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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 computationSat, 03 Dec 2011 12:51:28 -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/2011/Dec/03/t13229347077ed9jcvd9sx2pcm.htm/, Retrieved Sun, 28 Apr 2024 21:45:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150522, Retrieved Sun, 28 Apr 2024 21:45:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-12-03 17:51:28] [888e326c8b932e070d5e53fa2c51e0f3] [Current]
- R P     [Exponential Smoothing] [] [2011-12-06 20:04:42] [63b27a8f1021b1dec8e8fd0dfee8bfd3]
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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 time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150522&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150522&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150522&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' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0105300001854458
beta0.669962231605911
gamma0.230183992456836

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0105300001854458 \tabularnewline
beta & 0.669962231605911 \tabularnewline
gamma & 0.230183992456836 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150522&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]0.0105300001854458[/C][/ROW]
[ROW][C]beta[/C][C]0.669962231605911[/C][/ROW]
[ROW][C]gamma[/C][C]0.230183992456836[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150522&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150522&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
alpha0.0105300001854458
beta0.669962231605911
gamma0.230183992456836







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13652586636418.06730769216167.9326923079
14913831896192.36335811817638.6366418815
1511085441102247.28958746296.71041260357
1615558271548352.331749587474.6682504178
1716992831690465.55103498817.44896509731
1815094581506785.405946642672.59405335644
1932689752977855.78489077291119.215109231
2024250162665014.057907-239998.057906998
2113127031330826.92605923-18123.9260592286
2213654981308398.9782892157099.02171079
23934453952598.069779977-18145.0697799765
24775019899782.207905648-124763.207905648
25651142675561.942234234-24419.9422342341
26843192935001.614313837-91809.614313837
2711467661136306.4853235610459.5146764361
2816526011581738.6947794370862.3052205718
2914659061724287.43985791-258381.439857911
3016527341533971.35068583118762.64931417
3129223343070356.99921284-148022.999212835
3227028052627221.9287422275583.0712577822
3314589561344416.46037666114539.539623336
3414103631338978.6579186771384.3420813349
351019279964751.75533314354527.2446668567
36936574887491.6382700849082.3617299197
37708917688256.4619695520660.5380304503
38885295933440.476482092-48145.476482092
3910996631159424.32816195-59761.3281619453
4015762201618305.43853757-42085.4385375711
4114878701684310.40220131-196440.402201312
4214886351580616.08870402-91981.0887040203
4328825303052603.87095771-170073.870957712
4426770262658594.0017089618431.9982910408
4514043981382085.123635722312.8763643024
4613443701363222.1680807-18852.1680807022
47936865980944.136344332-44079.1363443315
48872705897448.364451774-24743.3644517744
49628151686484.423503429-58333.4235034289
50953712910130.06339903243581.9366009682
5111603841130045.986521430338.0134786034
5214006181590149.14032963-189531.140329626
5316615111614652.8387197346858.1612802658
5414953471534235.77597549-38888.7759754935
5529187862986294.39397479-67508.3939747885
5627756772634320.43200135141356.56799865
5714070261358878.8221112148147.1778887874
5813701991329983.3612132440215.6387867576
59964526942069.53745260422456.4625473956
60850851863635.614841921-12784.6148419211
61683118645188.79890428137929.2010957191
62847224893781.123067611-46557.123067611
6310732561109816.32025077-36560.3202507675
6415143261518750.53056872-4424.53056871518
6515037341599962.26613267-96228.2661326681
6615077121498418.135967159293.8640328527
6728656982944714.99113487-79016.9911348717
6827881282640359.05260156147768.947398436
6913915961343968.9102225147627.0897774922
7013663781313471.1454459452906.8545540588
71946295921945.321432224349.6785677993
72859626835817.37118957823808.6288104225

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 652586 & 636418.067307692 & 16167.9326923079 \tabularnewline
14 & 913831 & 896192.363358118 & 17638.6366418815 \tabularnewline
15 & 1108544 & 1102247.2895874 & 6296.71041260357 \tabularnewline
16 & 1555827 & 1548352.33174958 & 7474.6682504178 \tabularnewline
17 & 1699283 & 1690465.5510349 & 8817.44896509731 \tabularnewline
18 & 1509458 & 1506785.40594664 & 2672.59405335644 \tabularnewline
19 & 3268975 & 2977855.78489077 & 291119.215109231 \tabularnewline
20 & 2425016 & 2665014.057907 & -239998.057906998 \tabularnewline
21 & 1312703 & 1330826.92605923 & -18123.9260592286 \tabularnewline
22 & 1365498 & 1308398.97828921 & 57099.02171079 \tabularnewline
23 & 934453 & 952598.069779977 & -18145.0697799765 \tabularnewline
24 & 775019 & 899782.207905648 & -124763.207905648 \tabularnewline
25 & 651142 & 675561.942234234 & -24419.9422342341 \tabularnewline
26 & 843192 & 935001.614313837 & -91809.614313837 \tabularnewline
27 & 1146766 & 1136306.48532356 & 10459.5146764361 \tabularnewline
28 & 1652601 & 1581738.69477943 & 70862.3052205718 \tabularnewline
29 & 1465906 & 1724287.43985791 & -258381.439857911 \tabularnewline
30 & 1652734 & 1533971.35068583 & 118762.64931417 \tabularnewline
31 & 2922334 & 3070356.99921284 & -148022.999212835 \tabularnewline
32 & 2702805 & 2627221.92874222 & 75583.0712577822 \tabularnewline
33 & 1458956 & 1344416.46037666 & 114539.539623336 \tabularnewline
34 & 1410363 & 1338978.65791867 & 71384.3420813349 \tabularnewline
35 & 1019279 & 964751.755333143 & 54527.2446668567 \tabularnewline
36 & 936574 & 887491.63827008 & 49082.3617299197 \tabularnewline
37 & 708917 & 688256.46196955 & 20660.5380304503 \tabularnewline
38 & 885295 & 933440.476482092 & -48145.476482092 \tabularnewline
39 & 1099663 & 1159424.32816195 & -59761.3281619453 \tabularnewline
40 & 1576220 & 1618305.43853757 & -42085.4385375711 \tabularnewline
41 & 1487870 & 1684310.40220131 & -196440.402201312 \tabularnewline
42 & 1488635 & 1580616.08870402 & -91981.0887040203 \tabularnewline
43 & 2882530 & 3052603.87095771 & -170073.870957712 \tabularnewline
44 & 2677026 & 2658594.00170896 & 18431.9982910408 \tabularnewline
45 & 1404398 & 1382085.1236357 & 22312.8763643024 \tabularnewline
46 & 1344370 & 1363222.1680807 & -18852.1680807022 \tabularnewline
47 & 936865 & 980944.136344332 & -44079.1363443315 \tabularnewline
48 & 872705 & 897448.364451774 & -24743.3644517744 \tabularnewline
49 & 628151 & 686484.423503429 & -58333.4235034289 \tabularnewline
50 & 953712 & 910130.063399032 & 43581.9366009682 \tabularnewline
51 & 1160384 & 1130045.9865214 & 30338.0134786034 \tabularnewline
52 & 1400618 & 1590149.14032963 & -189531.140329626 \tabularnewline
53 & 1661511 & 1614652.83871973 & 46858.1612802658 \tabularnewline
54 & 1495347 & 1534235.77597549 & -38888.7759754935 \tabularnewline
55 & 2918786 & 2986294.39397479 & -67508.3939747885 \tabularnewline
56 & 2775677 & 2634320.43200135 & 141356.56799865 \tabularnewline
57 & 1407026 & 1358878.82211121 & 48147.1778887874 \tabularnewline
58 & 1370199 & 1329983.36121324 & 40215.6387867576 \tabularnewline
59 & 964526 & 942069.537452604 & 22456.4625473956 \tabularnewline
60 & 850851 & 863635.614841921 & -12784.6148419211 \tabularnewline
61 & 683118 & 645188.798904281 & 37929.2010957191 \tabularnewline
62 & 847224 & 893781.123067611 & -46557.123067611 \tabularnewline
63 & 1073256 & 1109816.32025077 & -36560.3202507675 \tabularnewline
64 & 1514326 & 1518750.53056872 & -4424.53056871518 \tabularnewline
65 & 1503734 & 1599962.26613267 & -96228.2661326681 \tabularnewline
66 & 1507712 & 1498418.13596715 & 9293.8640328527 \tabularnewline
67 & 2865698 & 2944714.99113487 & -79016.9911348717 \tabularnewline
68 & 2788128 & 2640359.05260156 & 147768.947398436 \tabularnewline
69 & 1391596 & 1343968.91022251 & 47627.0897774922 \tabularnewline
70 & 1366378 & 1313471.14544594 & 52906.8545540588 \tabularnewline
71 & 946295 & 921945.3214322 & 24349.6785677993 \tabularnewline
72 & 859626 & 835817.371189578 & 23808.6288104225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150522&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]896192.363358118[/C][C]17638.6366418815[/C][/ROW]
[ROW][C]15[/C][C]1108544[/C][C]1102247.2895874[/C][C]6296.71041260357[/C][/ROW]
[ROW][C]16[/C][C]1555827[/C][C]1548352.33174958[/C][C]7474.6682504178[/C][/ROW]
[ROW][C]17[/C][C]1699283[/C][C]1690465.5510349[/C][C]8817.44896509731[/C][/ROW]
[ROW][C]18[/C][C]1509458[/C][C]1506785.40594664[/C][C]2672.59405335644[/C][/ROW]
[ROW][C]19[/C][C]3268975[/C][C]2977855.78489077[/C][C]291119.215109231[/C][/ROW]
[ROW][C]20[/C][C]2425016[/C][C]2665014.057907[/C][C]-239998.057906998[/C][/ROW]
[ROW][C]21[/C][C]1312703[/C][C]1330826.92605923[/C][C]-18123.9260592286[/C][/ROW]
[ROW][C]22[/C][C]1365498[/C][C]1308398.97828921[/C][C]57099.02171079[/C][/ROW]
[ROW][C]23[/C][C]934453[/C][C]952598.069779977[/C][C]-18145.0697799765[/C][/ROW]
[ROW][C]24[/C][C]775019[/C][C]899782.207905648[/C][C]-124763.207905648[/C][/ROW]
[ROW][C]25[/C][C]651142[/C][C]675561.942234234[/C][C]-24419.9422342341[/C][/ROW]
[ROW][C]26[/C][C]843192[/C][C]935001.614313837[/C][C]-91809.614313837[/C][/ROW]
[ROW][C]27[/C][C]1146766[/C][C]1136306.48532356[/C][C]10459.5146764361[/C][/ROW]
[ROW][C]28[/C][C]1652601[/C][C]1581738.69477943[/C][C]70862.3052205718[/C][/ROW]
[ROW][C]29[/C][C]1465906[/C][C]1724287.43985791[/C][C]-258381.439857911[/C][/ROW]
[ROW][C]30[/C][C]1652734[/C][C]1533971.35068583[/C][C]118762.64931417[/C][/ROW]
[ROW][C]31[/C][C]2922334[/C][C]3070356.99921284[/C][C]-148022.999212835[/C][/ROW]
[ROW][C]32[/C][C]2702805[/C][C]2627221.92874222[/C][C]75583.0712577822[/C][/ROW]
[ROW][C]33[/C][C]1458956[/C][C]1344416.46037666[/C][C]114539.539623336[/C][/ROW]
[ROW][C]34[/C][C]1410363[/C][C]1338978.65791867[/C][C]71384.3420813349[/C][/ROW]
[ROW][C]35[/C][C]1019279[/C][C]964751.755333143[/C][C]54527.2446668567[/C][/ROW]
[ROW][C]36[/C][C]936574[/C][C]887491.63827008[/C][C]49082.3617299197[/C][/ROW]
[ROW][C]37[/C][C]708917[/C][C]688256.46196955[/C][C]20660.5380304503[/C][/ROW]
[ROW][C]38[/C][C]885295[/C][C]933440.476482092[/C][C]-48145.476482092[/C][/ROW]
[ROW][C]39[/C][C]1099663[/C][C]1159424.32816195[/C][C]-59761.3281619453[/C][/ROW]
[ROW][C]40[/C][C]1576220[/C][C]1618305.43853757[/C][C]-42085.4385375711[/C][/ROW]
[ROW][C]41[/C][C]1487870[/C][C]1684310.40220131[/C][C]-196440.402201312[/C][/ROW]
[ROW][C]42[/C][C]1488635[/C][C]1580616.08870402[/C][C]-91981.0887040203[/C][/ROW]
[ROW][C]43[/C][C]2882530[/C][C]3052603.87095771[/C][C]-170073.870957712[/C][/ROW]
[ROW][C]44[/C][C]2677026[/C][C]2658594.00170896[/C][C]18431.9982910408[/C][/ROW]
[ROW][C]45[/C][C]1404398[/C][C]1382085.1236357[/C][C]22312.8763643024[/C][/ROW]
[ROW][C]46[/C][C]1344370[/C][C]1363222.1680807[/C][C]-18852.1680807022[/C][/ROW]
[ROW][C]47[/C][C]936865[/C][C]980944.136344332[/C][C]-44079.1363443315[/C][/ROW]
[ROW][C]48[/C][C]872705[/C][C]897448.364451774[/C][C]-24743.3644517744[/C][/ROW]
[ROW][C]49[/C][C]628151[/C][C]686484.423503429[/C][C]-58333.4235034289[/C][/ROW]
[ROW][C]50[/C][C]953712[/C][C]910130.063399032[/C][C]43581.9366009682[/C][/ROW]
[ROW][C]51[/C][C]1160384[/C][C]1130045.9865214[/C][C]30338.0134786034[/C][/ROW]
[ROW][C]52[/C][C]1400618[/C][C]1590149.14032963[/C][C]-189531.140329626[/C][/ROW]
[ROW][C]53[/C][C]1661511[/C][C]1614652.83871973[/C][C]46858.1612802658[/C][/ROW]
[ROW][C]54[/C][C]1495347[/C][C]1534235.77597549[/C][C]-38888.7759754935[/C][/ROW]
[ROW][C]55[/C][C]2918786[/C][C]2986294.39397479[/C][C]-67508.3939747885[/C][/ROW]
[ROW][C]56[/C][C]2775677[/C][C]2634320.43200135[/C][C]141356.56799865[/C][/ROW]
[ROW][C]57[/C][C]1407026[/C][C]1358878.82211121[/C][C]48147.1778887874[/C][/ROW]
[ROW][C]58[/C][C]1370199[/C][C]1329983.36121324[/C][C]40215.6387867576[/C][/ROW]
[ROW][C]59[/C][C]964526[/C][C]942069.537452604[/C][C]22456.4625473956[/C][/ROW]
[ROW][C]60[/C][C]850851[/C][C]863635.614841921[/C][C]-12784.6148419211[/C][/ROW]
[ROW][C]61[/C][C]683118[/C][C]645188.798904281[/C][C]37929.2010957191[/C][/ROW]
[ROW][C]62[/C][C]847224[/C][C]893781.123067611[/C][C]-46557.123067611[/C][/ROW]
[ROW][C]63[/C][C]1073256[/C][C]1109816.32025077[/C][C]-36560.3202507675[/C][/ROW]
[ROW][C]64[/C][C]1514326[/C][C]1518750.53056872[/C][C]-4424.53056871518[/C][/ROW]
[ROW][C]65[/C][C]1503734[/C][C]1599962.26613267[/C][C]-96228.2661326681[/C][/ROW]
[ROW][C]66[/C][C]1507712[/C][C]1498418.13596715[/C][C]9293.8640328527[/C][/ROW]
[ROW][C]67[/C][C]2865698[/C][C]2944714.99113487[/C][C]-79016.9911348717[/C][/ROW]
[ROW][C]68[/C][C]2788128[/C][C]2640359.05260156[/C][C]147768.947398436[/C][/ROW]
[ROW][C]69[/C][C]1391596[/C][C]1343968.91022251[/C][C]47627.0897774922[/C][/ROW]
[ROW][C]70[/C][C]1366378[/C][C]1313471.14544594[/C][C]52906.8545540588[/C][/ROW]
[ROW][C]71[/C][C]946295[/C][C]921945.3214322[/C][C]24349.6785677993[/C][/ROW]
[ROW][C]72[/C][C]859626[/C][C]835817.371189578[/C][C]23808.6288104225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150522&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150522&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
14913831896192.36335811817638.6366418815
1511085441102247.28958746296.71041260357
1615558271548352.331749587474.6682504178
1716992831690465.55103498817.44896509731
1815094581506785.405946642672.59405335644
1932689752977855.78489077291119.215109231
2024250162665014.057907-239998.057906998
2113127031330826.92605923-18123.9260592286
2213654981308398.9782892157099.02171079
23934453952598.069779977-18145.0697799765
24775019899782.207905648-124763.207905648
25651142675561.942234234-24419.9422342341
26843192935001.614313837-91809.614313837
2711467661136306.4853235610459.5146764361
2816526011581738.6947794370862.3052205718
2914659061724287.43985791-258381.439857911
3016527341533971.35068583118762.64931417
3129223343070356.99921284-148022.999212835
3227028052627221.9287422275583.0712577822
3314589561344416.46037666114539.539623336
3414103631338978.6579186771384.3420813349
351019279964751.75533314354527.2446668567
36936574887491.6382700849082.3617299197
37708917688256.4619695520660.5380304503
38885295933440.476482092-48145.476482092
3910996631159424.32816195-59761.3281619453
4015762201618305.43853757-42085.4385375711
4114878701684310.40220131-196440.402201312
4214886351580616.08870402-91981.0887040203
4328825303052603.87095771-170073.870957712
4426770262658594.0017089618431.9982910408
4514043981382085.123635722312.8763643024
4613443701363222.1680807-18852.1680807022
47936865980944.136344332-44079.1363443315
48872705897448.364451774-24743.3644517744
49628151686484.423503429-58333.4235034289
50953712910130.06339903243581.9366009682
5111603841130045.986521430338.0134786034
5214006181590149.14032963-189531.140329626
5316615111614652.8387197346858.1612802658
5414953471534235.77597549-38888.7759754935
5529187862986294.39397479-67508.3939747885
5627756772634320.43200135141356.56799865
5714070261358878.8221112148147.1778887874
5813701991329983.3612132440215.6387867576
59964526942069.53745260422456.4625473956
60850851863635.614841921-12784.6148419211
61683118645188.79890428137929.2010957191
62847224893781.123067611-46557.123067611
6310732561109816.32025077-36560.3202507675
6415143261518750.53056872-4424.53056871518
6515037341599962.26613267-96228.2661326681
6615077121498418.135967159293.8640328527
6728656982944714.99113487-79016.9911348717
6827881282640359.05260156147768.947398436
6913915961343968.9102225147627.0897774922
7013663781313471.1454459452906.8545540588
71946295921945.321432224349.6785677993
72859626835817.37118957823808.6288104225







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73629877.173186943446566.48697834813187.859395546
74859130.609839542675791.5839945351042469.63568455
751078564.49881338895169.846023951261959.15160281
761496092.435845741312605.778988221679579.09270325
771557362.236521931373738.14534281740986.32770106
781482464.696362251298648.744208481666280.64851602
792910083.9972622726012.841988163094155.15253584
802660304.353705862475905.846610752844702.86080098
811340598.858860641155792.185128391525405.53259288
821311515.085506381126210.93914251496819.23187027
83913267.708003892727368.5036631581099166.91234463
84826928.088856204640328.212261441013527.96545097

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 629877.173186943 & 446566.48697834 & 813187.859395546 \tabularnewline
74 & 859130.609839542 & 675791.583994535 & 1042469.63568455 \tabularnewline
75 & 1078564.49881338 & 895169.84602395 & 1261959.15160281 \tabularnewline
76 & 1496092.43584574 & 1312605.77898822 & 1679579.09270325 \tabularnewline
77 & 1557362.23652193 & 1373738.1453428 & 1740986.32770106 \tabularnewline
78 & 1482464.69636225 & 1298648.74420848 & 1666280.64851602 \tabularnewline
79 & 2910083.997262 & 2726012.84198816 & 3094155.15253584 \tabularnewline
80 & 2660304.35370586 & 2475905.84661075 & 2844702.86080098 \tabularnewline
81 & 1340598.85886064 & 1155792.18512839 & 1525405.53259288 \tabularnewline
82 & 1311515.08550638 & 1126210.9391425 & 1496819.23187027 \tabularnewline
83 & 913267.708003892 & 727368.503663158 & 1099166.91234463 \tabularnewline
84 & 826928.088856204 & 640328.21226144 & 1013527.96545097 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150522&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]629877.173186943[/C][C]446566.48697834[/C][C]813187.859395546[/C][/ROW]
[ROW][C]74[/C][C]859130.609839542[/C][C]675791.583994535[/C][C]1042469.63568455[/C][/ROW]
[ROW][C]75[/C][C]1078564.49881338[/C][C]895169.84602395[/C][C]1261959.15160281[/C][/ROW]
[ROW][C]76[/C][C]1496092.43584574[/C][C]1312605.77898822[/C][C]1679579.09270325[/C][/ROW]
[ROW][C]77[/C][C]1557362.23652193[/C][C]1373738.1453428[/C][C]1740986.32770106[/C][/ROW]
[ROW][C]78[/C][C]1482464.69636225[/C][C]1298648.74420848[/C][C]1666280.64851602[/C][/ROW]
[ROW][C]79[/C][C]2910083.997262[/C][C]2726012.84198816[/C][C]3094155.15253584[/C][/ROW]
[ROW][C]80[/C][C]2660304.35370586[/C][C]2475905.84661075[/C][C]2844702.86080098[/C][/ROW]
[ROW][C]81[/C][C]1340598.85886064[/C][C]1155792.18512839[/C][C]1525405.53259288[/C][/ROW]
[ROW][C]82[/C][C]1311515.08550638[/C][C]1126210.9391425[/C][C]1496819.23187027[/C][/ROW]
[ROW][C]83[/C][C]913267.708003892[/C][C]727368.503663158[/C][C]1099166.91234463[/C][/ROW]
[ROW][C]84[/C][C]826928.088856204[/C][C]640328.21226144[/C][C]1013527.96545097[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150522&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150522&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
73629877.173186943446566.48697834813187.859395546
74859130.609839542675791.5839945351042469.63568455
751078564.49881338895169.846023951261959.15160281
761496092.435845741312605.778988221679579.09270325
771557362.236521931373738.14534281740986.32770106
781482464.696362251298648.744208481666280.64851602
792910083.9972622726012.841988163094155.15253584
802660304.353705862475905.846610752844702.86080098
811340598.858860641155792.185128391525405.53259288
821311515.085506381126210.93914251496819.23187027
83913267.708003892727368.5036631581099166.91234463
84826928.088856204640328.212261441013527.96545097



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')