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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 01 Dec 2014 20:54:41 +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/Dec/01/t14174673097qslwsyd5uu4s1g.htm/, Retrieved Thu, 16 May 2024 17:05:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=262280, Retrieved Thu, 16 May 2024 17:05:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-01 20:54:41] [5cac5f97919544233533b60e31cabb24] [Current]
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Dataseries X:
8378669
7557530
8656721
7729873
7067002
7222189
6758161
6745665
8203660
8799755
7995151
6844694
7400186
6146183
6793027
5815146
5993505
5838016
5926815
5642890
7120621
7781743
7638921
5886070
7358890
6981189
8423532
6819313
6727221
6923349
7578240
7228898
8988846
8404694
9601659
8213138
8434646
8466539
9106270
8438555
7723821
7538413
7199881
8168314
9045790
8544483
9020709
7932021
8435986
7920357
8333659
7415547
7770392
8188878
8092465
7188528
8152373
9025069
9233973
6916290
8171721
7012501
8779456
7308709
8084547
8255978
7658071
7371877
8780827
10116778
9567175
7455902




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262280&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262280&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262280&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.588460610154994
beta0.144021903700917
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.588460610154994 \tabularnewline
beta & 0.144021903700917 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262280&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]0.588460610154994[/C][/ROW]
[ROW][C]beta[/C][C]0.144021903700917[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262280&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262280&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
alpha0.588460610154994
beta0.144021903700917
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3865672167363911920330
477298737208040.86866951521832.131330494
570670026900955.73661217166046.263387827
672221896398577.25857558823611.741424421
767581616352952.26065222405208.739347778
867456656095455.51076764650209.489232361
982036606037238.097378922166421.90262108
1087997557054858.859389651744896.14061035
1179951517972310.3863183322840.6136816721
1268446947878335.8369638-1033641.8369638
1374001867075060.57612106325125.423878941
1461461837098921.10211033-952738.102110334
1567930276290063.56395298502963.436047019
1658151466380455.80461949-565309.804619486
1759935055794300.62816244199204.37183756
1858380165674914.74346565163101.256534352
1959268155548106.62754797378708.37245203
2056428905580270.802194462619.1978055965
2171206215431736.001507111688884.99849289
2277817436383329.625714921398413.37428508
2376389217282509.37650645356411.623493551
2458860707598718.46020538-1712648.46020538
2573588906552218.14274698806671.857253022
2669811897056605.01836207-75416.0183620676
2784235327035526.32512021388005.6748798
2868193137993248.82500107-1173935.82500107
2967272217343877.17644741-616656.176447413
3069233496970180.28828214-46831.2882821448
3175782406927833.89279718650406.107202816
3272288987350906.94982488-122008.949824877
3389888467309103.764078641679742.23592136
3484046948469920.37973491-65226.3797349092
3596016598598363.684036381003295.31596362
3682131389440620.41671937-1227482.41671937
3784346468866121.69464246-431475.694642458
3884665398723473.48355821-256934.483558213
3991062708661760.38979082444509.610209184
4084385559050492.24601041-611937.246010412
4177238218765684.31409526-1041863.31409526
4275384138139582.6416749-601169.641674901
4371998817721861.97766617-521980.977666171
4481683147306502.19991836861811.800081642
4590457907778489.563656241267300.43634376
4685444838596496.27239968-52013.2723996826
4790207098633730.64295705386978.35704295
4879320218962091.18246796-1030070.18246796
4984359868369274.7719020966711.2280979082
5079203578427524.87719518-507167.877195181
5183336598105086.63905059228572.360949412
5274155478234974.33619803-819427.336198031
5377703927678708.0278656191683.9721343927
5481888787666365.16420141522512.835798591
5580924657951831.71542461140633.284575385
5671885288024496.03499383-835968.03499383
5781523737451619.63755855700753.362441452
5890250697842432.951809541182636.04819046
5992339738617045.09007907616927.909920929
6069162909111045.66350199-2194755.66350199
6181717217764472.99152742407248.008472584
6270125017983591.75246079-971090.752460794
6387794567309311.321728481470144.67827152
6473087098196198.33322799-887489.333227992
6580845477620494.79444207464052.205557932
6682559787879449.20354448376528.796455516
6776580718118810.80778212-460739.807782122
6873718777826424.55872567-454547.558725674
6987808277499158.745391961281668.25460804
70101167788302210.493721431814567.50627857
7195671759572639.26592016-5464.26592015848
7274559029771587.92776081-2315685.92776081

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8656721 & 6736391 & 1920330 \tabularnewline
4 & 7729873 & 7208040.86866951 & 521832.131330494 \tabularnewline
5 & 7067002 & 6900955.73661217 & 166046.263387827 \tabularnewline
6 & 7222189 & 6398577.25857558 & 823611.741424421 \tabularnewline
7 & 6758161 & 6352952.26065222 & 405208.739347778 \tabularnewline
8 & 6745665 & 6095455.51076764 & 650209.489232361 \tabularnewline
9 & 8203660 & 6037238.09737892 & 2166421.90262108 \tabularnewline
10 & 8799755 & 7054858.85938965 & 1744896.14061035 \tabularnewline
11 & 7995151 & 7972310.38631833 & 22840.6136816721 \tabularnewline
12 & 6844694 & 7878335.8369638 & -1033641.8369638 \tabularnewline
13 & 7400186 & 7075060.57612106 & 325125.423878941 \tabularnewline
14 & 6146183 & 7098921.10211033 & -952738.102110334 \tabularnewline
15 & 6793027 & 6290063.56395298 & 502963.436047019 \tabularnewline
16 & 5815146 & 6380455.80461949 & -565309.804619486 \tabularnewline
17 & 5993505 & 5794300.62816244 & 199204.37183756 \tabularnewline
18 & 5838016 & 5674914.74346565 & 163101.256534352 \tabularnewline
19 & 5926815 & 5548106.62754797 & 378708.37245203 \tabularnewline
20 & 5642890 & 5580270.8021944 & 62619.1978055965 \tabularnewline
21 & 7120621 & 5431736.00150711 & 1688884.99849289 \tabularnewline
22 & 7781743 & 6383329.62571492 & 1398413.37428508 \tabularnewline
23 & 7638921 & 7282509.37650645 & 356411.623493551 \tabularnewline
24 & 5886070 & 7598718.46020538 & -1712648.46020538 \tabularnewline
25 & 7358890 & 6552218.14274698 & 806671.857253022 \tabularnewline
26 & 6981189 & 7056605.01836207 & -75416.0183620676 \tabularnewline
27 & 8423532 & 7035526.3251202 & 1388005.6748798 \tabularnewline
28 & 6819313 & 7993248.82500107 & -1173935.82500107 \tabularnewline
29 & 6727221 & 7343877.17644741 & -616656.176447413 \tabularnewline
30 & 6923349 & 6970180.28828214 & -46831.2882821448 \tabularnewline
31 & 7578240 & 6927833.89279718 & 650406.107202816 \tabularnewline
32 & 7228898 & 7350906.94982488 & -122008.949824877 \tabularnewline
33 & 8988846 & 7309103.76407864 & 1679742.23592136 \tabularnewline
34 & 8404694 & 8469920.37973491 & -65226.3797349092 \tabularnewline
35 & 9601659 & 8598363.68403638 & 1003295.31596362 \tabularnewline
36 & 8213138 & 9440620.41671937 & -1227482.41671937 \tabularnewline
37 & 8434646 & 8866121.69464246 & -431475.694642458 \tabularnewline
38 & 8466539 & 8723473.48355821 & -256934.483558213 \tabularnewline
39 & 9106270 & 8661760.38979082 & 444509.610209184 \tabularnewline
40 & 8438555 & 9050492.24601041 & -611937.246010412 \tabularnewline
41 & 7723821 & 8765684.31409526 & -1041863.31409526 \tabularnewline
42 & 7538413 & 8139582.6416749 & -601169.641674901 \tabularnewline
43 & 7199881 & 7721861.97766617 & -521980.977666171 \tabularnewline
44 & 8168314 & 7306502.19991836 & 861811.800081642 \tabularnewline
45 & 9045790 & 7778489.56365624 & 1267300.43634376 \tabularnewline
46 & 8544483 & 8596496.27239968 & -52013.2723996826 \tabularnewline
47 & 9020709 & 8633730.64295705 & 386978.35704295 \tabularnewline
48 & 7932021 & 8962091.18246796 & -1030070.18246796 \tabularnewline
49 & 8435986 & 8369274.77190209 & 66711.2280979082 \tabularnewline
50 & 7920357 & 8427524.87719518 & -507167.877195181 \tabularnewline
51 & 8333659 & 8105086.63905059 & 228572.360949412 \tabularnewline
52 & 7415547 & 8234974.33619803 & -819427.336198031 \tabularnewline
53 & 7770392 & 7678708.02786561 & 91683.9721343927 \tabularnewline
54 & 8188878 & 7666365.16420141 & 522512.835798591 \tabularnewline
55 & 8092465 & 7951831.71542461 & 140633.284575385 \tabularnewline
56 & 7188528 & 8024496.03499383 & -835968.03499383 \tabularnewline
57 & 8152373 & 7451619.63755855 & 700753.362441452 \tabularnewline
58 & 9025069 & 7842432.95180954 & 1182636.04819046 \tabularnewline
59 & 9233973 & 8617045.09007907 & 616927.909920929 \tabularnewline
60 & 6916290 & 9111045.66350199 & -2194755.66350199 \tabularnewline
61 & 8171721 & 7764472.99152742 & 407248.008472584 \tabularnewline
62 & 7012501 & 7983591.75246079 & -971090.752460794 \tabularnewline
63 & 8779456 & 7309311.32172848 & 1470144.67827152 \tabularnewline
64 & 7308709 & 8196198.33322799 & -887489.333227992 \tabularnewline
65 & 8084547 & 7620494.79444207 & 464052.205557932 \tabularnewline
66 & 8255978 & 7879449.20354448 & 376528.796455516 \tabularnewline
67 & 7658071 & 8118810.80778212 & -460739.807782122 \tabularnewline
68 & 7371877 & 7826424.55872567 & -454547.558725674 \tabularnewline
69 & 8780827 & 7499158.74539196 & 1281668.25460804 \tabularnewline
70 & 10116778 & 8302210.49372143 & 1814567.50627857 \tabularnewline
71 & 9567175 & 9572639.26592016 & -5464.26592015848 \tabularnewline
72 & 7455902 & 9771587.92776081 & -2315685.92776081 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262280&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]3[/C][C]8656721[/C][C]6736391[/C][C]1920330[/C][/ROW]
[ROW][C]4[/C][C]7729873[/C][C]7208040.86866951[/C][C]521832.131330494[/C][/ROW]
[ROW][C]5[/C][C]7067002[/C][C]6900955.73661217[/C][C]166046.263387827[/C][/ROW]
[ROW][C]6[/C][C]7222189[/C][C]6398577.25857558[/C][C]823611.741424421[/C][/ROW]
[ROW][C]7[/C][C]6758161[/C][C]6352952.26065222[/C][C]405208.739347778[/C][/ROW]
[ROW][C]8[/C][C]6745665[/C][C]6095455.51076764[/C][C]650209.489232361[/C][/ROW]
[ROW][C]9[/C][C]8203660[/C][C]6037238.09737892[/C][C]2166421.90262108[/C][/ROW]
[ROW][C]10[/C][C]8799755[/C][C]7054858.85938965[/C][C]1744896.14061035[/C][/ROW]
[ROW][C]11[/C][C]7995151[/C][C]7972310.38631833[/C][C]22840.6136816721[/C][/ROW]
[ROW][C]12[/C][C]6844694[/C][C]7878335.8369638[/C][C]-1033641.8369638[/C][/ROW]
[ROW][C]13[/C][C]7400186[/C][C]7075060.57612106[/C][C]325125.423878941[/C][/ROW]
[ROW][C]14[/C][C]6146183[/C][C]7098921.10211033[/C][C]-952738.102110334[/C][/ROW]
[ROW][C]15[/C][C]6793027[/C][C]6290063.56395298[/C][C]502963.436047019[/C][/ROW]
[ROW][C]16[/C][C]5815146[/C][C]6380455.80461949[/C][C]-565309.804619486[/C][/ROW]
[ROW][C]17[/C][C]5993505[/C][C]5794300.62816244[/C][C]199204.37183756[/C][/ROW]
[ROW][C]18[/C][C]5838016[/C][C]5674914.74346565[/C][C]163101.256534352[/C][/ROW]
[ROW][C]19[/C][C]5926815[/C][C]5548106.62754797[/C][C]378708.37245203[/C][/ROW]
[ROW][C]20[/C][C]5642890[/C][C]5580270.8021944[/C][C]62619.1978055965[/C][/ROW]
[ROW][C]21[/C][C]7120621[/C][C]5431736.00150711[/C][C]1688884.99849289[/C][/ROW]
[ROW][C]22[/C][C]7781743[/C][C]6383329.62571492[/C][C]1398413.37428508[/C][/ROW]
[ROW][C]23[/C][C]7638921[/C][C]7282509.37650645[/C][C]356411.623493551[/C][/ROW]
[ROW][C]24[/C][C]5886070[/C][C]7598718.46020538[/C][C]-1712648.46020538[/C][/ROW]
[ROW][C]25[/C][C]7358890[/C][C]6552218.14274698[/C][C]806671.857253022[/C][/ROW]
[ROW][C]26[/C][C]6981189[/C][C]7056605.01836207[/C][C]-75416.0183620676[/C][/ROW]
[ROW][C]27[/C][C]8423532[/C][C]7035526.3251202[/C][C]1388005.6748798[/C][/ROW]
[ROW][C]28[/C][C]6819313[/C][C]7993248.82500107[/C][C]-1173935.82500107[/C][/ROW]
[ROW][C]29[/C][C]6727221[/C][C]7343877.17644741[/C][C]-616656.176447413[/C][/ROW]
[ROW][C]30[/C][C]6923349[/C][C]6970180.28828214[/C][C]-46831.2882821448[/C][/ROW]
[ROW][C]31[/C][C]7578240[/C][C]6927833.89279718[/C][C]650406.107202816[/C][/ROW]
[ROW][C]32[/C][C]7228898[/C][C]7350906.94982488[/C][C]-122008.949824877[/C][/ROW]
[ROW][C]33[/C][C]8988846[/C][C]7309103.76407864[/C][C]1679742.23592136[/C][/ROW]
[ROW][C]34[/C][C]8404694[/C][C]8469920.37973491[/C][C]-65226.3797349092[/C][/ROW]
[ROW][C]35[/C][C]9601659[/C][C]8598363.68403638[/C][C]1003295.31596362[/C][/ROW]
[ROW][C]36[/C][C]8213138[/C][C]9440620.41671937[/C][C]-1227482.41671937[/C][/ROW]
[ROW][C]37[/C][C]8434646[/C][C]8866121.69464246[/C][C]-431475.694642458[/C][/ROW]
[ROW][C]38[/C][C]8466539[/C][C]8723473.48355821[/C][C]-256934.483558213[/C][/ROW]
[ROW][C]39[/C][C]9106270[/C][C]8661760.38979082[/C][C]444509.610209184[/C][/ROW]
[ROW][C]40[/C][C]8438555[/C][C]9050492.24601041[/C][C]-611937.246010412[/C][/ROW]
[ROW][C]41[/C][C]7723821[/C][C]8765684.31409526[/C][C]-1041863.31409526[/C][/ROW]
[ROW][C]42[/C][C]7538413[/C][C]8139582.6416749[/C][C]-601169.641674901[/C][/ROW]
[ROW][C]43[/C][C]7199881[/C][C]7721861.97766617[/C][C]-521980.977666171[/C][/ROW]
[ROW][C]44[/C][C]8168314[/C][C]7306502.19991836[/C][C]861811.800081642[/C][/ROW]
[ROW][C]45[/C][C]9045790[/C][C]7778489.56365624[/C][C]1267300.43634376[/C][/ROW]
[ROW][C]46[/C][C]8544483[/C][C]8596496.27239968[/C][C]-52013.2723996826[/C][/ROW]
[ROW][C]47[/C][C]9020709[/C][C]8633730.64295705[/C][C]386978.35704295[/C][/ROW]
[ROW][C]48[/C][C]7932021[/C][C]8962091.18246796[/C][C]-1030070.18246796[/C][/ROW]
[ROW][C]49[/C][C]8435986[/C][C]8369274.77190209[/C][C]66711.2280979082[/C][/ROW]
[ROW][C]50[/C][C]7920357[/C][C]8427524.87719518[/C][C]-507167.877195181[/C][/ROW]
[ROW][C]51[/C][C]8333659[/C][C]8105086.63905059[/C][C]228572.360949412[/C][/ROW]
[ROW][C]52[/C][C]7415547[/C][C]8234974.33619803[/C][C]-819427.336198031[/C][/ROW]
[ROW][C]53[/C][C]7770392[/C][C]7678708.02786561[/C][C]91683.9721343927[/C][/ROW]
[ROW][C]54[/C][C]8188878[/C][C]7666365.16420141[/C][C]522512.835798591[/C][/ROW]
[ROW][C]55[/C][C]8092465[/C][C]7951831.71542461[/C][C]140633.284575385[/C][/ROW]
[ROW][C]56[/C][C]7188528[/C][C]8024496.03499383[/C][C]-835968.03499383[/C][/ROW]
[ROW][C]57[/C][C]8152373[/C][C]7451619.63755855[/C][C]700753.362441452[/C][/ROW]
[ROW][C]58[/C][C]9025069[/C][C]7842432.95180954[/C][C]1182636.04819046[/C][/ROW]
[ROW][C]59[/C][C]9233973[/C][C]8617045.09007907[/C][C]616927.909920929[/C][/ROW]
[ROW][C]60[/C][C]6916290[/C][C]9111045.66350199[/C][C]-2194755.66350199[/C][/ROW]
[ROW][C]61[/C][C]8171721[/C][C]7764472.99152742[/C][C]407248.008472584[/C][/ROW]
[ROW][C]62[/C][C]7012501[/C][C]7983591.75246079[/C][C]-971090.752460794[/C][/ROW]
[ROW][C]63[/C][C]8779456[/C][C]7309311.32172848[/C][C]1470144.67827152[/C][/ROW]
[ROW][C]64[/C][C]7308709[/C][C]8196198.33322799[/C][C]-887489.333227992[/C][/ROW]
[ROW][C]65[/C][C]8084547[/C][C]7620494.79444207[/C][C]464052.205557932[/C][/ROW]
[ROW][C]66[/C][C]8255978[/C][C]7879449.20354448[/C][C]376528.796455516[/C][/ROW]
[ROW][C]67[/C][C]7658071[/C][C]8118810.80778212[/C][C]-460739.807782122[/C][/ROW]
[ROW][C]68[/C][C]7371877[/C][C]7826424.55872567[/C][C]-454547.558725674[/C][/ROW]
[ROW][C]69[/C][C]8780827[/C][C]7499158.74539196[/C][C]1281668.25460804[/C][/ROW]
[ROW][C]70[/C][C]10116778[/C][C]8302210.49372143[/C][C]1814567.50627857[/C][/ROW]
[ROW][C]71[/C][C]9567175[/C][C]9572639.26592016[/C][C]-5464.26592015848[/C][/ROW]
[ROW][C]72[/C][C]7455902[/C][C]9771587.92776081[/C][C]-2315685.92776081[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262280&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262280&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
3865672167363911920330
477298737208040.86866951521832.131330494
570670026900955.73661217166046.263387827
672221896398577.25857558823611.741424421
767581616352952.26065222405208.739347778
867456656095455.51076764650209.489232361
982036606037238.097378922166421.90262108
1087997557054858.859389651744896.14061035
1179951517972310.3863183322840.6136816721
1268446947878335.8369638-1033641.8369638
1374001867075060.57612106325125.423878941
1461461837098921.10211033-952738.102110334
1567930276290063.56395298502963.436047019
1658151466380455.80461949-565309.804619486
1759935055794300.62816244199204.37183756
1858380165674914.74346565163101.256534352
1959268155548106.62754797378708.37245203
2056428905580270.802194462619.1978055965
2171206215431736.001507111688884.99849289
2277817436383329.625714921398413.37428508
2376389217282509.37650645356411.623493551
2458860707598718.46020538-1712648.46020538
2573588906552218.14274698806671.857253022
2669811897056605.01836207-75416.0183620676
2784235327035526.32512021388005.6748798
2868193137993248.82500107-1173935.82500107
2967272217343877.17644741-616656.176447413
3069233496970180.28828214-46831.2882821448
3175782406927833.89279718650406.107202816
3272288987350906.94982488-122008.949824877
3389888467309103.764078641679742.23592136
3484046948469920.37973491-65226.3797349092
3596016598598363.684036381003295.31596362
3682131389440620.41671937-1227482.41671937
3784346468866121.69464246-431475.694642458
3884665398723473.48355821-256934.483558213
3991062708661760.38979082444509.610209184
4084385559050492.24601041-611937.246010412
4177238218765684.31409526-1041863.31409526
4275384138139582.6416749-601169.641674901
4371998817721861.97766617-521980.977666171
4481683147306502.19991836861811.800081642
4590457907778489.563656241267300.43634376
4685444838596496.27239968-52013.2723996826
4790207098633730.64295705386978.35704295
4879320218962091.18246796-1030070.18246796
4984359868369274.7719020966711.2280979082
5079203578427524.87719518-507167.877195181
5183336598105086.63905059228572.360949412
5274155478234974.33619803-819427.336198031
5377703927678708.0278656191683.9721343927
5481888787666365.16420141522512.835798591
5580924657951831.71542461140633.284575385
5671885288024496.03499383-835968.03499383
5781523737451619.63755855700753.362441452
5890250697842432.951809541182636.04819046
5992339738617045.09007907616927.909920929
6069162909111045.66350199-2194755.66350199
6181717217764472.99152742407248.008472584
6270125017983591.75246079-971090.752460794
6387794567309311.321728481470144.67827152
6473087098196198.33322799-887489.333227992
6580845477620494.79444207464052.205557932
6682559787879449.20354448376528.796455516
6776580718118810.80778212-460739.807782122
6873718777826424.55872567-454547.558725674
6987808277499158.745391961281668.25460804
70101167788302210.493721431814567.50627857
7195671759572639.26592016-5464.26592015848
7274559029771587.92776081-2315685.92776081







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738414804.939555486545002.4360780110284607.443033
748420711.905327626166677.4620797710674746.3485755
758426618.871099755764055.4658973311089182.2763022
768432525.836871885338644.2155937711526407.45815
778438432.802644014891677.3403981111985188.2648899
788444339.768416144424192.9312303912464486.6056019
798450246.734188283937083.035016912963410.4333597
808456153.699960413431126.6854790313481180.7144418
818462060.665732542907012.9977887214017108.3336764
828467967.631504672365357.9352808514570577.3277285
838473874.59727681806716.8618873115141032.3326663
848479781.563048931231594.1811009315727968.9449969

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8414804.93955548 & 6545002.43607801 & 10284607.443033 \tabularnewline
74 & 8420711.90532762 & 6166677.46207977 & 10674746.3485755 \tabularnewline
75 & 8426618.87109975 & 5764055.46589733 & 11089182.2763022 \tabularnewline
76 & 8432525.83687188 & 5338644.21559377 & 11526407.45815 \tabularnewline
77 & 8438432.80264401 & 4891677.34039811 & 11985188.2648899 \tabularnewline
78 & 8444339.76841614 & 4424192.93123039 & 12464486.6056019 \tabularnewline
79 & 8450246.73418828 & 3937083.0350169 & 12963410.4333597 \tabularnewline
80 & 8456153.69996041 & 3431126.68547903 & 13481180.7144418 \tabularnewline
81 & 8462060.66573254 & 2907012.99778872 & 14017108.3336764 \tabularnewline
82 & 8467967.63150467 & 2365357.93528085 & 14570577.3277285 \tabularnewline
83 & 8473874.5972768 & 1806716.86188731 & 15141032.3326663 \tabularnewline
84 & 8479781.56304893 & 1231594.18110093 & 15727968.9449969 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=262280&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]8414804.93955548[/C][C]6545002.43607801[/C][C]10284607.443033[/C][/ROW]
[ROW][C]74[/C][C]8420711.90532762[/C][C]6166677.46207977[/C][C]10674746.3485755[/C][/ROW]
[ROW][C]75[/C][C]8426618.87109975[/C][C]5764055.46589733[/C][C]11089182.2763022[/C][/ROW]
[ROW][C]76[/C][C]8432525.83687188[/C][C]5338644.21559377[/C][C]11526407.45815[/C][/ROW]
[ROW][C]77[/C][C]8438432.80264401[/C][C]4891677.34039811[/C][C]11985188.2648899[/C][/ROW]
[ROW][C]78[/C][C]8444339.76841614[/C][C]4424192.93123039[/C][C]12464486.6056019[/C][/ROW]
[ROW][C]79[/C][C]8450246.73418828[/C][C]3937083.0350169[/C][C]12963410.4333597[/C][/ROW]
[ROW][C]80[/C][C]8456153.69996041[/C][C]3431126.68547903[/C][C]13481180.7144418[/C][/ROW]
[ROW][C]81[/C][C]8462060.66573254[/C][C]2907012.99778872[/C][C]14017108.3336764[/C][/ROW]
[ROW][C]82[/C][C]8467967.63150467[/C][C]2365357.93528085[/C][C]14570577.3277285[/C][/ROW]
[ROW][C]83[/C][C]8473874.5972768[/C][C]1806716.86188731[/C][C]15141032.3326663[/C][/ROW]
[ROW][C]84[/C][C]8479781.56304893[/C][C]1231594.18110093[/C][C]15727968.9449969[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=262280&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=262280&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
738414804.939555486545002.4360780110284607.443033
748420711.905327626166677.4620797710674746.3485755
758426618.871099755764055.4658973311089182.2763022
768432525.836871885338644.2155937711526407.45815
778438432.802644014891677.3403981111985188.2648899
788444339.768416144424192.9312303912464486.6056019
798450246.734188283937083.035016912963410.4333597
808456153.699960413431126.6854790313481180.7144418
818462060.665732542907012.9977887214017108.3336764
828467967.631504672365357.9352808514570577.3277285
838473874.59727681806716.8618873115141032.3326663
848479781.563048931231594.1811009315727968.9449969



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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=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')