Free Statistics

of Irreproducible Research!

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, 30 Nov 2014 14:20:54 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/30/t1417357289i9gtg2079gukl3l.htm/, Retrieved Sun, 19 May 2024 12:56:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261457, Retrieved Sun, 19 May 2024 12:56:31 +0000
QR Codes:

Original text written by user:Type 3
IsPrivate?No (this computation is public)
User-defined keywordsExponential Smoothing
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Workshop 9] [2014-11-30 14:20:54] [99d5c1073827aabbadf7ab1e7da1d584] [Current]
Feedback Forum

Post a new message
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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261457&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261457&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261457&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0105300002194997
beta0.66996223840364
gamma0.230183992193615

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0105300002194997 \tabularnewline
beta & 0.66996223840364 \tabularnewline
gamma & 0.230183992193615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261457&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]0.0105300002194997[/C][/ROW]
[ROW][C]beta[/C][C]0.66996223840364[/C][/ROW]
[ROW][C]gamma[/C][C]0.230183992193615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261457&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261457&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
alpha0.0105300002194997
beta0.66996223840364
gamma0.230183992193615







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13652586636418.06730769316167.9326923072
14913831896192.36336019617638.6366398042
1511085441102247.289593236296.71040677093
1615558271548352.33175937474.66824070318
1716992831690465.551049148817.44895086391
1815094581506785.405966132672.59403387411
1932689752977855.78491535291119.215084651
2024250162665014.05797375-239998.057973754
2113127031330826.9261265-18123.9261265029
2213654981308398.9783623757099.0216376325
23934453952598.069866391-18145.0698663908
24775019899782.208000295-124763.208000295
25651142675561.942316613-24419.9423166127
26843192935001.614388078-91809.6143880782
2711467661136306.4853813210459.5146186771
2816526011581738.6948215570862.3051784467
2914659061724287.43989283-258381.439892827
3016527341533971.35067961118762.649320393
3129223343070356.999111-148022.999111003
3227028052627221.9287348875583.0712651229
3314589561344416.46028509114539.539714908
3414103631338978.6577946671384.3422053449
351019279964751.7552218754527.24477813
36936574887491.63818632949082.361813671
37708917688256.46186287520660.5381371245
38885295933440.476402001-48145.4764020011
3910996631159424.32806127-59761.3280612733
4015762201618305.43841886-42085.4384188592
4114878701684310.40216465-196440.402164646
4214886351580616.08854505-91981.0885450514
4328825303052603.87077989-170073.870779886
4426770262658594.0015315918431.9984684121
4514043981382085.123365922312.8766340988
4613443701363222.16777195-18852.1677719511
47936865980944.136017377-44079.1360173773
48872705897448.364107228-24743.3641072277
49628151686484.423104689-58333.4231046885
50953712910130.0629899243581.9370100797
5111603841130045.9860673330338.0139326691
5214006181590149.13983591-189531.139835909
5316615111614652.8382906846858.1617093235
5414953471534235.77542308-38888.7754230753
5529187862986294.39342919-67508.3934291936
5627756772634320.43141966141356.568580344
5714070261358878.8214867648147.1785132389
5813701991329983.3606005240215.6393994777
59964526942069.53687168322456.4631283171
60850851863635.614289114-12784.6142891144
61683118645188.79836578137929.2016342187
62847224893781.122553128-46557.1225531278
6310732561109816.31975001-36560.3197500149
6415143261518750.53013541-4424.53013541177
6515037341599962.26574946-96228.2657494585
6615077121498418.135550419293.86444959231
6728656982944714.99077897-79016.9907789668
6827881282640359.05220461147768.947795393
6913915961343968.9098603747627.0901396349
7013663781313471.1451348652906.8548651412
71946295921945.32118941724349.6788105826
72859626835817.3710139823808.62898602

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 652586 & 636418.067307693 & 16167.9326923072 \tabularnewline
14 & 913831 & 896192.363360196 & 17638.6366398042 \tabularnewline
15 & 1108544 & 1102247.28959323 & 6296.71040677093 \tabularnewline
16 & 1555827 & 1548352.3317593 & 7474.66824070318 \tabularnewline
17 & 1699283 & 1690465.55104914 & 8817.44895086391 \tabularnewline
18 & 1509458 & 1506785.40596613 & 2672.59403387411 \tabularnewline
19 & 3268975 & 2977855.78491535 & 291119.215084651 \tabularnewline
20 & 2425016 & 2665014.05797375 & -239998.057973754 \tabularnewline
21 & 1312703 & 1330826.9261265 & -18123.9261265029 \tabularnewline
22 & 1365498 & 1308398.97836237 & 57099.0216376325 \tabularnewline
23 & 934453 & 952598.069866391 & -18145.0698663908 \tabularnewline
24 & 775019 & 899782.208000295 & -124763.208000295 \tabularnewline
25 & 651142 & 675561.942316613 & -24419.9423166127 \tabularnewline
26 & 843192 & 935001.614388078 & -91809.6143880782 \tabularnewline
27 & 1146766 & 1136306.48538132 & 10459.5146186771 \tabularnewline
28 & 1652601 & 1581738.69482155 & 70862.3051784467 \tabularnewline
29 & 1465906 & 1724287.43989283 & -258381.439892827 \tabularnewline
30 & 1652734 & 1533971.35067961 & 118762.649320393 \tabularnewline
31 & 2922334 & 3070356.999111 & -148022.999111003 \tabularnewline
32 & 2702805 & 2627221.92873488 & 75583.0712651229 \tabularnewline
33 & 1458956 & 1344416.46028509 & 114539.539714908 \tabularnewline
34 & 1410363 & 1338978.65779466 & 71384.3422053449 \tabularnewline
35 & 1019279 & 964751.75522187 & 54527.24477813 \tabularnewline
36 & 936574 & 887491.638186329 & 49082.361813671 \tabularnewline
37 & 708917 & 688256.461862875 & 20660.5381371245 \tabularnewline
38 & 885295 & 933440.476402001 & -48145.4764020011 \tabularnewline
39 & 1099663 & 1159424.32806127 & -59761.3280612733 \tabularnewline
40 & 1576220 & 1618305.43841886 & -42085.4384188592 \tabularnewline
41 & 1487870 & 1684310.40216465 & -196440.402164646 \tabularnewline
42 & 1488635 & 1580616.08854505 & -91981.0885450514 \tabularnewline
43 & 2882530 & 3052603.87077989 & -170073.870779886 \tabularnewline
44 & 2677026 & 2658594.00153159 & 18431.9984684121 \tabularnewline
45 & 1404398 & 1382085.1233659 & 22312.8766340988 \tabularnewline
46 & 1344370 & 1363222.16777195 & -18852.1677719511 \tabularnewline
47 & 936865 & 980944.136017377 & -44079.1360173773 \tabularnewline
48 & 872705 & 897448.364107228 & -24743.3641072277 \tabularnewline
49 & 628151 & 686484.423104689 & -58333.4231046885 \tabularnewline
50 & 953712 & 910130.06298992 & 43581.9370100797 \tabularnewline
51 & 1160384 & 1130045.98606733 & 30338.0139326691 \tabularnewline
52 & 1400618 & 1590149.13983591 & -189531.139835909 \tabularnewline
53 & 1661511 & 1614652.83829068 & 46858.1617093235 \tabularnewline
54 & 1495347 & 1534235.77542308 & -38888.7754230753 \tabularnewline
55 & 2918786 & 2986294.39342919 & -67508.3934291936 \tabularnewline
56 & 2775677 & 2634320.43141966 & 141356.568580344 \tabularnewline
57 & 1407026 & 1358878.82148676 & 48147.1785132389 \tabularnewline
58 & 1370199 & 1329983.36060052 & 40215.6393994777 \tabularnewline
59 & 964526 & 942069.536871683 & 22456.4631283171 \tabularnewline
60 & 850851 & 863635.614289114 & -12784.6142891144 \tabularnewline
61 & 683118 & 645188.798365781 & 37929.2016342187 \tabularnewline
62 & 847224 & 893781.122553128 & -46557.1225531278 \tabularnewline
63 & 1073256 & 1109816.31975001 & -36560.3197500149 \tabularnewline
64 & 1514326 & 1518750.53013541 & -4424.53013541177 \tabularnewline
65 & 1503734 & 1599962.26574946 & -96228.2657494585 \tabularnewline
66 & 1507712 & 1498418.13555041 & 9293.86444959231 \tabularnewline
67 & 2865698 & 2944714.99077897 & -79016.9907789668 \tabularnewline
68 & 2788128 & 2640359.05220461 & 147768.947795393 \tabularnewline
69 & 1391596 & 1343968.90986037 & 47627.0901396349 \tabularnewline
70 & 1366378 & 1313471.14513486 & 52906.8548651412 \tabularnewline
71 & 946295 & 921945.321189417 & 24349.6788105826 \tabularnewline
72 & 859626 & 835817.37101398 & 23808.62898602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261457&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]636418.067307693[/C][C]16167.9326923072[/C][/ROW]
[ROW][C]14[/C][C]913831[/C][C]896192.363360196[/C][C]17638.6366398042[/C][/ROW]
[ROW][C]15[/C][C]1108544[/C][C]1102247.28959323[/C][C]6296.71040677093[/C][/ROW]
[ROW][C]16[/C][C]1555827[/C][C]1548352.3317593[/C][C]7474.66824070318[/C][/ROW]
[ROW][C]17[/C][C]1699283[/C][C]1690465.55104914[/C][C]8817.44895086391[/C][/ROW]
[ROW][C]18[/C][C]1509458[/C][C]1506785.40596613[/C][C]2672.59403387411[/C][/ROW]
[ROW][C]19[/C][C]3268975[/C][C]2977855.78491535[/C][C]291119.215084651[/C][/ROW]
[ROW][C]20[/C][C]2425016[/C][C]2665014.05797375[/C][C]-239998.057973754[/C][/ROW]
[ROW][C]21[/C][C]1312703[/C][C]1330826.9261265[/C][C]-18123.9261265029[/C][/ROW]
[ROW][C]22[/C][C]1365498[/C][C]1308398.97836237[/C][C]57099.0216376325[/C][/ROW]
[ROW][C]23[/C][C]934453[/C][C]952598.069866391[/C][C]-18145.0698663908[/C][/ROW]
[ROW][C]24[/C][C]775019[/C][C]899782.208000295[/C][C]-124763.208000295[/C][/ROW]
[ROW][C]25[/C][C]651142[/C][C]675561.942316613[/C][C]-24419.9423166127[/C][/ROW]
[ROW][C]26[/C][C]843192[/C][C]935001.614388078[/C][C]-91809.6143880782[/C][/ROW]
[ROW][C]27[/C][C]1146766[/C][C]1136306.48538132[/C][C]10459.5146186771[/C][/ROW]
[ROW][C]28[/C][C]1652601[/C][C]1581738.69482155[/C][C]70862.3051784467[/C][/ROW]
[ROW][C]29[/C][C]1465906[/C][C]1724287.43989283[/C][C]-258381.439892827[/C][/ROW]
[ROW][C]30[/C][C]1652734[/C][C]1533971.35067961[/C][C]118762.649320393[/C][/ROW]
[ROW][C]31[/C][C]2922334[/C][C]3070356.999111[/C][C]-148022.999111003[/C][/ROW]
[ROW][C]32[/C][C]2702805[/C][C]2627221.92873488[/C][C]75583.0712651229[/C][/ROW]
[ROW][C]33[/C][C]1458956[/C][C]1344416.46028509[/C][C]114539.539714908[/C][/ROW]
[ROW][C]34[/C][C]1410363[/C][C]1338978.65779466[/C][C]71384.3422053449[/C][/ROW]
[ROW][C]35[/C][C]1019279[/C][C]964751.75522187[/C][C]54527.24477813[/C][/ROW]
[ROW][C]36[/C][C]936574[/C][C]887491.638186329[/C][C]49082.361813671[/C][/ROW]
[ROW][C]37[/C][C]708917[/C][C]688256.461862875[/C][C]20660.5381371245[/C][/ROW]
[ROW][C]38[/C][C]885295[/C][C]933440.476402001[/C][C]-48145.4764020011[/C][/ROW]
[ROW][C]39[/C][C]1099663[/C][C]1159424.32806127[/C][C]-59761.3280612733[/C][/ROW]
[ROW][C]40[/C][C]1576220[/C][C]1618305.43841886[/C][C]-42085.4384188592[/C][/ROW]
[ROW][C]41[/C][C]1487870[/C][C]1684310.40216465[/C][C]-196440.402164646[/C][/ROW]
[ROW][C]42[/C][C]1488635[/C][C]1580616.08854505[/C][C]-91981.0885450514[/C][/ROW]
[ROW][C]43[/C][C]2882530[/C][C]3052603.87077989[/C][C]-170073.870779886[/C][/ROW]
[ROW][C]44[/C][C]2677026[/C][C]2658594.00153159[/C][C]18431.9984684121[/C][/ROW]
[ROW][C]45[/C][C]1404398[/C][C]1382085.1233659[/C][C]22312.8766340988[/C][/ROW]
[ROW][C]46[/C][C]1344370[/C][C]1363222.16777195[/C][C]-18852.1677719511[/C][/ROW]
[ROW][C]47[/C][C]936865[/C][C]980944.136017377[/C][C]-44079.1360173773[/C][/ROW]
[ROW][C]48[/C][C]872705[/C][C]897448.364107228[/C][C]-24743.3641072277[/C][/ROW]
[ROW][C]49[/C][C]628151[/C][C]686484.423104689[/C][C]-58333.4231046885[/C][/ROW]
[ROW][C]50[/C][C]953712[/C][C]910130.06298992[/C][C]43581.9370100797[/C][/ROW]
[ROW][C]51[/C][C]1160384[/C][C]1130045.98606733[/C][C]30338.0139326691[/C][/ROW]
[ROW][C]52[/C][C]1400618[/C][C]1590149.13983591[/C][C]-189531.139835909[/C][/ROW]
[ROW][C]53[/C][C]1661511[/C][C]1614652.83829068[/C][C]46858.1617093235[/C][/ROW]
[ROW][C]54[/C][C]1495347[/C][C]1534235.77542308[/C][C]-38888.7754230753[/C][/ROW]
[ROW][C]55[/C][C]2918786[/C][C]2986294.39342919[/C][C]-67508.3934291936[/C][/ROW]
[ROW][C]56[/C][C]2775677[/C][C]2634320.43141966[/C][C]141356.568580344[/C][/ROW]
[ROW][C]57[/C][C]1407026[/C][C]1358878.82148676[/C][C]48147.1785132389[/C][/ROW]
[ROW][C]58[/C][C]1370199[/C][C]1329983.36060052[/C][C]40215.6393994777[/C][/ROW]
[ROW][C]59[/C][C]964526[/C][C]942069.536871683[/C][C]22456.4631283171[/C][/ROW]
[ROW][C]60[/C][C]850851[/C][C]863635.614289114[/C][C]-12784.6142891144[/C][/ROW]
[ROW][C]61[/C][C]683118[/C][C]645188.798365781[/C][C]37929.2016342187[/C][/ROW]
[ROW][C]62[/C][C]847224[/C][C]893781.122553128[/C][C]-46557.1225531278[/C][/ROW]
[ROW][C]63[/C][C]1073256[/C][C]1109816.31975001[/C][C]-36560.3197500149[/C][/ROW]
[ROW][C]64[/C][C]1514326[/C][C]1518750.53013541[/C][C]-4424.53013541177[/C][/ROW]
[ROW][C]65[/C][C]1503734[/C][C]1599962.26574946[/C][C]-96228.2657494585[/C][/ROW]
[ROW][C]66[/C][C]1507712[/C][C]1498418.13555041[/C][C]9293.86444959231[/C][/ROW]
[ROW][C]67[/C][C]2865698[/C][C]2944714.99077897[/C][C]-79016.9907789668[/C][/ROW]
[ROW][C]68[/C][C]2788128[/C][C]2640359.05220461[/C][C]147768.947795393[/C][/ROW]
[ROW][C]69[/C][C]1391596[/C][C]1343968.90986037[/C][C]47627.0901396349[/C][/ROW]
[ROW][C]70[/C][C]1366378[/C][C]1313471.14513486[/C][C]52906.8548651412[/C][/ROW]
[ROW][C]71[/C][C]946295[/C][C]921945.321189417[/C][C]24349.6788105826[/C][/ROW]
[ROW][C]72[/C][C]859626[/C][C]835817.37101398[/C][C]23808.62898602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261457&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261457&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
13652586636418.06730769316167.9326923072
14913831896192.36336019617638.6366398042
1511085441102247.289593236296.71040677093
1615558271548352.33175937474.66824070318
1716992831690465.551049148817.44895086391
1815094581506785.405966132672.59403387411
1932689752977855.78491535291119.215084651
2024250162665014.05797375-239998.057973754
2113127031330826.9261265-18123.9261265029
2213654981308398.9783623757099.0216376325
23934453952598.069866391-18145.0698663908
24775019899782.208000295-124763.208000295
25651142675561.942316613-24419.9423166127
26843192935001.614388078-91809.6143880782
2711467661136306.4853813210459.5146186771
2816526011581738.6948215570862.3051784467
2914659061724287.43989283-258381.439892827
3016527341533971.35067961118762.649320393
3129223343070356.999111-148022.999111003
3227028052627221.9287348875583.0712651229
3314589561344416.46028509114539.539714908
3414103631338978.6577946671384.3422053449
351019279964751.7552218754527.24477813
36936574887491.63818632949082.361813671
37708917688256.46186287520660.5381371245
38885295933440.476402001-48145.4764020011
3910996631159424.32806127-59761.3280612733
4015762201618305.43841886-42085.4384188592
4114878701684310.40216465-196440.402164646
4214886351580616.08854505-91981.0885450514
4328825303052603.87077989-170073.870779886
4426770262658594.0015315918431.9984684121
4514043981382085.123365922312.8766340988
4613443701363222.16777195-18852.1677719511
47936865980944.136017377-44079.1360173773
48872705897448.364107228-24743.3641072277
49628151686484.423104689-58333.4231046885
50953712910130.0629899243581.9370100797
5111603841130045.9860673330338.0139326691
5214006181590149.13983591-189531.139835909
5316615111614652.8382906846858.1617093235
5414953471534235.77542308-38888.7754230753
5529187862986294.39342919-67508.3934291936
5627756772634320.43141966141356.568580344
5714070261358878.8214867648147.1785132389
5813701991329983.3606005240215.6393994777
59964526942069.53687168322456.4631283171
60850851863635.614289114-12784.6142891144
61683118645188.79836578137929.2016342187
62847224893781.122553128-46557.1225531278
6310732561109816.31975001-36560.3197500149
6415143261518750.53013541-4424.53013541177
6515037341599962.26574946-96228.2657494585
6615077121498418.135550419293.86444959231
6728656982944714.99077897-79016.9907789668
6827881282640359.05220461147768.947795393
6913915961343968.9098603747627.0901396349
7013663781313471.1451348652906.8548651412
71946295921945.32118941724349.6788105826
72859626835817.3710139823808.62898602







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73629877.173046372446566.486799175813187.859293568
74859130.609766151675791.5838821311042469.63565017
751078564.49877778895169.8459483121261959.15160724
761496092.435883181312605.778983781679579.09278258
771557362.236649251373738.145425281740986.32787321
781482464.696471961298648.744269091666280.64867484
792910083.997471222726012.842142443094155.1528
802660304.353859962475905.846702282844702.86101765
811340598.859081011155792.185276561525405.53288547
821311515.085774031126210.939326051496819.232222
83913267.708334358727368.5038952231099166.91277349
84826928.089238799640328.212528691013527.96594891

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 629877.173046372 & 446566.486799175 & 813187.859293568 \tabularnewline
74 & 859130.609766151 & 675791.583882131 & 1042469.63565017 \tabularnewline
75 & 1078564.49877778 & 895169.845948312 & 1261959.15160724 \tabularnewline
76 & 1496092.43588318 & 1312605.77898378 & 1679579.09278258 \tabularnewline
77 & 1557362.23664925 & 1373738.14542528 & 1740986.32787321 \tabularnewline
78 & 1482464.69647196 & 1298648.74426909 & 1666280.64867484 \tabularnewline
79 & 2910083.99747122 & 2726012.84214244 & 3094155.1528 \tabularnewline
80 & 2660304.35385996 & 2475905.84670228 & 2844702.86101765 \tabularnewline
81 & 1340598.85908101 & 1155792.18527656 & 1525405.53288547 \tabularnewline
82 & 1311515.08577403 & 1126210.93932605 & 1496819.232222 \tabularnewline
83 & 913267.708334358 & 727368.503895223 & 1099166.91277349 \tabularnewline
84 & 826928.089238799 & 640328.21252869 & 1013527.96594891 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261457&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]629877.173046372[/C][C]446566.486799175[/C][C]813187.859293568[/C][/ROW]
[ROW][C]74[/C][C]859130.609766151[/C][C]675791.583882131[/C][C]1042469.63565017[/C][/ROW]
[ROW][C]75[/C][C]1078564.49877778[/C][C]895169.845948312[/C][C]1261959.15160724[/C][/ROW]
[ROW][C]76[/C][C]1496092.43588318[/C][C]1312605.77898378[/C][C]1679579.09278258[/C][/ROW]
[ROW][C]77[/C][C]1557362.23664925[/C][C]1373738.14542528[/C][C]1740986.32787321[/C][/ROW]
[ROW][C]78[/C][C]1482464.69647196[/C][C]1298648.74426909[/C][C]1666280.64867484[/C][/ROW]
[ROW][C]79[/C][C]2910083.99747122[/C][C]2726012.84214244[/C][C]3094155.1528[/C][/ROW]
[ROW][C]80[/C][C]2660304.35385996[/C][C]2475905.84670228[/C][C]2844702.86101765[/C][/ROW]
[ROW][C]81[/C][C]1340598.85908101[/C][C]1155792.18527656[/C][C]1525405.53288547[/C][/ROW]
[ROW][C]82[/C][C]1311515.08577403[/C][C]1126210.93932605[/C][C]1496819.232222[/C][/ROW]
[ROW][C]83[/C][C]913267.708334358[/C][C]727368.503895223[/C][C]1099166.91277349[/C][/ROW]
[ROW][C]84[/C][C]826928.089238799[/C][C]640328.21252869[/C][C]1013527.96594891[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261457&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261457&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
73629877.173046372446566.486799175813187.859293568
74859130.609766151675791.5838821311042469.63565017
751078564.49877778895169.8459483121261959.15160724
761496092.435883181312605.778983781679579.09278258
771557362.236649251373738.145425281740986.32787321
781482464.696471961298648.744269091666280.64867484
792910083.997471222726012.842142443094155.1528
802660304.353859962475905.846702282844702.86101765
811340598.859081011155792.185276561525405.53288547
821311515.085774031126210.939326051496819.232222
83913267.708334358727368.5038952231099166.91277349
84826928.089238799640328.212528691013527.96594891



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')