Leon County Curve Evaluations
27
Distict LINEAR REGRESSION Year Actual Data Year Inde Projections 1940 31,646 -5 19,972 1950 51,590 -3 52,094 1960 74,225 -1 84,215 1970 103,047 1 116,337 1980 148,655 3 148,458 1990 192,493 5 180,580 2000 7 212,701 2010 9 244,823 2020 11 276,944 Y Int 100276.00 Slope 16060.74 1930 - 50,000 100,000 150,000 200,000 250,000 Klosterm Pop (in 000's)
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Leon County Curve Evaluations
Transcript of Leon County Curve Evaluations
DistictLINEAR REGRESSION
Year Actual Data Year IndexProjections1940 31,646 -5 19,972 1950 51,590 -3 52,094 1960 74,225 -1 84,215 1970 103,047 1 116,337 1980 148,655 3 148,458 1990 192,493 5 180,580 2000 7 212,701 2010 9 244,823 2020 11 276,944
Y Int 100276.00Slope 16060.74
1930 1940 1950 1960 1970 1980 1990 2000 2010 -
50,000
100,000
150,000
200,000
250,000
Klosterman Linear Regression: Even
Year
Po
p (
in 0
00
's)
1930 1940 1950 1960 1970 1980 1990 2000 2010 -
50,000
100,000
150,000
200,000
250,000
Klosterman Linear Regression: Even
Year
Po
p (
in 0
00
's)
DistrictGEOMETRIC CURVE
Year Actual Data Log of Pop Log Proj Projection1940 31,646 4.5003 4.5368 34,420 1950 51,590 4.7126 4.6923 49,237 1960 74,225 4.8706 4.8478 70,432 1970 103,047 5.0130 5.0033 100,751 1980 148,655 5.1722 5.1587 144,122 1990 192,493 5.2844 5.3142 206,163 2000 5.4697 294,911 2010 5.6252 421,863 2020 5.7807 603,465
Y Int (25.626)Slope 0.0155
Year 1940 1950 1960 1970 1980 1990 2000 2010 -
100,000
200,000
300,000
400,000
500,000
600,000
700,000
Leon County Geometric Curve Projections
Actual Data
Projection
Year
Po
pu
lati
on
Year 1940 1950 1960 1970 1980 1990 2000 2010 -
100,000
200,000
300,000
400,000
500,000
600,000
700,000
Leon County Geometric Curve Projections
Actual Data
Projection
Year
Po
pu
lati
on
DistrictPARABOLIC CURVE
Even Number of ObservationsYear Actual Data Index Value Index Squared Index ^4
1940 31,646 -5 25 6251950 51,590 -3 9 811960 74,225 -1 1 11970 103,047 1 1 11980 148,655 3 9 811990 192,493 5 25 6252000 7 49 24012010 9 81 65612020 11 121 14641
Totals 601656 27 70 1414(SUM Y) (SUM X^2) (SUM X^4)
N= 6 (Number of Observations)(XY)= 1124252(X^2*Y) 7582952
CALCULATING PARAMETER c:
c = (N*SumX^2*Y - SumX^2*SumY)/(N*SumX^4 - (SumX^2)^2) =
where:
N*SumX^2*Y =
SumX^2*SumY =
N*SumX^4 =
(SumX^2)^2)=
CALCULATING PARAMETER a:
a = (SumY - c*SumX^2)/N =
where:
SumY =
c*SumX^2 =
N =
CALCULATING PARAMETER b:
b = SumXY/SumX^2 =
where:
SumXY =
SumX^2 =
EQUATIONYc = a + b
Odd Number of ObservationsYear Actual Data Index Value Index Squared Index ^4
1930 23,476 -3 9 811940 31,646 -2 4 161950 51,590 -1 1 11960 74,225 0 0 01970 103,047 1 1 11980 148,655 2 4 161990 192,493 3 9 812000 4 16 2562010 5 25 6252020 6 36 1296
Totals 625,132 - 28 196 (SUM Y) (SUM X^2) (SUM X^4)
N= 7 (Number of Observations)(XY)= 792526(X^2*Y) 2819562
CALCULATING PARAMETER c:
c = (N*SumX^2*Y - SumX^2*SumY)/(N*SumX^4 - (SumX^2)^2) =
where:
N*SumX^2*Y =
SumX^2*SumY =
N*SumX^4 =
(SumX^2)^2)=
CALCULATING PARAMETER a:
a = (SumY - c*SumX^2)/N =
where:
SumY =
c*SumX^2 =
N =
CALCULATING PARAMETER b:
b = SumXY/SumX^2 =
where:
SumXY =
SumX^2 =
EQUATIONYc = a + b
Product of Index Column Fand Observed Squared Projections
-158230 791150 32,553 -154770 464310 49,578
-74225 74225 74,150 103047 103047 106,272 445965 1337895 145,942 962465 4812325 193,161
247,928 310,244 380,109
1124252 7582952(SUM X*Y) (SUM X^2*Y)
Denotes different formulas due to Evennumber of observations
45497712
42115920
8484
4900
c = 943.580
601656
66050.625
6
a = 89267.56
1124252
70
b = 16060.74
* X + c * X^2
Year 1940 1950 1960 1970 1980 1990 2000 2010 -
50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
Leon County Parablic Curve
Actual DataProjections
YearP
op
(in
000's
)
Product of Index Column Fand Observed Squared Projections
-70428 211284 23,381 -63292 126584 32,696 -51590 51590 49,606
0 0 74,112 103047 103047 106,215 297310 594620 145,914 577479 1732437 193,208
248,099 310,586 380,668
792,526 2,819,562 (SUM X*Y) (SUM X^2*Y)
19736934
17503696
1372
784
c = 3798.024
625132
106344.667
7
a = 74112.48
792526
28
b = 28304.50
* X + c * X^2
Year 1940 1950 1960 1970 1980 1990 2000 2010 -
50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
Leon County Parablic Curve
Actual DataProjections
Year
Po
p (
in 0
00's
)
DistrictMODIFIED EXPONENTIAL CURVE
Number of Observation Divisible by ThreeYear Actual Data UL-Obs Log of UL-Obs Index
1940 31,646 468,354 5.6706 -51950 51,590 448,410 5.6517 -31960 74,225 425,775 5.6292 -11970 103,047 396,953 5.5987 11980 148,655 351,345 5.5457 31990 192,493 307,507 5.4879 52000 72010 92020 11
Total 601,656 33.584 Sum Log(c-Y)
N = 6UPPER LIMIT 500000Sum X^2 70 For Even # of Observation Formula is (N(N^2-1)/3)
Log a 5.5973 Sum Log(c-Y) / N
Log b -0.0180 SUM (UL-Obs*Index) / SUM X^2
a 395,633.38 b 0.9593
Product Error ofX^2 Col D * Col E Projection Estimate
25 -28.3529 13115.5 (18,530)9 -16.9550 51902.3 312 1 -5.6292 87599.2 13,374 1 5.5987 120452.3 17,405 9 16.6372 150688.3 2,033
25 27.4393 178515.6 (13,977)204126.0227696.3249388.9
70 (1.26186)SUM (UL-Obs*Index)
SUM (UL-Obs*Index) / SUM X^219
4019
5019
6019
7019
8019
9020
0020
1020
200.0
50000.0
100000.0
150000.0
200000.0
250000.0
300000.0
Leon County Pop ProjectionsModified Exponential Curve (UL =500,000)
Actual Data
Projection
Year
Po
pu
lati
on
1940
1950
1960
1970
1980
1990
2000
2010
2020
0.0
50000.0
100000.0
150000.0
200000.0
250000.0
300000.0
Leon County Pop ProjectionsModified Exponential Curve (UL =500,000)
Actual Data
Projection
Year
Po
pu
lati
on
LEON COUNTYGOMPERTZ CURVE (See Pages 228-235)
Number of Observation Divisible by ThreeLog Difference Log of
Year Actual Data Log of Obs (Log UL-Log Y) Log Diff Index Value1940 31,646 4.5003 1.1987 0.0787 -51950 51,590 4.7126 0.9864 -0.0059 -31960 74,225 4.8706 0.8284 -0.0817 -11970 103,047 5.0130 0.6859 -0.1637 11980 148,655 5.1722 0.5268 -0.2784 31990 192,493 5.2844 0.4146 -0.3824 52000 72010 92020 11
Total 601,656 (0.8335)Sum(log(log c-log a))
N 6Sum of X^2 70 UPPER LIMIT 500000Log of UL 5.69897
log (log a) -0.1389 Sum(log(log c-log a))/N
log b -0.0458 Sum(Xlog (log c - log y))/Sum of X^2
log a 0.726
b 0.8999
Product Log of Error ofIndex*Log Diff Projection Projection Estimate
-0.3935 4.469 29,425 2221.20.0178 4.703 50,417 1173.10.0817 4.892 77,980 -3755.1
-0.1637 5.045 111,016 -7969.2-0.8351 5.170 147,784 870.7-1.9121 5.270 186,317 6176.0
5.352 224,775 5.418 261,670 5.471 295,945
(3.2048)Sum(Xlog (log c - log y))
1940
1950
1960
1970
1980
1990
2000
2010
2020
-
50,000
100,000
150,000
200,000
250,000
300,000
350,000
Leon County ProjectionsGompertz Curve (UL = 500,000)
Actual Data
Projection
Year
Po
pu
lati
on
1940
1950
1960
1970
1980
1990
2000
2010
2020
-
50,000
100,000
150,000
200,000
250,000
300,000
350,000
Leon County ProjectionsGompertz Curve (UL = 500,000)
Actual Data
Projection
Year
Po
pu
lati
on
LEON COUNTYLOGISTIC CURVE (See Pages 236-242)
Number of Observation Divisible by ThreeReciprocal Reciprocal Log of
Year Actual Data of Observed Difference Rec. Diff1940 31,646 0.00003160 0.0000296 -4.5291950 51,590 0.00001938 0.0000174 -4.7601960 74,225 0.00001347 0.0000115 -4.9401970 103,047 0.00000970 0.0000077 -5.1131980 148,655 0.00000673 0.0000047 -5.3251990 192,493 0.00000519 0.0000032 -5.496200020102020
Total 601,656 (30.1631)Sum(log difference)
N 6Sum of X^2 70 UPPER LIMIT 500000Reciprocal of UL 0.000002
log (log a) -5.0272 Sum(log difference)/N
log b -0.0958 Sum(Log Product)/Sum of X^2
log a 0.00000939
b 0.8021
Index Product ReciprocalValue (X) (X LogY) of Projection Projection Error
-5 22.644 0.00003029 33,013 1367.3-3 14.280 0.00002020 49,501 -2089.3-1 4.940 0.00001371 72,936 -1288.71 -5.113 0.00000953 104,884 1837.03 -15.976 0.00000685 146,040 -2614.95 -27.478 0.00000512 195,361 2867.77 0.00000401 249,593 9 0.00000329 303,863
11 0.00000283 353,285 (6.7037)
Sum(log difference) Sum(Log product)
Sum(Log Product)/Sum of X^2
1940 1950 1960 1970 1980 1990 2000 2010 2020 -
50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
Leon County Pop ProjectionsLogistic Curve (UL = 500,000)
Actual Data
Projection
Year
Po
pu
lati
on
LEON COUNTY POPULATION PROJECTIONS, 2000-2020USING THE EXTRAPOLATION TECHNIQUE (BASE PERIOD 1940-1990)
Year Observed Linear Geometric Parabolic Mod Exp*1940 31646 19,972 34,420 32,553 32,883 1950 51590 52,094 49,237 49,578 50,353 1960 74225 84,215 70,432 74,150 73,414 1970 103047 116,337 100,751 106,272 103,858 1980 148655 148,458 144,122 145,942 144,047 1990 192493 180,580 206,163 193,161 197,101 2000 212,701 294,911 247,928 267,138 2010 244,823 421,863 310,244 359,595 2020 276,944 603,465 380,109 481,649
*Used "Best Fitting Curve"
1940
1950
1960
1970
1980
1990
2000
2010
2020
0
100,000
200,000
300,000
400,000
500,000
600,000
Leon County Population Projection 2000-2020Modified Exponential Curve, Base Period 1940-1990
Observed
Mod Exp*
Year
Po
pu
lati
on
Gompertz* Logistic* 32,800 32,589 49,774 49,265 73,185 73,044 104,512 105,414 145,276 146,804 196,970 195,688 260,974 248,287 338,489 299,504 430,470 344,748
*Used "Best Fitting Curve"
LEON COUNTY POPULATION PROJECTIONS, 2000-2020USING THE EXTRAPOLATION TECHNIQUE (BASE PERIOD 1940-1990)
Year Observed Cen 2000 Linear Geometric Parabolic1940 31,646 1950 51,590 1960 74,225 1970 103,047 1980 148,655 1990 192,493 2000 239,452 212,701 294,911 247,928 2010 244,823 421,863 310,244 2020 276,944 603,465 380,109
Mod Exp* Gompertz* Logistic*
267,138 260,974 248,287 359,595 338,489 299,504 481,649 430,470 344,748
