520.5

20005264,0025.42165.4373273,7269723.6

201065.5480353,169

202075.6442440,755

203085.7278534,378

Total825,138





n2

b^n0.756(Sum 7-9) - (Sum 4-6) / (Sum 4-6) - (Sum 1-3)

b0.869

a(2)(Sum 4-6) - (Sum 1-3) X ((b-1)/(b^n-1)^2))


Gomp Eval

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Logistic

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Log Eval



CURVE EVALUATION



195034,7044.5437,910(3,206)9.24%

196069,1684.840.299563,3195,8498.46%

197097,1154.990.14740.49298,906(1,791)1.84%

1980148,4425.170.18431.250145,7542,6881.81%

1990211,7075.330.15420.837204,1867,5213.55%

2000264,0025.420.09590.622273,726(9,724)3.68%

2010353,169

2020440,755

2030534,378

Mean Error223

MAPE4.76%




CRV41.5

Summary







1950034,7040.000028820.00002695937,0932388.7

1960169,1680.000014460.00001631361,300-7868.0

1970297,1150.000010300.00001024697,601486.0

19803148,4420.000006740.000006788147,321-1121.4

19904211,7070.000004720.000004817207,588-4119.0

20005264,0020.000003790.000003694270,7006698.1

201060.000003054327,434

202070.000002689371,848

203080.000002481403,002

Total




Total for All

n2

b^n0.325(Sum 7-9) - (Sum 4-6) / (Sum 4-6) - (Sum 1-3)

b0.570

a0.00002475(Sum 4-6) - (Sum 1-3) X ((b-1)/(b^n-1)^2))


Summary

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Best Fitting



CURVE EVALUATION



195034,7040.000028837,093(2,389)6.88%

196069,1680.0000145(0.0000144)61,3007,86811.38%

197097,1150.0000103(0.0000042)0.29097,601(486)0.50%

1980148,4420.0000067(0.0000036)0.856147,3211,1210.76%

1990211,7070.0000047(0.0000020)0.565207,5884,1191.95%

2000264,0020.0000038(0.0000009)0.465270,700(6,698)2.54%

2010327,434

2020371,848

2030403,002

Mean Error589

MAPE4.00%




CRV43.6

All Curves


CURVE EVALUATIONS



CRVMEMAPE

Linear31.3-0.012.04%

Geometric43.1-1637.410.45%


Mod Exp*40.9-0.04.94%

Gompertz*41.5222.94.76%

Logistic*43.6589.24.00%





195034,70421,42141,28135,13638,24237,91037,093

196069,16867,86261,45465,11865,63063,31961,300

197097,115114,30391,484103,330100,53598,90697,601

1980148,442160,743136,189149,771145,022145,754147,321

1990211,707207,184202,741204,441201,722204,186207,588

2000264,002253,625301,813267,341273,987273,726270,700

2010300,066449,298338,471366,090353,169327,434

2020346,507668,855417,830483,476440,755371,848

2030392,948995,702505,419633,087534,378403,002





194031,646

195051,590

196074,225

1970103,047

1980148,655

1990192,493

2000239,452212,701294,911247,928267,138260,974248,287

2010244,823421,863310,244359,595338,489299,504

2020276,944603,465380,109481,649430,470344,748


316461940194019401940194019401940

515901950195019501950195019501950

742251960196019601960196019601960

1030471970197019701970197019701970

1486551980198019801980198019801980

1924931990199019901990199019901990

2000239452212701.2294911.358774184247928.2267138.355667061260973.538154462248286.77724716

20102010244822.685714286421863.275628557310244.257142857359595.413357568338488.682706828299503.897770785

20202020276944.171428571603464.797231922380108.957142857481649.03548955430469.572388299344748.009890723

Observed

Cen 2000

Linear

Geometric

Parabolic

Mod Exp*

Gompertz*

Logistic*

Year

Population


Modified Exponential Curve (Y = c + abX ) The first of the Asymptotic Curves. Takes into account an upper or lower limit when computing projected values. The asymptote can be derived from local analysis or supplied by the model itself. Advantage: --Growth limit is introduced --Best fitting growth limit Disadvantage: --Much more complex calculations --Misleading Growth limit (high and low) Example:Yc = 114 - 64(0.75)XThe growth limit is 114. The curve takes into account the number of time periods and as X gets larger the closer you get to the Growth limit. When X = 0, Y = 50; when X = 2, Y = 78, etc. Evaluation: This curve largely depends upon the growth limit. If the limit is reasonable, then the curve can be a good one. Also, the ability to calculate the growth limit within the model is very useful.

Manatee County Modified Exponential Curve

YearIndexActual DataProjection1950034,704 38,242 1960169,168 65,630 1970297,115 100,535 19803148,442 145,022 19904211,707 201,722 20005264,002 273,987 20106 366,090 20207 483,476 20308 633,087 Total 825,138

Chart5

3470438242.4604285176

6916865629.5395714824

97115100534.821985702

148442145022.178014298

211707201722.044324758

264002273986.955675243

2010366089.772706579

2020483476.326520581

2030633087.418346787

Actual Data

Projection

Year

Population


Chapin Lin Reg


LINEAR REGRESSION



195034,70421,421

196069,16867,862

197097,115114,303

1980148,442160,743

1990211,707207,184

2000264,002253,625

2010300,066

2020346,507

2030392,948

Y Int-9034568.85714286

Slope4644.0971428571

Chapin Lin Reg

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


LR Eval



CURVE EVALUATION

FirstAbsolute


195034,70421,42113,28338.28%

196069,16834,46467,8621,3061.89%

197097,11527,947114,303(17,188)17.70%

1980148,44251,327160,743(12,301)8.29%

1990211,70763,265207,1844,5232.14%

2000264,00252,295253,62510,3773.93%

2010300,066

2020346,507

2030392,948

Mean Error-0

MAPE12.04%




CRV31.32

Chapin Geometric




195034,7044.54044.615841,281

196069,1684.83994.788561,454

197097,1154.98734.961391,484

1980148,4425.17165.1341136,189

1990211,7075.32575.3069202,741

2000264,0025.42165.4797301,813

20105.6525449,298

20205.8253668,855

20305.9981995,702

Y Int(29.080)

Slope0.0173

Chapin Geometric

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Geo Eval



CURVE EVALUATION



195034,7044.54041,281(6,577)18.95%

196069,1684.8400.30061,4547,71411.15%

197097,1154.9870.14791,4845,6315.80%

1980148,4425.1720.184136,18912,2538.25%

1990211,7075.3260.154202,7418,9664.24%

2000264,0025.4220.096301,813(37,811)14.32%

2010449,298

2020668,855

2030995,702

Mean Error(1,637)

MAPE10.45%




CRV43.1

Parabolic





195034,704-525625-17352086760035,136

196069,168-3981-20750462251265,118

197097,115-111-9711597115103,330

1980148,442111148442148442149,771

1990211,70739816351211905363204,441

2000264,00252562513200106600050267,341

20107492401338,471

20209816561417,830

20301112114641505,419

Totals82513827701414162543410241082




(X^2*Y)10241082



where:

N*SumX^2*Y =61446492

SumX^2*SumY =57759660

N*SumX^4 =8484

(SumX^2)^2)=4900

c =1028.692



where:

SumY =825138

c*SumX^2 =72008.438

N =6

a =125521.59


b = SumXY/SumX^2 =

where:

SumXY =1625434

SumX^2 =70

b =23220.49

EQUATION

Yc =a+b* X +c* X^2



193023,476-3981-7042821128423,381

194031,646-2416-6329212658432,696

195051,590-111-515905159049,606

196074,2250000074,112

1970103,047111103047103047106,215

1980148,6552416297310594620145,914

1990192,49339815774791732437193,208

2000416256248,099

2010525625310,586

20206361296380,668

Totals625,1320.028196792,5262,819,562



(XY)=792526

(X^2*Y)2819562



where:

N*SumX^2*Y =19736934

SumX^2*SumY =17503696

N*SumX^4 =1372

(SumX^2)^2)=784

c =3798.024



where:

SumY =625132

c*SumX^2 =106344.667

N =7

a =74112.48


b = SumXY/SumX^2 =

where:

SumXY =792526

SumX^2 =28

b =28304.50

EQUATION

Yc =a+b* X +c* X^2

Parabolic

00

00

00

00

00

00

00

00

00

Actual Data

Projections

Year

Pop


Par Eval

11

#REF!

#REF!

Year

Pop (in 000's)


Mod Exponential



CURVE EVALUATION

FirstSecondAbsolute


195034,70435,136(432)1.25%

196069,16834,46465,1184,0505.85%

197097,11527,947(6,517)103,330(6,215)6.40%

1980148,44251,32723,380149,771(1,329)0.90%

1990211,70763,26511,938204,4417,2663.43%

2000264,00252,295(10,970)267,341(3,339)1.26%

2010338,471

2020417,830

2030505,419

Mean Error0

MAPE3.18%




CRV360.0

ME Eval






1950034,70438,2423,538

1960169,16865,630(3,538)

1970297,115100,5353,420

19803148,442145,022(3,420)

19904211,707201,722(9,985)

20005264,002273,9879,985

20106366,090

20207483,476

20308633,087

Total825,138





n2N/3

b^n1.624(Sum 7-9) - (Sum 4-6) / (Sum 4-6) - (Sum 1-3)

b1.275

a99,765(Sum 4-6) - (Sum 1-3) X ((b-1)/(b^n-1)^2))


ME Eval

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Gompertz



CURVE EVALUATION



195034,70438,242(3,538)10.20%

196069,16834,46465,6303,5385.12%

197097,11527,9470.811100,535(3,420)3.52%

1980148,44251,3271.837145,0223,4202.30%

1990211,70763,2651.233201,7229,9854.72%

2000264,00252,2950.827273,987(9,985)3.78%

2010366,090

2020483,476

2030633,087

Mean Error-0

MAPE4.94%




CRV40.9

Gomp Eval







1950034,7044.54044.578837,9103205.8

1960169,1684.83994.801563,319-5849.1

1970297,1154.98734.995298,9061791.1

19803148,4425.17165.1636145,754-2688.1

19904211,7075.32575.3100204,186-7520.5

20005264,0025.42165.4373273,7269723.6

201065.5480353,169

202075.6442440,755

203085.7278534,378

Total825,138





n2

b^n0.756(Sum 7-9) - (Sum 4-6) / (Sum 4-6) - (Sum 1-3)

b0.869

a(2)(Sum 4-6) - (Sum 1-3) X ((b-1)/(b^n-1)^2))


Gomp Eval

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Logistic

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Log Eval



CURVE EVALUATION



195034,7044.5437,910(3,206)9.24%

196069,1684.840.299563,3195,8498.46%

197097,1154.990.14740.49298,906(1,791)1.84%

1980148,4425.170.18431.250145,7542,6881.81%

1990211,7075.330.15420.837204,1867,5213.55%

2000264,0025.420.09590.622273,726(9,724)3.68%

2010353,169

2020440,755

2030534,378

Mean Error223

MAPE4.76%




CRV41.5

Summary







1950034,7040.000028820.00002695937,0932388.7

1960169,1680.000014460.00001631361,300-7868.0

1970297,1150.000010300.00001024697,601486.0

19803148,4420.000006740.000006788147,321-1121.4

19904211,7070.000004720.000004817207,588-4119.0

20005264,0020.000003790.000003694270,7006698.1

201060.000003054327,434

202070.000002689371,848

203080.000002481403,002

Total




Total for All

n2

b^n0.325(Sum 7-9) - (Sum 4-6) / (Sum 4-6) - (Sum 1-3)

b0.570

a0.00002475(Sum 4-6) - (Sum 1-3) X ((b-1)/(b^n-1)^2))


Summary

00

00

00

00

00

00

00

00

00

Actual Data

Projection

Year

Population


Best Fitting



CURVE EVALUATION



195034,7040.000028837,093(2,389)6.88%

196069,1680.0000145(0.0000144)61,3007,86811.38%

197097,1150.0000103(0.0000042)0.29097,601(486)0.50%

1980148,4420.0000067(0.0000036)0.856147,3211,1210.76%

1990211,7070.0000047(0.0000020)0.565207,5884,1191.95%

2000264,0020.0000038(0.0000009)0.465270,700(6,698)2.54%

2010327,434

2020371,848

2030403,002

Mean Error589

MAPE4.00%




CRV43.6

All Curves


CURVE EVALUATIONS



CRVMEMAPE

Linear31.3-0.012.04%

Geometric43.1-1637.410.45%


Mod Exp*40.9-0.04.94%

Gompertz*41.5222.94.76%

Logistic*43.6589.24.00%





195034,70421,42141,28135,13638,24237,91037,093

196069,16867,86261,45465,11865,63063,31961,300

197097,115114,30391,484103,330100,53598,90697,601

1980148,442160,743136,189149,771145,022145,754147,321

1990211,707207,184202,741204,441201,722204,186207,588

2000264,002253,625301,813267,341273,987273,726270,700

2010300,066449,298338,471366,090353,169327,434

2020346,507668,855417,830483,476440,755371,848

2030392,948995,702505,419633,087534,378403,002





194031,646

195051,590

196074,225

1970103,047

1980148,655

1990192,493

2000239,452212,701294,911247,928267,138260,974248,287

2010244,823421,863310,244359,595338,489299,504

2020276,944603,465380,109481,649430,470344,748


316461940194019401940194019401940

515901950195019501950195019501950

742251960196019601960196019601960

1030471970197019701970197019701970

1486551980198019801980198019801980

1924931990199019901990199019901990

2000239452212701.2294911.358774184247928.2267138.355667061260973.538154462248286.77724716

20102010244822.685714286421863.275628557310244.257142857359595.413357568338488.682706828299503.897770785

20202020276944.171428571603464.797231922380108.957142857481649.03548955430469.572388299344748.009890723

Observed

Cen 2000

Linear

Geometric

Parabolic

Mod Exp*

Gompertz*

Logistic*

Year

Population


The Gompertz Curve (Y = c(a) exp (bX)) Describes a growth pattern that is initially quite slow, increases for a period and then tapers off. Like the Mod Exp curve, the upper limit can be assumed or derived by the model. Advantage: --Reflects very common growth patterns Disadvantages: --Getting even more complex --Misleading growth limit (limit can be high or low) Example:log Yc = 2.699 - 1.056(0.9221)XThe equation itself is tough to understand. When X = 0, Log Y = 1.64, so Y = 44.0 (via antilog calculation). Note: Antilog of 2.699 is 500 (the growth limit) Evaluation: A very useful curve that can be fitted to all kinds of growth patterns. However, as with the previous curve, using an assumed growth limit can be problematic unless it is reasonable and makes sense for the case at hand.

Manatee County Gompertz Curve

ActualLog ofLog ofYearIndexDataObs ValueProjProjection1950034,7044.54044.5788 37,910 1960169,1684.83994.8015 63,319 1970297,1154.98734.9952 98,906 19803148,4425.17165.1636 145,754 19904211,7075.32575.3100 204,186 20005264,0025.42165.4373 273,726 201065.5480 353,169 202075.6442 440,755 203085.7278 534,378 Total 825,138

Chart6

3470437909.8037616848

6916863318.8788601981

9711598906.0985733891

148442145753.851763785

211707204186.48000334

264002273725.622837936

2010353168.553557869

2020440755.018327915

2030534377.654903617

Actual Data

Projection

Year

Population


Chapin Lin Reg


LINEAR REGRESSION



195034,70421,421

196069,16867,862

197097,115114,303

1980148,442160,743

1990211,707207,184

2000264,002253,

extrapolation technique summarized

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