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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 16 Dec 2012 09:53:14 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/16/t1355669602ifa6yb611jv1b7z.htm/, Retrieved Thu, 18 Apr 2024 05:57:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200403, Retrieved Thu, 18 Apr 2024 05:57:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-16 14:53:14] [843149dd24ea3aaab20d8c5630e75083] [Current]
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Dataseries X:
655362
873127
1107897
1555964
1671159
1493308
2957796
2638691
1305669
1280496
921900
867888
652586
913831
1108544
1555827
1699283
1509458
3268975
2425016
1312703
1365498
934453
775019
651142
843192
1146766
1652601
1465906
1652734
2922334
2702805
1458956
1410363
1019279
936574
708917
885295
1099663
1576220
1487870
1488635
2882530
2677026
1404398
1344370
936865
872705
628151
953712
1160384
1400618
1661511
1495347
2918786
2775677
1407026
1370199
964526
850851
683118
847224
1073256
1514326
1503734
1507712
2865698
2788128
1391596
1366378
946295
859626




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net

\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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200403&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200403&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200403&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0105300001851509
beta0.669962231629128
gamma0.230183992455485

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0105300001851509 \tabularnewline
beta & 0.669962231629128 \tabularnewline
gamma & 0.230183992455485 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200403&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]0.0105300001851509[/C][/ROW]
[ROW][C]beta[/C][C]0.669962231629128[/C][/ROW]
[ROW][C]gamma[/C][C]0.230183992455485[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200403&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200403&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
alpha0.0105300001851509
beta0.669962231629128
gamma0.230183992455485







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13652586636418.06730769216167.9326923079
14913831896192.36335811517638.6366418853
1511085441102247.289587396296.71041261102
1615558271548352.331749577474.66825042525
1716992831690465.55103498817.44896510453
1815094581506785.405946642672.59405336319
1932689752977855.78489076291119.215109236
2024250162665014.05790692-239998.057906924
2113127031330826.92605923-18123.9260592323
2213654981308398.9782892257099.0217107756
23934453952598.069779982-18145.0697799816
24775019899782.207905665-124763.207905665
25651142675561.942234268-24419.9422342679
26843192935001.614313876-91809.6143138763
2711467661136306.4853236410459.5146763599
2816526011581738.6947794970862.3052205064
2914659061724287.43985795-258381.43985795
3016527341533971.35068594118762.649314062
3129223343070356.99921253-148022.999212531
3227028052627221.9287426475583.0712573645
3314589561344416.46037674114539.539623259
3414103631338978.657918671384.3420813992
351019279964751.75533315154527.2446668491
36936574887491.63827020149082.3617297986
37708917688256.46196950220660.5380304984
38885295933440.476482122-48145.4764821216
3910996631159424.32816186-59761.3281618634
4015762201618305.43853743-42085.4385374265
4114878701684310.4022016-196440.402201597
4214886351580616.08870386-91981.0887038573
4328825303052603.87095762-170073.870957623
4426770262658594.0017091418431.9982908643
4514043981382085.1236355722312.8763644323
4613443701363222.16808053-18852.1680805301
47936865980944.136344243-44079.1363442433
48872705897448.364451787-24743.3644517865
49628151686484.423503342-58333.4235033424
50953712910130.06339908643581.936600914
5111603841130045.9865213330338.013478674
5214006181590149.14032944-189531.140329436
5316615111614652.8387200946858.1612799126
5414953471534235.77597528-38888.7759752774
5529187862986294.3939747-67508.3939746995
5627756772634320.43200119141356.567998813
5714070261358878.8221107748147.1778892272
5813701991329983.3612128240215.6387871804
59964526942069.5374522722456.4625477302
60850851863635.614841634-12784.6148416336
61683118645188.79890397337929.2010960269
62847224893781.123067276-46557.1230672763
6310732561109816.3202504-36560.3202504017
6415143261518750.53056858-4424.53056857688
6515037341599962.26613262-96228.2661326197
6615077121498418.135966849293.86403316399
6728656982944714.99113471-79016.991134706
6827881282640359.0526011147768.947398896
6913915961343968.9102219847627.0897780184
7013663781313471.1454454752906.8545545335
71946295921945.32143184224349.6785681581
72859626835817.37118932823808.6288106719

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 652586 & 636418.067307692 & 16167.9326923079 \tabularnewline
14 & 913831 & 896192.363358115 & 17638.6366418853 \tabularnewline
15 & 1108544 & 1102247.28958739 & 6296.71041261102 \tabularnewline
16 & 1555827 & 1548352.33174957 & 7474.66825042525 \tabularnewline
17 & 1699283 & 1690465.5510349 & 8817.44896510453 \tabularnewline
18 & 1509458 & 1506785.40594664 & 2672.59405336319 \tabularnewline
19 & 3268975 & 2977855.78489076 & 291119.215109236 \tabularnewline
20 & 2425016 & 2665014.05790692 & -239998.057906924 \tabularnewline
21 & 1312703 & 1330826.92605923 & -18123.9260592323 \tabularnewline
22 & 1365498 & 1308398.97828922 & 57099.0217107756 \tabularnewline
23 & 934453 & 952598.069779982 & -18145.0697799816 \tabularnewline
24 & 775019 & 899782.207905665 & -124763.207905665 \tabularnewline
25 & 651142 & 675561.942234268 & -24419.9422342679 \tabularnewline
26 & 843192 & 935001.614313876 & -91809.6143138763 \tabularnewline
27 & 1146766 & 1136306.48532364 & 10459.5146763599 \tabularnewline
28 & 1652601 & 1581738.69477949 & 70862.3052205064 \tabularnewline
29 & 1465906 & 1724287.43985795 & -258381.43985795 \tabularnewline
30 & 1652734 & 1533971.35068594 & 118762.649314062 \tabularnewline
31 & 2922334 & 3070356.99921253 & -148022.999212531 \tabularnewline
32 & 2702805 & 2627221.92874264 & 75583.0712573645 \tabularnewline
33 & 1458956 & 1344416.46037674 & 114539.539623259 \tabularnewline
34 & 1410363 & 1338978.6579186 & 71384.3420813992 \tabularnewline
35 & 1019279 & 964751.755333151 & 54527.2446668491 \tabularnewline
36 & 936574 & 887491.638270201 & 49082.3617297986 \tabularnewline
37 & 708917 & 688256.461969502 & 20660.5380304984 \tabularnewline
38 & 885295 & 933440.476482122 & -48145.4764821216 \tabularnewline
39 & 1099663 & 1159424.32816186 & -59761.3281618634 \tabularnewline
40 & 1576220 & 1618305.43853743 & -42085.4385374265 \tabularnewline
41 & 1487870 & 1684310.4022016 & -196440.402201597 \tabularnewline
42 & 1488635 & 1580616.08870386 & -91981.0887038573 \tabularnewline
43 & 2882530 & 3052603.87095762 & -170073.870957623 \tabularnewline
44 & 2677026 & 2658594.00170914 & 18431.9982908643 \tabularnewline
45 & 1404398 & 1382085.12363557 & 22312.8763644323 \tabularnewline
46 & 1344370 & 1363222.16808053 & -18852.1680805301 \tabularnewline
47 & 936865 & 980944.136344243 & -44079.1363442433 \tabularnewline
48 & 872705 & 897448.364451787 & -24743.3644517865 \tabularnewline
49 & 628151 & 686484.423503342 & -58333.4235033424 \tabularnewline
50 & 953712 & 910130.063399086 & 43581.936600914 \tabularnewline
51 & 1160384 & 1130045.98652133 & 30338.013478674 \tabularnewline
52 & 1400618 & 1590149.14032944 & -189531.140329436 \tabularnewline
53 & 1661511 & 1614652.83872009 & 46858.1612799126 \tabularnewline
54 & 1495347 & 1534235.77597528 & -38888.7759752774 \tabularnewline
55 & 2918786 & 2986294.3939747 & -67508.3939746995 \tabularnewline
56 & 2775677 & 2634320.43200119 & 141356.567998813 \tabularnewline
57 & 1407026 & 1358878.82211077 & 48147.1778892272 \tabularnewline
58 & 1370199 & 1329983.36121282 & 40215.6387871804 \tabularnewline
59 & 964526 & 942069.53745227 & 22456.4625477302 \tabularnewline
60 & 850851 & 863635.614841634 & -12784.6148416336 \tabularnewline
61 & 683118 & 645188.798903973 & 37929.2010960269 \tabularnewline
62 & 847224 & 893781.123067276 & -46557.1230672763 \tabularnewline
63 & 1073256 & 1109816.3202504 & -36560.3202504017 \tabularnewline
64 & 1514326 & 1518750.53056858 & -4424.53056857688 \tabularnewline
65 & 1503734 & 1599962.26613262 & -96228.2661326197 \tabularnewline
66 & 1507712 & 1498418.13596684 & 9293.86403316399 \tabularnewline
67 & 2865698 & 2944714.99113471 & -79016.991134706 \tabularnewline
68 & 2788128 & 2640359.0526011 & 147768.947398896 \tabularnewline
69 & 1391596 & 1343968.91022198 & 47627.0897780184 \tabularnewline
70 & 1366378 & 1313471.14544547 & 52906.8545545335 \tabularnewline
71 & 946295 & 921945.321431842 & 24349.6785681581 \tabularnewline
72 & 859626 & 835817.371189328 & 23808.6288106719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200403&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]652586[/C][C]636418.067307692[/C][C]16167.9326923079[/C][/ROW]
[ROW][C]14[/C][C]913831[/C][C]896192.363358115[/C][C]17638.6366418853[/C][/ROW]
[ROW][C]15[/C][C]1108544[/C][C]1102247.28958739[/C][C]6296.71041261102[/C][/ROW]
[ROW][C]16[/C][C]1555827[/C][C]1548352.33174957[/C][C]7474.66825042525[/C][/ROW]
[ROW][C]17[/C][C]1699283[/C][C]1690465.5510349[/C][C]8817.44896510453[/C][/ROW]
[ROW][C]18[/C][C]1509458[/C][C]1506785.40594664[/C][C]2672.59405336319[/C][/ROW]
[ROW][C]19[/C][C]3268975[/C][C]2977855.78489076[/C][C]291119.215109236[/C][/ROW]
[ROW][C]20[/C][C]2425016[/C][C]2665014.05790692[/C][C]-239998.057906924[/C][/ROW]
[ROW][C]21[/C][C]1312703[/C][C]1330826.92605923[/C][C]-18123.9260592323[/C][/ROW]
[ROW][C]22[/C][C]1365498[/C][C]1308398.97828922[/C][C]57099.0217107756[/C][/ROW]
[ROW][C]23[/C][C]934453[/C][C]952598.069779982[/C][C]-18145.0697799816[/C][/ROW]
[ROW][C]24[/C][C]775019[/C][C]899782.207905665[/C][C]-124763.207905665[/C][/ROW]
[ROW][C]25[/C][C]651142[/C][C]675561.942234268[/C][C]-24419.9422342679[/C][/ROW]
[ROW][C]26[/C][C]843192[/C][C]935001.614313876[/C][C]-91809.6143138763[/C][/ROW]
[ROW][C]27[/C][C]1146766[/C][C]1136306.48532364[/C][C]10459.5146763599[/C][/ROW]
[ROW][C]28[/C][C]1652601[/C][C]1581738.69477949[/C][C]70862.3052205064[/C][/ROW]
[ROW][C]29[/C][C]1465906[/C][C]1724287.43985795[/C][C]-258381.43985795[/C][/ROW]
[ROW][C]30[/C][C]1652734[/C][C]1533971.35068594[/C][C]118762.649314062[/C][/ROW]
[ROW][C]31[/C][C]2922334[/C][C]3070356.99921253[/C][C]-148022.999212531[/C][/ROW]
[ROW][C]32[/C][C]2702805[/C][C]2627221.92874264[/C][C]75583.0712573645[/C][/ROW]
[ROW][C]33[/C][C]1458956[/C][C]1344416.46037674[/C][C]114539.539623259[/C][/ROW]
[ROW][C]34[/C][C]1410363[/C][C]1338978.6579186[/C][C]71384.3420813992[/C][/ROW]
[ROW][C]35[/C][C]1019279[/C][C]964751.755333151[/C][C]54527.2446668491[/C][/ROW]
[ROW][C]36[/C][C]936574[/C][C]887491.638270201[/C][C]49082.3617297986[/C][/ROW]
[ROW][C]37[/C][C]708917[/C][C]688256.461969502[/C][C]20660.5380304984[/C][/ROW]
[ROW][C]38[/C][C]885295[/C][C]933440.476482122[/C][C]-48145.4764821216[/C][/ROW]
[ROW][C]39[/C][C]1099663[/C][C]1159424.32816186[/C][C]-59761.3281618634[/C][/ROW]
[ROW][C]40[/C][C]1576220[/C][C]1618305.43853743[/C][C]-42085.4385374265[/C][/ROW]
[ROW][C]41[/C][C]1487870[/C][C]1684310.4022016[/C][C]-196440.402201597[/C][/ROW]
[ROW][C]42[/C][C]1488635[/C][C]1580616.08870386[/C][C]-91981.0887038573[/C][/ROW]
[ROW][C]43[/C][C]2882530[/C][C]3052603.87095762[/C][C]-170073.870957623[/C][/ROW]
[ROW][C]44[/C][C]2677026[/C][C]2658594.00170914[/C][C]18431.9982908643[/C][/ROW]
[ROW][C]45[/C][C]1404398[/C][C]1382085.12363557[/C][C]22312.8763644323[/C][/ROW]
[ROW][C]46[/C][C]1344370[/C][C]1363222.16808053[/C][C]-18852.1680805301[/C][/ROW]
[ROW][C]47[/C][C]936865[/C][C]980944.136344243[/C][C]-44079.1363442433[/C][/ROW]
[ROW][C]48[/C][C]872705[/C][C]897448.364451787[/C][C]-24743.3644517865[/C][/ROW]
[ROW][C]49[/C][C]628151[/C][C]686484.423503342[/C][C]-58333.4235033424[/C][/ROW]
[ROW][C]50[/C][C]953712[/C][C]910130.063399086[/C][C]43581.936600914[/C][/ROW]
[ROW][C]51[/C][C]1160384[/C][C]1130045.98652133[/C][C]30338.013478674[/C][/ROW]
[ROW][C]52[/C][C]1400618[/C][C]1590149.14032944[/C][C]-189531.140329436[/C][/ROW]
[ROW][C]53[/C][C]1661511[/C][C]1614652.83872009[/C][C]46858.1612799126[/C][/ROW]
[ROW][C]54[/C][C]1495347[/C][C]1534235.77597528[/C][C]-38888.7759752774[/C][/ROW]
[ROW][C]55[/C][C]2918786[/C][C]2986294.3939747[/C][C]-67508.3939746995[/C][/ROW]
[ROW][C]56[/C][C]2775677[/C][C]2634320.43200119[/C][C]141356.567998813[/C][/ROW]
[ROW][C]57[/C][C]1407026[/C][C]1358878.82211077[/C][C]48147.1778892272[/C][/ROW]
[ROW][C]58[/C][C]1370199[/C][C]1329983.36121282[/C][C]40215.6387871804[/C][/ROW]
[ROW][C]59[/C][C]964526[/C][C]942069.53745227[/C][C]22456.4625477302[/C][/ROW]
[ROW][C]60[/C][C]850851[/C][C]863635.614841634[/C][C]-12784.6148416336[/C][/ROW]
[ROW][C]61[/C][C]683118[/C][C]645188.798903973[/C][C]37929.2010960269[/C][/ROW]
[ROW][C]62[/C][C]847224[/C][C]893781.123067276[/C][C]-46557.1230672763[/C][/ROW]
[ROW][C]63[/C][C]1073256[/C][C]1109816.3202504[/C][C]-36560.3202504017[/C][/ROW]
[ROW][C]64[/C][C]1514326[/C][C]1518750.53056858[/C][C]-4424.53056857688[/C][/ROW]
[ROW][C]65[/C][C]1503734[/C][C]1599962.26613262[/C][C]-96228.2661326197[/C][/ROW]
[ROW][C]66[/C][C]1507712[/C][C]1498418.13596684[/C][C]9293.86403316399[/C][/ROW]
[ROW][C]67[/C][C]2865698[/C][C]2944714.99113471[/C][C]-79016.991134706[/C][/ROW]
[ROW][C]68[/C][C]2788128[/C][C]2640359.0526011[/C][C]147768.947398896[/C][/ROW]
[ROW][C]69[/C][C]1391596[/C][C]1343968.91022198[/C][C]47627.0897780184[/C][/ROW]
[ROW][C]70[/C][C]1366378[/C][C]1313471.14544547[/C][C]52906.8545545335[/C][/ROW]
[ROW][C]71[/C][C]946295[/C][C]921945.321431842[/C][C]24349.6785681581[/C][/ROW]
[ROW][C]72[/C][C]859626[/C][C]835817.371189328[/C][C]23808.6288106719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200403&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200403&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
13652586636418.06730769216167.9326923079
14913831896192.36335811517638.6366418853
1511085441102247.289587396296.71041261102
1615558271548352.331749577474.66825042525
1716992831690465.55103498817.44896510453
1815094581506785.405946642672.59405336319
1932689752977855.78489076291119.215109236
2024250162665014.05790692-239998.057906924
2113127031330826.92605923-18123.9260592323
2213654981308398.9782892257099.0217107756
23934453952598.069779982-18145.0697799816
24775019899782.207905665-124763.207905665
25651142675561.942234268-24419.9422342679
26843192935001.614313876-91809.6143138763
2711467661136306.4853236410459.5146763599
2816526011581738.6947794970862.3052205064
2914659061724287.43985795-258381.43985795
3016527341533971.35068594118762.649314062
3129223343070356.99921253-148022.999212531
3227028052627221.9287426475583.0712573645
3314589561344416.46037674114539.539623259
3414103631338978.657918671384.3420813992
351019279964751.75533315154527.2446668491
36936574887491.63827020149082.3617297986
37708917688256.46196950220660.5380304984
38885295933440.476482122-48145.4764821216
3910996631159424.32816186-59761.3281618634
4015762201618305.43853743-42085.4385374265
4114878701684310.4022016-196440.402201597
4214886351580616.08870386-91981.0887038573
4328825303052603.87095762-170073.870957623
4426770262658594.0017091418431.9982908643
4514043981382085.1236355722312.8763644323
4613443701363222.16808053-18852.1680805301
47936865980944.136344243-44079.1363442433
48872705897448.364451787-24743.3644517865
49628151686484.423503342-58333.4235033424
50953712910130.06339908643581.936600914
5111603841130045.9865213330338.013478674
5214006181590149.14032944-189531.140329436
5316615111614652.8387200946858.1612799126
5414953471534235.77597528-38888.7759752774
5529187862986294.3939747-67508.3939746995
5627756772634320.43200119141356.567998813
5714070261358878.8221107748147.1778892272
5813701991329983.3612128240215.6387871804
59964526942069.5374522722456.4625477302
60850851863635.614841634-12784.6148416336
61683118645188.79890397337929.2010960269
62847224893781.123067276-46557.1230672763
6310732561109816.3202504-36560.3202504017
6415143261518750.53056858-4424.53056857688
6515037341599962.26613262-96228.2661326197
6615077121498418.135966849293.86403316399
6728656982944714.99113471-79016.991134706
6827881282640359.0526011147768.947398896
6913915961343968.9102219847627.0897780184
7013663781313471.1454454752906.8545545335
71946295921945.32143184224349.6785681581
72859626835817.37118932823808.6288106719







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73629877.173186633446566.486978015813187.859395251
74859130.609839352675791.5839943311042469.63568437
751078564.49881316895169.8460237181261959.15160261
761496092.435845661312605.778988141679579.09270319
771557362.236522061373738.145342921740986.3277012
781482464.696362051298648.744208271666280.64851583
792910083.997262052726012.84198823094155.1525359
802660304.35370542475905.846610272844702.86080053
811340598.858860311155792.185128051525405.53259256
821311515.085506111126210.939142211496819.23187001
83913267.708003758727368.5036630071099166.91234451
84826928.088856162640328.2122613761013527.96545095

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 629877.173186633 & 446566.486978015 & 813187.859395251 \tabularnewline
74 & 859130.609839352 & 675791.583994331 & 1042469.63568437 \tabularnewline
75 & 1078564.49881316 & 895169.846023718 & 1261959.15160261 \tabularnewline
76 & 1496092.43584566 & 1312605.77898814 & 1679579.09270319 \tabularnewline
77 & 1557362.23652206 & 1373738.14534292 & 1740986.3277012 \tabularnewline
78 & 1482464.69636205 & 1298648.74420827 & 1666280.64851583 \tabularnewline
79 & 2910083.99726205 & 2726012.8419882 & 3094155.1525359 \tabularnewline
80 & 2660304.3537054 & 2475905.84661027 & 2844702.86080053 \tabularnewline
81 & 1340598.85886031 & 1155792.18512805 & 1525405.53259256 \tabularnewline
82 & 1311515.08550611 & 1126210.93914221 & 1496819.23187001 \tabularnewline
83 & 913267.708003758 & 727368.503663007 & 1099166.91234451 \tabularnewline
84 & 826928.088856162 & 640328.212261376 & 1013527.96545095 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200403&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]73[/C][C]629877.173186633[/C][C]446566.486978015[/C][C]813187.859395251[/C][/ROW]
[ROW][C]74[/C][C]859130.609839352[/C][C]675791.583994331[/C][C]1042469.63568437[/C][/ROW]
[ROW][C]75[/C][C]1078564.49881316[/C][C]895169.846023718[/C][C]1261959.15160261[/C][/ROW]
[ROW][C]76[/C][C]1496092.43584566[/C][C]1312605.77898814[/C][C]1679579.09270319[/C][/ROW]
[ROW][C]77[/C][C]1557362.23652206[/C][C]1373738.14534292[/C][C]1740986.3277012[/C][/ROW]
[ROW][C]78[/C][C]1482464.69636205[/C][C]1298648.74420827[/C][C]1666280.64851583[/C][/ROW]
[ROW][C]79[/C][C]2910083.99726205[/C][C]2726012.8419882[/C][C]3094155.1525359[/C][/ROW]
[ROW][C]80[/C][C]2660304.3537054[/C][C]2475905.84661027[/C][C]2844702.86080053[/C][/ROW]
[ROW][C]81[/C][C]1340598.85886031[/C][C]1155792.18512805[/C][C]1525405.53259256[/C][/ROW]
[ROW][C]82[/C][C]1311515.08550611[/C][C]1126210.93914221[/C][C]1496819.23187001[/C][/ROW]
[ROW][C]83[/C][C]913267.708003758[/C][C]727368.503663007[/C][C]1099166.91234451[/C][/ROW]
[ROW][C]84[/C][C]826928.088856162[/C][C]640328.212261376[/C][C]1013527.96545095[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200403&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200403&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
73629877.173186633446566.486978015813187.859395251
74859130.609839352675791.5839943311042469.63568437
751078564.49881316895169.8460237181261959.15160261
761496092.435845661312605.778988141679579.09270319
771557362.236522061373738.145342921740986.3277012
781482464.696362051298648.744208271666280.64851583
792910083.997262052726012.84198823094155.1525359
802660304.35370542475905.846610272844702.86080053
811340598.858860311155792.185128051525405.53259256
821311515.085506111126210.939142211496819.23187001
83913267.708003758727368.5036630071099166.91234451
84826928.088856162640328.2122613761013527.96545095



Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
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')