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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 12:55:19 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t1243969010vg8d95j5ghf2fiq.htm/, Retrieved Fri, 10 May 2024 10:41:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41376, Retrieved Fri, 10 May 2024 10:41:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Cijferreeks - Con...] [2009-06-02 18:55:19] [b527803d8be4913968ad45e628c1cc71] [Current]
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Dataseries X:
1686
1591
2304
1712
1471
1377
1966
2453
1984
2596
4087
5179
1530
1523
1633
1976
1170
1480
1781
2472
1981
2273
3857
4551
1510
1329
1518
1790
1537
1449
1954
1897
1706
2514
3593
4524
1609
1638
2030
1375
1320
1245
1600
2298
2191
2511
3440
4923
1609
1435
2061
1789
1567
1404
1597
3159
1759
2504
4273
5274
1771
1682
1846
1589
1896
1379
1645
2512
1771
3727
4388
5434
1606
1523
1577
1605
1765
1403
2584
3318
1562
2349
3987
5891
1389
1442
1548
1935
1518
1250
1847
1930
2638
3114
4405
7242
1853
1779
2108
2336
1728
1661
2230
1645
2421
3740
4988
6757
1757
1394
1982
1650
1654
1406
1971
1968
2608
3845
4514
6694
1720
1321
1859
1628
1615
1457
1899
1605
2424
3116
4286
6047
1902
2049
1874
1279
1432
1540
2214
1857
2408
3252
3627
6153
1577
1667
1993
1997
1783
1625
2076
1773
2377
3088
4096
6119
1494
1564
1898
2121
1831
1515
2048
2795
1749
3339
4227
6410
1197
1968
1720
1725
1674
1693
2031
1495
2968
3385
3729
5999
1070
1402
1897
1862
1670
1688
2031




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41376&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41376&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41376&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0513226259983897
beta0.0966756503497419
gamma0.289021407755364

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0513226259983897 \tabularnewline
beta & 0.0966756503497419 \tabularnewline
gamma & 0.289021407755364 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41376&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.0513226259983897[/C][/ROW]
[ROW][C]beta[/C][C]0.0966756503497419[/C][/ROW]
[ROW][C]gamma[/C][C]0.289021407755364[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41376&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41376&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0513226259983897
beta0.0966756503497419
gamma0.289021407755364







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315301571.36956742168-41.3695674216813
1415231559.41355733058-36.4135573305755
1516331661.44277370245-28.4427737024482
1619762010.62382343132-34.6238234313171
1711701195.53270921403-25.532709214026
1814801527.04041924606-47.0404192460585
1917811887.25217515444-106.252175154443
2024722343.73790116042128.262098839582
2119811915.6149718191865.3850281808197
2222732515.90243214176-242.902432141756
2338573920.75558687946-63.7555868794584
2445514952.19395853118-401.193958531177
2515101439.1870515459370.8129484540675
2613291432.76298315525-103.762983155249
2715181522.51441955630-4.51441955629775
2817901840.53881135034-50.5388113503438
2915371090.56603322183446.433966778171
3014491420.6350007973028.3649992026976
3119541749.02749779951204.972502200494
3218972262.81532258757-365.815322587573
3317061819.69896462105-113.69896462105
3425142293.30509548857220.694904511431
3535933695.08334293361-102.083342933606
3645244585.05251444474-61.0525144447438
3716091387.84395244362221.156047556384
3816381346.19070221032291.809297789679
3920301485.19299204736544.807007952642
4013751826.84678259232-451.846782592321
4113201201.96861097173118.031389028272
4212451399.87514559808-154.875145598079
4316001760.46891453843-160.46891453843
4422982087.95634566304210.043654336961
4521911754.87500961160436.124990388398
4625112355.47328598542155.526714014577
4734403678.14977409732-238.149774097320
4849234589.76924873895333.230751261051
4916091467.12279329130141.877206708697
5014351444.90491821398-9.90491821398382
5120611639.68583640788421.314163592121
5217891703.5280605600785.4719394399292
5315671259.27740092053307.722599079470
5414041401.005905890442.99409410955582
5515971790.57274270083-193.572742700826
5631592246.79639245545912.203607544546
5717592004.52103938439-245.521039384386
5825042529.08187679151-25.0818767915098
5942733810.32457662363462.675423376371
6052745008.43781085013265.562189149866
6117711617.23043546127153.769564538729
6216821556.00217237582125.997827624182
6318461910.29634476034-64.2963447603395
6415891860.14889917992-271.148899179915
6518961435.51995975500460.480040244997
6613791509.12651646586-130.126516465859
6716451866.42217942539-221.422179425388
6825122682.3656637486-170.365663748599
6917712036.14989717429-265.149897174291
7037272651.070298196241075.92970180376
7143884234.93388676277153.066113237232
7254345451.98241944138-17.9824194413832
7316061777.73118049791-171.731180497907
7415231688.22924153534-165.229241535336
7515771990.02633091137-413.026330911373
7616051858.16304094875-253.163040948755
7717651622.42739289942142.572607100581
7814031511.17084789707-108.170847897075
7925841849.24228707975734.757712920249
8033182772.45776661536545.542233384639
8115622095.90533819581-533.905338195808
8223493121.98476929198-772.984769291976
8339874382.89146049274-395.891460492743
8458915530.86930769623360.130692303774
8513891759.01873624210-370.018736242102
8614421655.20105760569-213.201057605691
8715481881.01759002865-333.017590028652
8819351791.01264162245143.987358377548
8915181679.36240015113-161.362400151134
9012501479.27854465245-229.278544652452
9118472028.45850166658-181.458501666584
9219302808.12293876142-878.122938761418
9326381809.55138663845828.448613361552
9431142788.75676695808325.243233041916
9544054165.79071306925239.20928693075
9672425517.720192704661724.27980729534
9718531642.87618284972210.123817150283
9817791612.43132140277166.568678597235
9921081832.17691824364275.823081756362
10023361913.25538826244422.744611737562
10117281728.48274969031-0.482749690310129
10216611511.36252751633149.637472483672
10322302152.1907018882777.8092981117297
10416452824.74458434354-1179.74458434354
10524212239.81056904462181.189430955378
10637403125.4009086972614.5990913028
10749884635.28849398666352.711506013341
10867576590.43627772738166.563722272623
10917571851.26421649304-94.2642164930446
11013941792.77004687517-398.770046875165
11119822029.44603515612-47.446035156117
11216502138.31674096811-488.316740968107
11316541776.79978277586-122.799782775855
11414061585.86604854665-179.866048546651
11519712188.58427687695-217.584276876952
11619682483.44085859961-515.44085859961
11726082296.99085634624311.009143653760
11838453302.63442170321542.365578296792
11945144724.08581106525-210.085811065246
12066946560.6124596845133.387540315506
12117201797.56528271134-77.565282711344
12213211651.26638180696-330.266381806965
12318591974.72876687268-115.728766872676
12416281950.68045521917-322.680455219167
12516151697.38990829453-82.3899082945263
12614571492.69848121522-35.6984812152232
12718992071.86679540881-172.86679540881
12816052273.68483240167-668.684832401673
12924242295.64718499123128.352815008765
13031163299.83911495731-183.839114957309
13142864392.12206144793-106.122061447928
13260476186.82230988632-139.822309886315
13319021653.94483594882248.055164051182
13420491461.01216917940587.987830820604
13518741874.95322391386-0.953223913864122
13612791800.52637332201-521.526373322009
13714321607.41138442942-175.411384429416
13815401416.53574035029123.464259649714
13922141942.63425230185271.365747698154
14018572026.50256677048-169.502566770484
14124082290.03682171637117.963178283627
14232523195.4216629922656.5783370077388
14336274313.37392652558-686.373926525584
14461536041.36336182473111.636638175273
14515771696.80043384051-119.800433840508
14616671577.7422739536289.2577260463793
14719931791.93181604168201.06818395832
14819971589.46956603025407.53043396975
14917831541.89180518140241.108194818598
15016251458.08910228096166.91089771904
15120762036.3192443224639.6807556775368
15217731991.75687219657-218.756872196566
15323772338.4145901403138.5854098596942
15430883234.15033715064-146.150337150636
15540964147.42124307446-51.4212430744556
15661196168.93311760892-49.9331176089154
15714941692.16775339754-198.167753397543
15815641629.08203605577-65.0820360557659
15918981871.7075697224326.2924302775675
16021211716.17913443011404.820865569887
16118311623.09644518333207.90355481667
16215151517.45368394950-2.4536839494956
16320482054.60361080717-6.60361080717075
16427951936.68703788415858.31296211585
16517492429.72128285821-680.721282858206
16633393258.3244195149580.6755804850477
16742274239.46805951502-12.4680595150185
16864106328.1902910794681.8097089205357
16911971688.65155391750-491.651553917496
17019681648.42787070931319.572129290693
17117201949.84385869242-229.843858692416
17217251884.99067625603-159.990676256032
17316741705.97102352283-31.9710235228338
17416931527.87608325712165.123916742876
17520312079.12161922621-48.1216192262145
17614952191.77632527178-696.776325271781
17729682170.98314099033797.01685900967
17833853283.36275573104101.637244268963
17937294237.95546307917-508.95546307917
18059996306.78823787491-307.788237874912
18110701533.69189439295-463.691894392953
18214021710.98349019132-308.983490191325
18318971818.1827681656678.8172318343404
18418621784.0927968664777.9072031335277
18516701652.1201980766117.8798019233927
18616881530.36178913519157.638210864809
18720312005.4364825625625.5635174374422

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1530 & 1571.36956742168 & -41.3695674216813 \tabularnewline
14 & 1523 & 1559.41355733058 & -36.4135573305755 \tabularnewline
15 & 1633 & 1661.44277370245 & -28.4427737024482 \tabularnewline
16 & 1976 & 2010.62382343132 & -34.6238234313171 \tabularnewline
17 & 1170 & 1195.53270921403 & -25.532709214026 \tabularnewline
18 & 1480 & 1527.04041924606 & -47.0404192460585 \tabularnewline
19 & 1781 & 1887.25217515444 & -106.252175154443 \tabularnewline
20 & 2472 & 2343.73790116042 & 128.262098839582 \tabularnewline
21 & 1981 & 1915.61497181918 & 65.3850281808197 \tabularnewline
22 & 2273 & 2515.90243214176 & -242.902432141756 \tabularnewline
23 & 3857 & 3920.75558687946 & -63.7555868794584 \tabularnewline
24 & 4551 & 4952.19395853118 & -401.193958531177 \tabularnewline
25 & 1510 & 1439.18705154593 & 70.8129484540675 \tabularnewline
26 & 1329 & 1432.76298315525 & -103.762983155249 \tabularnewline
27 & 1518 & 1522.51441955630 & -4.51441955629775 \tabularnewline
28 & 1790 & 1840.53881135034 & -50.5388113503438 \tabularnewline
29 & 1537 & 1090.56603322183 & 446.433966778171 \tabularnewline
30 & 1449 & 1420.63500079730 & 28.3649992026976 \tabularnewline
31 & 1954 & 1749.02749779951 & 204.972502200494 \tabularnewline
32 & 1897 & 2262.81532258757 & -365.815322587573 \tabularnewline
33 & 1706 & 1819.69896462105 & -113.69896462105 \tabularnewline
34 & 2514 & 2293.30509548857 & 220.694904511431 \tabularnewline
35 & 3593 & 3695.08334293361 & -102.083342933606 \tabularnewline
36 & 4524 & 4585.05251444474 & -61.0525144447438 \tabularnewline
37 & 1609 & 1387.84395244362 & 221.156047556384 \tabularnewline
38 & 1638 & 1346.19070221032 & 291.809297789679 \tabularnewline
39 & 2030 & 1485.19299204736 & 544.807007952642 \tabularnewline
40 & 1375 & 1826.84678259232 & -451.846782592321 \tabularnewline
41 & 1320 & 1201.96861097173 & 118.031389028272 \tabularnewline
42 & 1245 & 1399.87514559808 & -154.875145598079 \tabularnewline
43 & 1600 & 1760.46891453843 & -160.46891453843 \tabularnewline
44 & 2298 & 2087.95634566304 & 210.043654336961 \tabularnewline
45 & 2191 & 1754.87500961160 & 436.124990388398 \tabularnewline
46 & 2511 & 2355.47328598542 & 155.526714014577 \tabularnewline
47 & 3440 & 3678.14977409732 & -238.149774097320 \tabularnewline
48 & 4923 & 4589.76924873895 & 333.230751261051 \tabularnewline
49 & 1609 & 1467.12279329130 & 141.877206708697 \tabularnewline
50 & 1435 & 1444.90491821398 & -9.90491821398382 \tabularnewline
51 & 2061 & 1639.68583640788 & 421.314163592121 \tabularnewline
52 & 1789 & 1703.52806056007 & 85.4719394399292 \tabularnewline
53 & 1567 & 1259.27740092053 & 307.722599079470 \tabularnewline
54 & 1404 & 1401.00590589044 & 2.99409410955582 \tabularnewline
55 & 1597 & 1790.57274270083 & -193.572742700826 \tabularnewline
56 & 3159 & 2246.79639245545 & 912.203607544546 \tabularnewline
57 & 1759 & 2004.52103938439 & -245.521039384386 \tabularnewline
58 & 2504 & 2529.08187679151 & -25.0818767915098 \tabularnewline
59 & 4273 & 3810.32457662363 & 462.675423376371 \tabularnewline
60 & 5274 & 5008.43781085013 & 265.562189149866 \tabularnewline
61 & 1771 & 1617.23043546127 & 153.769564538729 \tabularnewline
62 & 1682 & 1556.00217237582 & 125.997827624182 \tabularnewline
63 & 1846 & 1910.29634476034 & -64.2963447603395 \tabularnewline
64 & 1589 & 1860.14889917992 & -271.148899179915 \tabularnewline
65 & 1896 & 1435.51995975500 & 460.480040244997 \tabularnewline
66 & 1379 & 1509.12651646586 & -130.126516465859 \tabularnewline
67 & 1645 & 1866.42217942539 & -221.422179425388 \tabularnewline
68 & 2512 & 2682.3656637486 & -170.365663748599 \tabularnewline
69 & 1771 & 2036.14989717429 & -265.149897174291 \tabularnewline
70 & 3727 & 2651.07029819624 & 1075.92970180376 \tabularnewline
71 & 4388 & 4234.93388676277 & 153.066113237232 \tabularnewline
72 & 5434 & 5451.98241944138 & -17.9824194413832 \tabularnewline
73 & 1606 & 1777.73118049791 & -171.731180497907 \tabularnewline
74 & 1523 & 1688.22924153534 & -165.229241535336 \tabularnewline
75 & 1577 & 1990.02633091137 & -413.026330911373 \tabularnewline
76 & 1605 & 1858.16304094875 & -253.163040948755 \tabularnewline
77 & 1765 & 1622.42739289942 & 142.572607100581 \tabularnewline
78 & 1403 & 1511.17084789707 & -108.170847897075 \tabularnewline
79 & 2584 & 1849.24228707975 & 734.757712920249 \tabularnewline
80 & 3318 & 2772.45776661536 & 545.542233384639 \tabularnewline
81 & 1562 & 2095.90533819581 & -533.905338195808 \tabularnewline
82 & 2349 & 3121.98476929198 & -772.984769291976 \tabularnewline
83 & 3987 & 4382.89146049274 & -395.891460492743 \tabularnewline
84 & 5891 & 5530.86930769623 & 360.130692303774 \tabularnewline
85 & 1389 & 1759.01873624210 & -370.018736242102 \tabularnewline
86 & 1442 & 1655.20105760569 & -213.201057605691 \tabularnewline
87 & 1548 & 1881.01759002865 & -333.017590028652 \tabularnewline
88 & 1935 & 1791.01264162245 & 143.987358377548 \tabularnewline
89 & 1518 & 1679.36240015113 & -161.362400151134 \tabularnewline
90 & 1250 & 1479.27854465245 & -229.278544652452 \tabularnewline
91 & 1847 & 2028.45850166658 & -181.458501666584 \tabularnewline
92 & 1930 & 2808.12293876142 & -878.122938761418 \tabularnewline
93 & 2638 & 1809.55138663845 & 828.448613361552 \tabularnewline
94 & 3114 & 2788.75676695808 & 325.243233041916 \tabularnewline
95 & 4405 & 4165.79071306925 & 239.20928693075 \tabularnewline
96 & 7242 & 5517.72019270466 & 1724.27980729534 \tabularnewline
97 & 1853 & 1642.87618284972 & 210.123817150283 \tabularnewline
98 & 1779 & 1612.43132140277 & 166.568678597235 \tabularnewline
99 & 2108 & 1832.17691824364 & 275.823081756362 \tabularnewline
100 & 2336 & 1913.25538826244 & 422.744611737562 \tabularnewline
101 & 1728 & 1728.48274969031 & -0.482749690310129 \tabularnewline
102 & 1661 & 1511.36252751633 & 149.637472483672 \tabularnewline
103 & 2230 & 2152.19070188827 & 77.8092981117297 \tabularnewline
104 & 1645 & 2824.74458434354 & -1179.74458434354 \tabularnewline
105 & 2421 & 2239.81056904462 & 181.189430955378 \tabularnewline
106 & 3740 & 3125.4009086972 & 614.5990913028 \tabularnewline
107 & 4988 & 4635.28849398666 & 352.711506013341 \tabularnewline
108 & 6757 & 6590.43627772738 & 166.563722272623 \tabularnewline
109 & 1757 & 1851.26421649304 & -94.2642164930446 \tabularnewline
110 & 1394 & 1792.77004687517 & -398.770046875165 \tabularnewline
111 & 1982 & 2029.44603515612 & -47.446035156117 \tabularnewline
112 & 1650 & 2138.31674096811 & -488.316740968107 \tabularnewline
113 & 1654 & 1776.79978277586 & -122.799782775855 \tabularnewline
114 & 1406 & 1585.86604854665 & -179.866048546651 \tabularnewline
115 & 1971 & 2188.58427687695 & -217.584276876952 \tabularnewline
116 & 1968 & 2483.44085859961 & -515.44085859961 \tabularnewline
117 & 2608 & 2296.99085634624 & 311.009143653760 \tabularnewline
118 & 3845 & 3302.63442170321 & 542.365578296792 \tabularnewline
119 & 4514 & 4724.08581106525 & -210.085811065246 \tabularnewline
120 & 6694 & 6560.6124596845 & 133.387540315506 \tabularnewline
121 & 1720 & 1797.56528271134 & -77.565282711344 \tabularnewline
122 & 1321 & 1651.26638180696 & -330.266381806965 \tabularnewline
123 & 1859 & 1974.72876687268 & -115.728766872676 \tabularnewline
124 & 1628 & 1950.68045521917 & -322.680455219167 \tabularnewline
125 & 1615 & 1697.38990829453 & -82.3899082945263 \tabularnewline
126 & 1457 & 1492.69848121522 & -35.6984812152232 \tabularnewline
127 & 1899 & 2071.86679540881 & -172.86679540881 \tabularnewline
128 & 1605 & 2273.68483240167 & -668.684832401673 \tabularnewline
129 & 2424 & 2295.64718499123 & 128.352815008765 \tabularnewline
130 & 3116 & 3299.83911495731 & -183.839114957309 \tabularnewline
131 & 4286 & 4392.12206144793 & -106.122061447928 \tabularnewline
132 & 6047 & 6186.82230988632 & -139.822309886315 \tabularnewline
133 & 1902 & 1653.94483594882 & 248.055164051182 \tabularnewline
134 & 2049 & 1461.01216917940 & 587.987830820604 \tabularnewline
135 & 1874 & 1874.95322391386 & -0.953223913864122 \tabularnewline
136 & 1279 & 1800.52637332201 & -521.526373322009 \tabularnewline
137 & 1432 & 1607.41138442942 & -175.411384429416 \tabularnewline
138 & 1540 & 1416.53574035029 & 123.464259649714 \tabularnewline
139 & 2214 & 1942.63425230185 & 271.365747698154 \tabularnewline
140 & 1857 & 2026.50256677048 & -169.502566770484 \tabularnewline
141 & 2408 & 2290.03682171637 & 117.963178283627 \tabularnewline
142 & 3252 & 3195.42166299226 & 56.5783370077388 \tabularnewline
143 & 3627 & 4313.37392652558 & -686.373926525584 \tabularnewline
144 & 6153 & 6041.36336182473 & 111.636638175273 \tabularnewline
145 & 1577 & 1696.80043384051 & -119.800433840508 \tabularnewline
146 & 1667 & 1577.74227395362 & 89.2577260463793 \tabularnewline
147 & 1993 & 1791.93181604168 & 201.06818395832 \tabularnewline
148 & 1997 & 1589.46956603025 & 407.53043396975 \tabularnewline
149 & 1783 & 1541.89180518140 & 241.108194818598 \tabularnewline
150 & 1625 & 1458.08910228096 & 166.91089771904 \tabularnewline
151 & 2076 & 2036.31924432246 & 39.6807556775368 \tabularnewline
152 & 1773 & 1991.75687219657 & -218.756872196566 \tabularnewline
153 & 2377 & 2338.41459014031 & 38.5854098596942 \tabularnewline
154 & 3088 & 3234.15033715064 & -146.150337150636 \tabularnewline
155 & 4096 & 4147.42124307446 & -51.4212430744556 \tabularnewline
156 & 6119 & 6168.93311760892 & -49.9331176089154 \tabularnewline
157 & 1494 & 1692.16775339754 & -198.167753397543 \tabularnewline
158 & 1564 & 1629.08203605577 & -65.0820360557659 \tabularnewline
159 & 1898 & 1871.70756972243 & 26.2924302775675 \tabularnewline
160 & 2121 & 1716.17913443011 & 404.820865569887 \tabularnewline
161 & 1831 & 1623.09644518333 & 207.90355481667 \tabularnewline
162 & 1515 & 1517.45368394950 & -2.4536839494956 \tabularnewline
163 & 2048 & 2054.60361080717 & -6.60361080717075 \tabularnewline
164 & 2795 & 1936.68703788415 & 858.31296211585 \tabularnewline
165 & 1749 & 2429.72128285821 & -680.721282858206 \tabularnewline
166 & 3339 & 3258.32441951495 & 80.6755804850477 \tabularnewline
167 & 4227 & 4239.46805951502 & -12.4680595150185 \tabularnewline
168 & 6410 & 6328.19029107946 & 81.8097089205357 \tabularnewline
169 & 1197 & 1688.65155391750 & -491.651553917496 \tabularnewline
170 & 1968 & 1648.42787070931 & 319.572129290693 \tabularnewline
171 & 1720 & 1949.84385869242 & -229.843858692416 \tabularnewline
172 & 1725 & 1884.99067625603 & -159.990676256032 \tabularnewline
173 & 1674 & 1705.97102352283 & -31.9710235228338 \tabularnewline
174 & 1693 & 1527.87608325712 & 165.123916742876 \tabularnewline
175 & 2031 & 2079.12161922621 & -48.1216192262145 \tabularnewline
176 & 1495 & 2191.77632527178 & -696.776325271781 \tabularnewline
177 & 2968 & 2170.98314099033 & 797.01685900967 \tabularnewline
178 & 3385 & 3283.36275573104 & 101.637244268963 \tabularnewline
179 & 3729 & 4237.95546307917 & -508.95546307917 \tabularnewline
180 & 5999 & 6306.78823787491 & -307.788237874912 \tabularnewline
181 & 1070 & 1533.69189439295 & -463.691894392953 \tabularnewline
182 & 1402 & 1710.98349019132 & -308.983490191325 \tabularnewline
183 & 1897 & 1818.18276816566 & 78.8172318343404 \tabularnewline
184 & 1862 & 1784.09279686647 & 77.9072031335277 \tabularnewline
185 & 1670 & 1652.12019807661 & 17.8798019233927 \tabularnewline
186 & 1688 & 1530.36178913519 & 157.638210864809 \tabularnewline
187 & 2031 & 2005.43648256256 & 25.5635174374422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41376&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]1530[/C][C]1571.36956742168[/C][C]-41.3695674216813[/C][/ROW]
[ROW][C]14[/C][C]1523[/C][C]1559.41355733058[/C][C]-36.4135573305755[/C][/ROW]
[ROW][C]15[/C][C]1633[/C][C]1661.44277370245[/C][C]-28.4427737024482[/C][/ROW]
[ROW][C]16[/C][C]1976[/C][C]2010.62382343132[/C][C]-34.6238234313171[/C][/ROW]
[ROW][C]17[/C][C]1170[/C][C]1195.53270921403[/C][C]-25.532709214026[/C][/ROW]
[ROW][C]18[/C][C]1480[/C][C]1527.04041924606[/C][C]-47.0404192460585[/C][/ROW]
[ROW][C]19[/C][C]1781[/C][C]1887.25217515444[/C][C]-106.252175154443[/C][/ROW]
[ROW][C]20[/C][C]2472[/C][C]2343.73790116042[/C][C]128.262098839582[/C][/ROW]
[ROW][C]21[/C][C]1981[/C][C]1915.61497181918[/C][C]65.3850281808197[/C][/ROW]
[ROW][C]22[/C][C]2273[/C][C]2515.90243214176[/C][C]-242.902432141756[/C][/ROW]
[ROW][C]23[/C][C]3857[/C][C]3920.75558687946[/C][C]-63.7555868794584[/C][/ROW]
[ROW][C]24[/C][C]4551[/C][C]4952.19395853118[/C][C]-401.193958531177[/C][/ROW]
[ROW][C]25[/C][C]1510[/C][C]1439.18705154593[/C][C]70.8129484540675[/C][/ROW]
[ROW][C]26[/C][C]1329[/C][C]1432.76298315525[/C][C]-103.762983155249[/C][/ROW]
[ROW][C]27[/C][C]1518[/C][C]1522.51441955630[/C][C]-4.51441955629775[/C][/ROW]
[ROW][C]28[/C][C]1790[/C][C]1840.53881135034[/C][C]-50.5388113503438[/C][/ROW]
[ROW][C]29[/C][C]1537[/C][C]1090.56603322183[/C][C]446.433966778171[/C][/ROW]
[ROW][C]30[/C][C]1449[/C][C]1420.63500079730[/C][C]28.3649992026976[/C][/ROW]
[ROW][C]31[/C][C]1954[/C][C]1749.02749779951[/C][C]204.972502200494[/C][/ROW]
[ROW][C]32[/C][C]1897[/C][C]2262.81532258757[/C][C]-365.815322587573[/C][/ROW]
[ROW][C]33[/C][C]1706[/C][C]1819.69896462105[/C][C]-113.69896462105[/C][/ROW]
[ROW][C]34[/C][C]2514[/C][C]2293.30509548857[/C][C]220.694904511431[/C][/ROW]
[ROW][C]35[/C][C]3593[/C][C]3695.08334293361[/C][C]-102.083342933606[/C][/ROW]
[ROW][C]36[/C][C]4524[/C][C]4585.05251444474[/C][C]-61.0525144447438[/C][/ROW]
[ROW][C]37[/C][C]1609[/C][C]1387.84395244362[/C][C]221.156047556384[/C][/ROW]
[ROW][C]38[/C][C]1638[/C][C]1346.19070221032[/C][C]291.809297789679[/C][/ROW]
[ROW][C]39[/C][C]2030[/C][C]1485.19299204736[/C][C]544.807007952642[/C][/ROW]
[ROW][C]40[/C][C]1375[/C][C]1826.84678259232[/C][C]-451.846782592321[/C][/ROW]
[ROW][C]41[/C][C]1320[/C][C]1201.96861097173[/C][C]118.031389028272[/C][/ROW]
[ROW][C]42[/C][C]1245[/C][C]1399.87514559808[/C][C]-154.875145598079[/C][/ROW]
[ROW][C]43[/C][C]1600[/C][C]1760.46891453843[/C][C]-160.46891453843[/C][/ROW]
[ROW][C]44[/C][C]2298[/C][C]2087.95634566304[/C][C]210.043654336961[/C][/ROW]
[ROW][C]45[/C][C]2191[/C][C]1754.87500961160[/C][C]436.124990388398[/C][/ROW]
[ROW][C]46[/C][C]2511[/C][C]2355.47328598542[/C][C]155.526714014577[/C][/ROW]
[ROW][C]47[/C][C]3440[/C][C]3678.14977409732[/C][C]-238.149774097320[/C][/ROW]
[ROW][C]48[/C][C]4923[/C][C]4589.76924873895[/C][C]333.230751261051[/C][/ROW]
[ROW][C]49[/C][C]1609[/C][C]1467.12279329130[/C][C]141.877206708697[/C][/ROW]
[ROW][C]50[/C][C]1435[/C][C]1444.90491821398[/C][C]-9.90491821398382[/C][/ROW]
[ROW][C]51[/C][C]2061[/C][C]1639.68583640788[/C][C]421.314163592121[/C][/ROW]
[ROW][C]52[/C][C]1789[/C][C]1703.52806056007[/C][C]85.4719394399292[/C][/ROW]
[ROW][C]53[/C][C]1567[/C][C]1259.27740092053[/C][C]307.722599079470[/C][/ROW]
[ROW][C]54[/C][C]1404[/C][C]1401.00590589044[/C][C]2.99409410955582[/C][/ROW]
[ROW][C]55[/C][C]1597[/C][C]1790.57274270083[/C][C]-193.572742700826[/C][/ROW]
[ROW][C]56[/C][C]3159[/C][C]2246.79639245545[/C][C]912.203607544546[/C][/ROW]
[ROW][C]57[/C][C]1759[/C][C]2004.52103938439[/C][C]-245.521039384386[/C][/ROW]
[ROW][C]58[/C][C]2504[/C][C]2529.08187679151[/C][C]-25.0818767915098[/C][/ROW]
[ROW][C]59[/C][C]4273[/C][C]3810.32457662363[/C][C]462.675423376371[/C][/ROW]
[ROW][C]60[/C][C]5274[/C][C]5008.43781085013[/C][C]265.562189149866[/C][/ROW]
[ROW][C]61[/C][C]1771[/C][C]1617.23043546127[/C][C]153.769564538729[/C][/ROW]
[ROW][C]62[/C][C]1682[/C][C]1556.00217237582[/C][C]125.997827624182[/C][/ROW]
[ROW][C]63[/C][C]1846[/C][C]1910.29634476034[/C][C]-64.2963447603395[/C][/ROW]
[ROW][C]64[/C][C]1589[/C][C]1860.14889917992[/C][C]-271.148899179915[/C][/ROW]
[ROW][C]65[/C][C]1896[/C][C]1435.51995975500[/C][C]460.480040244997[/C][/ROW]
[ROW][C]66[/C][C]1379[/C][C]1509.12651646586[/C][C]-130.126516465859[/C][/ROW]
[ROW][C]67[/C][C]1645[/C][C]1866.42217942539[/C][C]-221.422179425388[/C][/ROW]
[ROW][C]68[/C][C]2512[/C][C]2682.3656637486[/C][C]-170.365663748599[/C][/ROW]
[ROW][C]69[/C][C]1771[/C][C]2036.14989717429[/C][C]-265.149897174291[/C][/ROW]
[ROW][C]70[/C][C]3727[/C][C]2651.07029819624[/C][C]1075.92970180376[/C][/ROW]
[ROW][C]71[/C][C]4388[/C][C]4234.93388676277[/C][C]153.066113237232[/C][/ROW]
[ROW][C]72[/C][C]5434[/C][C]5451.98241944138[/C][C]-17.9824194413832[/C][/ROW]
[ROW][C]73[/C][C]1606[/C][C]1777.73118049791[/C][C]-171.731180497907[/C][/ROW]
[ROW][C]74[/C][C]1523[/C][C]1688.22924153534[/C][C]-165.229241535336[/C][/ROW]
[ROW][C]75[/C][C]1577[/C][C]1990.02633091137[/C][C]-413.026330911373[/C][/ROW]
[ROW][C]76[/C][C]1605[/C][C]1858.16304094875[/C][C]-253.163040948755[/C][/ROW]
[ROW][C]77[/C][C]1765[/C][C]1622.42739289942[/C][C]142.572607100581[/C][/ROW]
[ROW][C]78[/C][C]1403[/C][C]1511.17084789707[/C][C]-108.170847897075[/C][/ROW]
[ROW][C]79[/C][C]2584[/C][C]1849.24228707975[/C][C]734.757712920249[/C][/ROW]
[ROW][C]80[/C][C]3318[/C][C]2772.45776661536[/C][C]545.542233384639[/C][/ROW]
[ROW][C]81[/C][C]1562[/C][C]2095.90533819581[/C][C]-533.905338195808[/C][/ROW]
[ROW][C]82[/C][C]2349[/C][C]3121.98476929198[/C][C]-772.984769291976[/C][/ROW]
[ROW][C]83[/C][C]3987[/C][C]4382.89146049274[/C][C]-395.891460492743[/C][/ROW]
[ROW][C]84[/C][C]5891[/C][C]5530.86930769623[/C][C]360.130692303774[/C][/ROW]
[ROW][C]85[/C][C]1389[/C][C]1759.01873624210[/C][C]-370.018736242102[/C][/ROW]
[ROW][C]86[/C][C]1442[/C][C]1655.20105760569[/C][C]-213.201057605691[/C][/ROW]
[ROW][C]87[/C][C]1548[/C][C]1881.01759002865[/C][C]-333.017590028652[/C][/ROW]
[ROW][C]88[/C][C]1935[/C][C]1791.01264162245[/C][C]143.987358377548[/C][/ROW]
[ROW][C]89[/C][C]1518[/C][C]1679.36240015113[/C][C]-161.362400151134[/C][/ROW]
[ROW][C]90[/C][C]1250[/C][C]1479.27854465245[/C][C]-229.278544652452[/C][/ROW]
[ROW][C]91[/C][C]1847[/C][C]2028.45850166658[/C][C]-181.458501666584[/C][/ROW]
[ROW][C]92[/C][C]1930[/C][C]2808.12293876142[/C][C]-878.122938761418[/C][/ROW]
[ROW][C]93[/C][C]2638[/C][C]1809.55138663845[/C][C]828.448613361552[/C][/ROW]
[ROW][C]94[/C][C]3114[/C][C]2788.75676695808[/C][C]325.243233041916[/C][/ROW]
[ROW][C]95[/C][C]4405[/C][C]4165.79071306925[/C][C]239.20928693075[/C][/ROW]
[ROW][C]96[/C][C]7242[/C][C]5517.72019270466[/C][C]1724.27980729534[/C][/ROW]
[ROW][C]97[/C][C]1853[/C][C]1642.87618284972[/C][C]210.123817150283[/C][/ROW]
[ROW][C]98[/C][C]1779[/C][C]1612.43132140277[/C][C]166.568678597235[/C][/ROW]
[ROW][C]99[/C][C]2108[/C][C]1832.17691824364[/C][C]275.823081756362[/C][/ROW]
[ROW][C]100[/C][C]2336[/C][C]1913.25538826244[/C][C]422.744611737562[/C][/ROW]
[ROW][C]101[/C][C]1728[/C][C]1728.48274969031[/C][C]-0.482749690310129[/C][/ROW]
[ROW][C]102[/C][C]1661[/C][C]1511.36252751633[/C][C]149.637472483672[/C][/ROW]
[ROW][C]103[/C][C]2230[/C][C]2152.19070188827[/C][C]77.8092981117297[/C][/ROW]
[ROW][C]104[/C][C]1645[/C][C]2824.74458434354[/C][C]-1179.74458434354[/C][/ROW]
[ROW][C]105[/C][C]2421[/C][C]2239.81056904462[/C][C]181.189430955378[/C][/ROW]
[ROW][C]106[/C][C]3740[/C][C]3125.4009086972[/C][C]614.5990913028[/C][/ROW]
[ROW][C]107[/C][C]4988[/C][C]4635.28849398666[/C][C]352.711506013341[/C][/ROW]
[ROW][C]108[/C][C]6757[/C][C]6590.43627772738[/C][C]166.563722272623[/C][/ROW]
[ROW][C]109[/C][C]1757[/C][C]1851.26421649304[/C][C]-94.2642164930446[/C][/ROW]
[ROW][C]110[/C][C]1394[/C][C]1792.77004687517[/C][C]-398.770046875165[/C][/ROW]
[ROW][C]111[/C][C]1982[/C][C]2029.44603515612[/C][C]-47.446035156117[/C][/ROW]
[ROW][C]112[/C][C]1650[/C][C]2138.31674096811[/C][C]-488.316740968107[/C][/ROW]
[ROW][C]113[/C][C]1654[/C][C]1776.79978277586[/C][C]-122.799782775855[/C][/ROW]
[ROW][C]114[/C][C]1406[/C][C]1585.86604854665[/C][C]-179.866048546651[/C][/ROW]
[ROW][C]115[/C][C]1971[/C][C]2188.58427687695[/C][C]-217.584276876952[/C][/ROW]
[ROW][C]116[/C][C]1968[/C][C]2483.44085859961[/C][C]-515.44085859961[/C][/ROW]
[ROW][C]117[/C][C]2608[/C][C]2296.99085634624[/C][C]311.009143653760[/C][/ROW]
[ROW][C]118[/C][C]3845[/C][C]3302.63442170321[/C][C]542.365578296792[/C][/ROW]
[ROW][C]119[/C][C]4514[/C][C]4724.08581106525[/C][C]-210.085811065246[/C][/ROW]
[ROW][C]120[/C][C]6694[/C][C]6560.6124596845[/C][C]133.387540315506[/C][/ROW]
[ROW][C]121[/C][C]1720[/C][C]1797.56528271134[/C][C]-77.565282711344[/C][/ROW]
[ROW][C]122[/C][C]1321[/C][C]1651.26638180696[/C][C]-330.266381806965[/C][/ROW]
[ROW][C]123[/C][C]1859[/C][C]1974.72876687268[/C][C]-115.728766872676[/C][/ROW]
[ROW][C]124[/C][C]1628[/C][C]1950.68045521917[/C][C]-322.680455219167[/C][/ROW]
[ROW][C]125[/C][C]1615[/C][C]1697.38990829453[/C][C]-82.3899082945263[/C][/ROW]
[ROW][C]126[/C][C]1457[/C][C]1492.69848121522[/C][C]-35.6984812152232[/C][/ROW]
[ROW][C]127[/C][C]1899[/C][C]2071.86679540881[/C][C]-172.86679540881[/C][/ROW]
[ROW][C]128[/C][C]1605[/C][C]2273.68483240167[/C][C]-668.684832401673[/C][/ROW]
[ROW][C]129[/C][C]2424[/C][C]2295.64718499123[/C][C]128.352815008765[/C][/ROW]
[ROW][C]130[/C][C]3116[/C][C]3299.83911495731[/C][C]-183.839114957309[/C][/ROW]
[ROW][C]131[/C][C]4286[/C][C]4392.12206144793[/C][C]-106.122061447928[/C][/ROW]
[ROW][C]132[/C][C]6047[/C][C]6186.82230988632[/C][C]-139.822309886315[/C][/ROW]
[ROW][C]133[/C][C]1902[/C][C]1653.94483594882[/C][C]248.055164051182[/C][/ROW]
[ROW][C]134[/C][C]2049[/C][C]1461.01216917940[/C][C]587.987830820604[/C][/ROW]
[ROW][C]135[/C][C]1874[/C][C]1874.95322391386[/C][C]-0.953223913864122[/C][/ROW]
[ROW][C]136[/C][C]1279[/C][C]1800.52637332201[/C][C]-521.526373322009[/C][/ROW]
[ROW][C]137[/C][C]1432[/C][C]1607.41138442942[/C][C]-175.411384429416[/C][/ROW]
[ROW][C]138[/C][C]1540[/C][C]1416.53574035029[/C][C]123.464259649714[/C][/ROW]
[ROW][C]139[/C][C]2214[/C][C]1942.63425230185[/C][C]271.365747698154[/C][/ROW]
[ROW][C]140[/C][C]1857[/C][C]2026.50256677048[/C][C]-169.502566770484[/C][/ROW]
[ROW][C]141[/C][C]2408[/C][C]2290.03682171637[/C][C]117.963178283627[/C][/ROW]
[ROW][C]142[/C][C]3252[/C][C]3195.42166299226[/C][C]56.5783370077388[/C][/ROW]
[ROW][C]143[/C][C]3627[/C][C]4313.37392652558[/C][C]-686.373926525584[/C][/ROW]
[ROW][C]144[/C][C]6153[/C][C]6041.36336182473[/C][C]111.636638175273[/C][/ROW]
[ROW][C]145[/C][C]1577[/C][C]1696.80043384051[/C][C]-119.800433840508[/C][/ROW]
[ROW][C]146[/C][C]1667[/C][C]1577.74227395362[/C][C]89.2577260463793[/C][/ROW]
[ROW][C]147[/C][C]1993[/C][C]1791.93181604168[/C][C]201.06818395832[/C][/ROW]
[ROW][C]148[/C][C]1997[/C][C]1589.46956603025[/C][C]407.53043396975[/C][/ROW]
[ROW][C]149[/C][C]1783[/C][C]1541.89180518140[/C][C]241.108194818598[/C][/ROW]
[ROW][C]150[/C][C]1625[/C][C]1458.08910228096[/C][C]166.91089771904[/C][/ROW]
[ROW][C]151[/C][C]2076[/C][C]2036.31924432246[/C][C]39.6807556775368[/C][/ROW]
[ROW][C]152[/C][C]1773[/C][C]1991.75687219657[/C][C]-218.756872196566[/C][/ROW]
[ROW][C]153[/C][C]2377[/C][C]2338.41459014031[/C][C]38.5854098596942[/C][/ROW]
[ROW][C]154[/C][C]3088[/C][C]3234.15033715064[/C][C]-146.150337150636[/C][/ROW]
[ROW][C]155[/C][C]4096[/C][C]4147.42124307446[/C][C]-51.4212430744556[/C][/ROW]
[ROW][C]156[/C][C]6119[/C][C]6168.93311760892[/C][C]-49.9331176089154[/C][/ROW]
[ROW][C]157[/C][C]1494[/C][C]1692.16775339754[/C][C]-198.167753397543[/C][/ROW]
[ROW][C]158[/C][C]1564[/C][C]1629.08203605577[/C][C]-65.0820360557659[/C][/ROW]
[ROW][C]159[/C][C]1898[/C][C]1871.70756972243[/C][C]26.2924302775675[/C][/ROW]
[ROW][C]160[/C][C]2121[/C][C]1716.17913443011[/C][C]404.820865569887[/C][/ROW]
[ROW][C]161[/C][C]1831[/C][C]1623.09644518333[/C][C]207.90355481667[/C][/ROW]
[ROW][C]162[/C][C]1515[/C][C]1517.45368394950[/C][C]-2.4536839494956[/C][/ROW]
[ROW][C]163[/C][C]2048[/C][C]2054.60361080717[/C][C]-6.60361080717075[/C][/ROW]
[ROW][C]164[/C][C]2795[/C][C]1936.68703788415[/C][C]858.31296211585[/C][/ROW]
[ROW][C]165[/C][C]1749[/C][C]2429.72128285821[/C][C]-680.721282858206[/C][/ROW]
[ROW][C]166[/C][C]3339[/C][C]3258.32441951495[/C][C]80.6755804850477[/C][/ROW]
[ROW][C]167[/C][C]4227[/C][C]4239.46805951502[/C][C]-12.4680595150185[/C][/ROW]
[ROW][C]168[/C][C]6410[/C][C]6328.19029107946[/C][C]81.8097089205357[/C][/ROW]
[ROW][C]169[/C][C]1197[/C][C]1688.65155391750[/C][C]-491.651553917496[/C][/ROW]
[ROW][C]170[/C][C]1968[/C][C]1648.42787070931[/C][C]319.572129290693[/C][/ROW]
[ROW][C]171[/C][C]1720[/C][C]1949.84385869242[/C][C]-229.843858692416[/C][/ROW]
[ROW][C]172[/C][C]1725[/C][C]1884.99067625603[/C][C]-159.990676256032[/C][/ROW]
[ROW][C]173[/C][C]1674[/C][C]1705.97102352283[/C][C]-31.9710235228338[/C][/ROW]
[ROW][C]174[/C][C]1693[/C][C]1527.87608325712[/C][C]165.123916742876[/C][/ROW]
[ROW][C]175[/C][C]2031[/C][C]2079.12161922621[/C][C]-48.1216192262145[/C][/ROW]
[ROW][C]176[/C][C]1495[/C][C]2191.77632527178[/C][C]-696.776325271781[/C][/ROW]
[ROW][C]177[/C][C]2968[/C][C]2170.98314099033[/C][C]797.01685900967[/C][/ROW]
[ROW][C]178[/C][C]3385[/C][C]3283.36275573104[/C][C]101.637244268963[/C][/ROW]
[ROW][C]179[/C][C]3729[/C][C]4237.95546307917[/C][C]-508.95546307917[/C][/ROW]
[ROW][C]180[/C][C]5999[/C][C]6306.78823787491[/C][C]-307.788237874912[/C][/ROW]
[ROW][C]181[/C][C]1070[/C][C]1533.69189439295[/C][C]-463.691894392953[/C][/ROW]
[ROW][C]182[/C][C]1402[/C][C]1710.98349019132[/C][C]-308.983490191325[/C][/ROW]
[ROW][C]183[/C][C]1897[/C][C]1818.18276816566[/C][C]78.8172318343404[/C][/ROW]
[ROW][C]184[/C][C]1862[/C][C]1784.09279686647[/C][C]77.9072031335277[/C][/ROW]
[ROW][C]185[/C][C]1670[/C][C]1652.12019807661[/C][C]17.8798019233927[/C][/ROW]
[ROW][C]186[/C][C]1688[/C][C]1530.36178913519[/C][C]157.638210864809[/C][/ROW]
[ROW][C]187[/C][C]2031[/C][C]2005.43648256256[/C][C]25.5635174374422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41376&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41376&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315301571.36956742168-41.3695674216813
1415231559.41355733058-36.4135573305755
1516331661.44277370245-28.4427737024482
1619762010.62382343132-34.6238234313171
1711701195.53270921403-25.532709214026
1814801527.04041924606-47.0404192460585
1917811887.25217515444-106.252175154443
2024722343.73790116042128.262098839582
2119811915.6149718191865.3850281808197
2222732515.90243214176-242.902432141756
2338573920.75558687946-63.7555868794584
2445514952.19395853118-401.193958531177
2515101439.1870515459370.8129484540675
2613291432.76298315525-103.762983155249
2715181522.51441955630-4.51441955629775
2817901840.53881135034-50.5388113503438
2915371090.56603322183446.433966778171
3014491420.6350007973028.3649992026976
3119541749.02749779951204.972502200494
3218972262.81532258757-365.815322587573
3317061819.69896462105-113.69896462105
3425142293.30509548857220.694904511431
3535933695.08334293361-102.083342933606
3645244585.05251444474-61.0525144447438
3716091387.84395244362221.156047556384
3816381346.19070221032291.809297789679
3920301485.19299204736544.807007952642
4013751826.84678259232-451.846782592321
4113201201.96861097173118.031389028272
4212451399.87514559808-154.875145598079
4316001760.46891453843-160.46891453843
4422982087.95634566304210.043654336961
4521911754.87500961160436.124990388398
4625112355.47328598542155.526714014577
4734403678.14977409732-238.149774097320
4849234589.76924873895333.230751261051
4916091467.12279329130141.877206708697
5014351444.90491821398-9.90491821398382
5120611639.68583640788421.314163592121
5217891703.5280605600785.4719394399292
5315671259.27740092053307.722599079470
5414041401.005905890442.99409410955582
5515971790.57274270083-193.572742700826
5631592246.79639245545912.203607544546
5717592004.52103938439-245.521039384386
5825042529.08187679151-25.0818767915098
5942733810.32457662363462.675423376371
6052745008.43781085013265.562189149866
6117711617.23043546127153.769564538729
6216821556.00217237582125.997827624182
6318461910.29634476034-64.2963447603395
6415891860.14889917992-271.148899179915
6518961435.51995975500460.480040244997
6613791509.12651646586-130.126516465859
6716451866.42217942539-221.422179425388
6825122682.3656637486-170.365663748599
6917712036.14989717429-265.149897174291
7037272651.070298196241075.92970180376
7143884234.93388676277153.066113237232
7254345451.98241944138-17.9824194413832
7316061777.73118049791-171.731180497907
7415231688.22924153534-165.229241535336
7515771990.02633091137-413.026330911373
7616051858.16304094875-253.163040948755
7717651622.42739289942142.572607100581
7814031511.17084789707-108.170847897075
7925841849.24228707975734.757712920249
8033182772.45776661536545.542233384639
8115622095.90533819581-533.905338195808
8223493121.98476929198-772.984769291976
8339874382.89146049274-395.891460492743
8458915530.86930769623360.130692303774
8513891759.01873624210-370.018736242102
8614421655.20105760569-213.201057605691
8715481881.01759002865-333.017590028652
8819351791.01264162245143.987358377548
8915181679.36240015113-161.362400151134
9012501479.27854465245-229.278544652452
9118472028.45850166658-181.458501666584
9219302808.12293876142-878.122938761418
9326381809.55138663845828.448613361552
9431142788.75676695808325.243233041916
9544054165.79071306925239.20928693075
9672425517.720192704661724.27980729534
9718531642.87618284972210.123817150283
9817791612.43132140277166.568678597235
9921081832.17691824364275.823081756362
10023361913.25538826244422.744611737562
10117281728.48274969031-0.482749690310129
10216611511.36252751633149.637472483672
10322302152.1907018882777.8092981117297
10416452824.74458434354-1179.74458434354
10524212239.81056904462181.189430955378
10637403125.4009086972614.5990913028
10749884635.28849398666352.711506013341
10867576590.43627772738166.563722272623
10917571851.26421649304-94.2642164930446
11013941792.77004687517-398.770046875165
11119822029.44603515612-47.446035156117
11216502138.31674096811-488.316740968107
11316541776.79978277586-122.799782775855
11414061585.86604854665-179.866048546651
11519712188.58427687695-217.584276876952
11619682483.44085859961-515.44085859961
11726082296.99085634624311.009143653760
11838453302.63442170321542.365578296792
11945144724.08581106525-210.085811065246
12066946560.6124596845133.387540315506
12117201797.56528271134-77.565282711344
12213211651.26638180696-330.266381806965
12318591974.72876687268-115.728766872676
12416281950.68045521917-322.680455219167
12516151697.38990829453-82.3899082945263
12614571492.69848121522-35.6984812152232
12718992071.86679540881-172.86679540881
12816052273.68483240167-668.684832401673
12924242295.64718499123128.352815008765
13031163299.83911495731-183.839114957309
13142864392.12206144793-106.122061447928
13260476186.82230988632-139.822309886315
13319021653.94483594882248.055164051182
13420491461.01216917940587.987830820604
13518741874.95322391386-0.953223913864122
13612791800.52637332201-521.526373322009
13714321607.41138442942-175.411384429416
13815401416.53574035029123.464259649714
13922141942.63425230185271.365747698154
14018572026.50256677048-169.502566770484
14124082290.03682171637117.963178283627
14232523195.4216629922656.5783370077388
14336274313.37392652558-686.373926525584
14461536041.36336182473111.636638175273
14515771696.80043384051-119.800433840508
14616671577.7422739536289.2577260463793
14719931791.93181604168201.06818395832
14819971589.46956603025407.53043396975
14917831541.89180518140241.108194818598
15016251458.08910228096166.91089771904
15120762036.3192443224639.6807556775368
15217731991.75687219657-218.756872196566
15323772338.4145901403138.5854098596942
15430883234.15033715064-146.150337150636
15540964147.42124307446-51.4212430744556
15661196168.93311760892-49.9331176089154
15714941692.16775339754-198.167753397543
15815641629.08203605577-65.0820360557659
15918981871.7075697224326.2924302775675
16021211716.17913443011404.820865569887
16118311623.09644518333207.90355481667
16215151517.45368394950-2.4536839494956
16320482054.60361080717-6.60361080717075
16427951936.68703788415858.31296211585
16517492429.72128285821-680.721282858206
16633393258.3244195149580.6755804850477
16742274239.46805951502-12.4680595150185
16864106328.1902910794681.8097089205357
16911971688.65155391750-491.651553917496
17019681648.42787070931319.572129290693
17117201949.84385869242-229.843858692416
17217251884.99067625603-159.990676256032
17316741705.97102352283-31.9710235228338
17416931527.87608325712165.123916742876
17520312079.12161922621-48.1216192262145
17614952191.77632527178-696.776325271781
17729682170.98314099033797.01685900967
17833853283.36275573104101.637244268963
17937294237.95546307917-508.95546307917
18059996306.78823787491-307.788237874912
18110701533.69189439295-463.691894392953
18214021710.98349019132-308.983490191325
18318971818.1827681656678.8172318343404
18418621784.0927968664777.9072031335277
18516701652.1201980766117.8798019233927
18616881530.36178913519157.638210864809
18720312005.4364825625625.5635174374422







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1881939.058637780151711.215998707862166.90127685245
1892353.399065232712120.580958991132586.2171714743
1903199.619934539822955.043616286753444.19625279289
1913944.41758082653682.845977377474205.98918427552
1926016.988822416575700.213097269156333.76454756399
1931359.747879210201125.540852049951593.95490637044
1941598.633757961671356.301671345601840.96584457773
1951828.21496577851574.797764647162081.63216690985
1961791.600607635421532.756557494182050.44465777667
1971641.680976366651381.446060031441901.91589270187
1981558.802923396971295.054402811351822.55144398258
1991983.429121874211786.194989386242180.66325436218

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
188 & 1939.05863778015 & 1711.21599870786 & 2166.90127685245 \tabularnewline
189 & 2353.39906523271 & 2120.58095899113 & 2586.2171714743 \tabularnewline
190 & 3199.61993453982 & 2955.04361628675 & 3444.19625279289 \tabularnewline
191 & 3944.4175808265 & 3682.84597737747 & 4205.98918427552 \tabularnewline
192 & 6016.98882241657 & 5700.21309726915 & 6333.76454756399 \tabularnewline
193 & 1359.74787921020 & 1125.54085204995 & 1593.95490637044 \tabularnewline
194 & 1598.63375796167 & 1356.30167134560 & 1840.96584457773 \tabularnewline
195 & 1828.2149657785 & 1574.79776464716 & 2081.63216690985 \tabularnewline
196 & 1791.60060763542 & 1532.75655749418 & 2050.44465777667 \tabularnewline
197 & 1641.68097636665 & 1381.44606003144 & 1901.91589270187 \tabularnewline
198 & 1558.80292339697 & 1295.05440281135 & 1822.55144398258 \tabularnewline
199 & 1983.42912187421 & 1786.19498938624 & 2180.66325436218 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41376&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]188[/C][C]1939.05863778015[/C][C]1711.21599870786[/C][C]2166.90127685245[/C][/ROW]
[ROW][C]189[/C][C]2353.39906523271[/C][C]2120.58095899113[/C][C]2586.2171714743[/C][/ROW]
[ROW][C]190[/C][C]3199.61993453982[/C][C]2955.04361628675[/C][C]3444.19625279289[/C][/ROW]
[ROW][C]191[/C][C]3944.4175808265[/C][C]3682.84597737747[/C][C]4205.98918427552[/C][/ROW]
[ROW][C]192[/C][C]6016.98882241657[/C][C]5700.21309726915[/C][C]6333.76454756399[/C][/ROW]
[ROW][C]193[/C][C]1359.74787921020[/C][C]1125.54085204995[/C][C]1593.95490637044[/C][/ROW]
[ROW][C]194[/C][C]1598.63375796167[/C][C]1356.30167134560[/C][C]1840.96584457773[/C][/ROW]
[ROW][C]195[/C][C]1828.2149657785[/C][C]1574.79776464716[/C][C]2081.63216690985[/C][/ROW]
[ROW][C]196[/C][C]1791.60060763542[/C][C]1532.75655749418[/C][C]2050.44465777667[/C][/ROW]
[ROW][C]197[/C][C]1641.68097636665[/C][C]1381.44606003144[/C][C]1901.91589270187[/C][/ROW]
[ROW][C]198[/C][C]1558.80292339697[/C][C]1295.05440281135[/C][C]1822.55144398258[/C][/ROW]
[ROW][C]199[/C][C]1983.42912187421[/C][C]1786.19498938624[/C][C]2180.66325436218[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41376&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41376&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1881939.058637780151711.215998707862166.90127685245
1892353.399065232712120.580958991132586.2171714743
1903199.619934539822955.043616286753444.19625279289
1913944.41758082653682.845977377474205.98918427552
1926016.988822416575700.213097269156333.76454756399
1931359.747879210201125.540852049951593.95490637044
1941598.633757961671356.301671345601840.96584457773
1951828.21496577851574.797764647162081.63216690985
1961791.600607635421532.756557494182050.44465777667
1971641.680976366651381.446060031441901.91589270187
1981558.802923396971295.054402811351822.55144398258
1991983.429121874211786.194989386242180.66325436218



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')