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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 Dec 2011 14:12:52 -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/28/t13250995987bz8k6lcqsysixz.htm/, Retrieved Fri, 03 May 2024 10:56:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160887, Retrieved Fri, 03 May 2024 10:56:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-12-28 19:12:52] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
14097,80
14776,80
16833,30
15385,50
15172,60
16858,90
14143,50
14731,80
16471,60
15214,00
17637,40
17972,40
16896,20
16698,00
19691,60
15930,70
17444,60
17699,40
15189,80
15672,70
17180,80
17664,90
17862,90
16162,30
17463,60
16772,10
19106,90
16721,30
18161,30
18509,90
17802,70
16409,90
17967,70
20286,60
19537,30
18021,90
20194,30
19049,60
20244,70
21473,30
19673,60
21053,20
20159,50
18203,60
21289,50
20432,30
17180,40
15816,80
15076,60
14531,60
15761,30
14345,50
13916,80
15496,80
14285,60
13597,30
16263,10
16773,30
15986,90
16842,60
15911,90
15782,90
18622,80
17422,50
16989,80
18990,50
16849,30
16511,30
18704,50
19111,10
19420,70
18985,10




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160887&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160887&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160887&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.522539492318595
beta0.121675058777556
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.522539492318595 \tabularnewline
beta & 0.121675058777556 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160887&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]0.522539492318595[/C][/ROW]
[ROW][C]beta[/C][C]0.121675058777556[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160887&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160887&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
alpha0.522539492318595
beta0.121675058777556
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
316833.315455.81377.5
415385.516942.1796329595-1556.67963295947
515172.616796.3608025863-1623.76080258634
616858.916512.2506620005346.649337999519
714143.517279.7976089717-3136.29760897175
814731.816027.9613510022-1296.16135100223
916471.615655.2589899885816.341010011491
101521416438.3255207735-1224.32552077348
1117637.416077.22055325981560.17944674023
1217972.417270.3256436259702.074356374087
1316896.218059.674839752-1163.47483975204
141669817800.2271484541-1102.22714845407
1519691.617502.70416673612188.89583326389
1615930.719064.0929654329-3133.39296543294
1717444.617645.1544790923-200.554479092258
1817699.417745.9886679745-46.5886679744908
1915189.817924.3139650307-2734.5139650307
2015672.716524.2316799752-851.5316799752
2117180.816053.94159802351126.85840197646
2217664.916689.0841487159975.815851284086
2317862.917307.3433963502555.55660364982
2416162.317741.3228919666-1579.02289196655
2517463.616959.505989144504.09401085597
2616772.117298.2502441896-526.150244189594
2719106.917065.19854438022041.70145561981
2816721.318303.7621945474-1582.46219454741
2918161.317547.9442274522613.355772547802
3018509.917978.5250405035531.374959496494
3117802.718400.0524735041-597.352473504114
3216409.918193.7955624303-1783.89556243031
3317967.717254.1029063784713.597093621564
3420286.617664.81931482952621.78068517045
3519537.319239.3298858808297.970114119216
3618021.919618.5026077309-1596.60260773088
3720194.318906.17423011851288.12576988145
3819049.619783.1294210654-733.529421065414
3920244.719557.0521171053687.647882894686
4021473.320117.31674856521355.98325143485
4119673.621113.026451113-1439.42645111298
4221053.220556.505419365496.69458063503
4320159.521043.2639416939-883.763941693942
4418203.620752.4886364686-2548.88863646864
4521289.519429.56151933231859.93848066774
4620432.320528.6756179053-96.3756179053089
4717180.420599.4107765487-3419.01077654868
4815816.818716.5570609151-2899.75706091507
4915076.616920.6672963257-1844.06729632567
5014531.615559.1712834427-1027.57128344274
5115761.314558.99367632271202.30632367725
5214345.514800.4578462031-454.957846203055
5313916.814147.0098075898-230.209807589845
5415496.813596.36475001021900.43524998984
5514285.614279.89559687265.70440312737992
5613597.313973.7174350197-376.41743501975
5716263.113443.93289251532819.1671074847
5816773.314763.21018529152010.08981470846
5915986.915787.5141977926199.385802207416
6016842.615878.3308088403964.269191159667
6115911.916430.1374554119-518.237455411925
6215782.916174.3262819617-391.426281961723
6318622.815959.89206252382662.90793747622
6417422.517510.7758445694-88.2758445694453
6516989.817618.4448696028-628.644869602776
6618990.517403.78048308481586.71951691521
6716849.318447.6151424791-1598.31514247911
6816511.317725.5224937107-1214.22249371073
6918704.517126.93312801981577.5668719802
7019111.118087.46569883841023.63430116156
7119420.718823.6293181861597.070681813901
7218985.119374.8583683842-389.758368384191

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 16833.3 & 15455.8 & 1377.5 \tabularnewline
4 & 15385.5 & 16942.1796329595 & -1556.67963295947 \tabularnewline
5 & 15172.6 & 16796.3608025863 & -1623.76080258634 \tabularnewline
6 & 16858.9 & 16512.2506620005 & 346.649337999519 \tabularnewline
7 & 14143.5 & 17279.7976089717 & -3136.29760897175 \tabularnewline
8 & 14731.8 & 16027.9613510022 & -1296.16135100223 \tabularnewline
9 & 16471.6 & 15655.2589899885 & 816.341010011491 \tabularnewline
10 & 15214 & 16438.3255207735 & -1224.32552077348 \tabularnewline
11 & 17637.4 & 16077.2205532598 & 1560.17944674023 \tabularnewline
12 & 17972.4 & 17270.3256436259 & 702.074356374087 \tabularnewline
13 & 16896.2 & 18059.674839752 & -1163.47483975204 \tabularnewline
14 & 16698 & 17800.2271484541 & -1102.22714845407 \tabularnewline
15 & 19691.6 & 17502.7041667361 & 2188.89583326389 \tabularnewline
16 & 15930.7 & 19064.0929654329 & -3133.39296543294 \tabularnewline
17 & 17444.6 & 17645.1544790923 & -200.554479092258 \tabularnewline
18 & 17699.4 & 17745.9886679745 & -46.5886679744908 \tabularnewline
19 & 15189.8 & 17924.3139650307 & -2734.5139650307 \tabularnewline
20 & 15672.7 & 16524.2316799752 & -851.5316799752 \tabularnewline
21 & 17180.8 & 16053.9415980235 & 1126.85840197646 \tabularnewline
22 & 17664.9 & 16689.0841487159 & 975.815851284086 \tabularnewline
23 & 17862.9 & 17307.3433963502 & 555.55660364982 \tabularnewline
24 & 16162.3 & 17741.3228919666 & -1579.02289196655 \tabularnewline
25 & 17463.6 & 16959.505989144 & 504.09401085597 \tabularnewline
26 & 16772.1 & 17298.2502441896 & -526.150244189594 \tabularnewline
27 & 19106.9 & 17065.1985443802 & 2041.70145561981 \tabularnewline
28 & 16721.3 & 18303.7621945474 & -1582.46219454741 \tabularnewline
29 & 18161.3 & 17547.9442274522 & 613.355772547802 \tabularnewline
30 & 18509.9 & 17978.5250405035 & 531.374959496494 \tabularnewline
31 & 17802.7 & 18400.0524735041 & -597.352473504114 \tabularnewline
32 & 16409.9 & 18193.7955624303 & -1783.89556243031 \tabularnewline
33 & 17967.7 & 17254.1029063784 & 713.597093621564 \tabularnewline
34 & 20286.6 & 17664.8193148295 & 2621.78068517045 \tabularnewline
35 & 19537.3 & 19239.3298858808 & 297.970114119216 \tabularnewline
36 & 18021.9 & 19618.5026077309 & -1596.60260773088 \tabularnewline
37 & 20194.3 & 18906.1742301185 & 1288.12576988145 \tabularnewline
38 & 19049.6 & 19783.1294210654 & -733.529421065414 \tabularnewline
39 & 20244.7 & 19557.0521171053 & 687.647882894686 \tabularnewline
40 & 21473.3 & 20117.3167485652 & 1355.98325143485 \tabularnewline
41 & 19673.6 & 21113.026451113 & -1439.42645111298 \tabularnewline
42 & 21053.2 & 20556.505419365 & 496.69458063503 \tabularnewline
43 & 20159.5 & 21043.2639416939 & -883.763941693942 \tabularnewline
44 & 18203.6 & 20752.4886364686 & -2548.88863646864 \tabularnewline
45 & 21289.5 & 19429.5615193323 & 1859.93848066774 \tabularnewline
46 & 20432.3 & 20528.6756179053 & -96.3756179053089 \tabularnewline
47 & 17180.4 & 20599.4107765487 & -3419.01077654868 \tabularnewline
48 & 15816.8 & 18716.5570609151 & -2899.75706091507 \tabularnewline
49 & 15076.6 & 16920.6672963257 & -1844.06729632567 \tabularnewline
50 & 14531.6 & 15559.1712834427 & -1027.57128344274 \tabularnewline
51 & 15761.3 & 14558.9936763227 & 1202.30632367725 \tabularnewline
52 & 14345.5 & 14800.4578462031 & -454.957846203055 \tabularnewline
53 & 13916.8 & 14147.0098075898 & -230.209807589845 \tabularnewline
54 & 15496.8 & 13596.3647500102 & 1900.43524998984 \tabularnewline
55 & 14285.6 & 14279.8955968726 & 5.70440312737992 \tabularnewline
56 & 13597.3 & 13973.7174350197 & -376.41743501975 \tabularnewline
57 & 16263.1 & 13443.9328925153 & 2819.1671074847 \tabularnewline
58 & 16773.3 & 14763.2101852915 & 2010.08981470846 \tabularnewline
59 & 15986.9 & 15787.5141977926 & 199.385802207416 \tabularnewline
60 & 16842.6 & 15878.3308088403 & 964.269191159667 \tabularnewline
61 & 15911.9 & 16430.1374554119 & -518.237455411925 \tabularnewline
62 & 15782.9 & 16174.3262819617 & -391.426281961723 \tabularnewline
63 & 18622.8 & 15959.8920625238 & 2662.90793747622 \tabularnewline
64 & 17422.5 & 17510.7758445694 & -88.2758445694453 \tabularnewline
65 & 16989.8 & 17618.4448696028 & -628.644869602776 \tabularnewline
66 & 18990.5 & 17403.7804830848 & 1586.71951691521 \tabularnewline
67 & 16849.3 & 18447.6151424791 & -1598.31514247911 \tabularnewline
68 & 16511.3 & 17725.5224937107 & -1214.22249371073 \tabularnewline
69 & 18704.5 & 17126.9331280198 & 1577.5668719802 \tabularnewline
70 & 19111.1 & 18087.4656988384 & 1023.63430116156 \tabularnewline
71 & 19420.7 & 18823.6293181861 & 597.070681813901 \tabularnewline
72 & 18985.1 & 19374.8583683842 & -389.758368384191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160887&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]16833.3[/C][C]15455.8[/C][C]1377.5[/C][/ROW]
[ROW][C]4[/C][C]15385.5[/C][C]16942.1796329595[/C][C]-1556.67963295947[/C][/ROW]
[ROW][C]5[/C][C]15172.6[/C][C]16796.3608025863[/C][C]-1623.76080258634[/C][/ROW]
[ROW][C]6[/C][C]16858.9[/C][C]16512.2506620005[/C][C]346.649337999519[/C][/ROW]
[ROW][C]7[/C][C]14143.5[/C][C]17279.7976089717[/C][C]-3136.29760897175[/C][/ROW]
[ROW][C]8[/C][C]14731.8[/C][C]16027.9613510022[/C][C]-1296.16135100223[/C][/ROW]
[ROW][C]9[/C][C]16471.6[/C][C]15655.2589899885[/C][C]816.341010011491[/C][/ROW]
[ROW][C]10[/C][C]15214[/C][C]16438.3255207735[/C][C]-1224.32552077348[/C][/ROW]
[ROW][C]11[/C][C]17637.4[/C][C]16077.2205532598[/C][C]1560.17944674023[/C][/ROW]
[ROW][C]12[/C][C]17972.4[/C][C]17270.3256436259[/C][C]702.074356374087[/C][/ROW]
[ROW][C]13[/C][C]16896.2[/C][C]18059.674839752[/C][C]-1163.47483975204[/C][/ROW]
[ROW][C]14[/C][C]16698[/C][C]17800.2271484541[/C][C]-1102.22714845407[/C][/ROW]
[ROW][C]15[/C][C]19691.6[/C][C]17502.7041667361[/C][C]2188.89583326389[/C][/ROW]
[ROW][C]16[/C][C]15930.7[/C][C]19064.0929654329[/C][C]-3133.39296543294[/C][/ROW]
[ROW][C]17[/C][C]17444.6[/C][C]17645.1544790923[/C][C]-200.554479092258[/C][/ROW]
[ROW][C]18[/C][C]17699.4[/C][C]17745.9886679745[/C][C]-46.5886679744908[/C][/ROW]
[ROW][C]19[/C][C]15189.8[/C][C]17924.3139650307[/C][C]-2734.5139650307[/C][/ROW]
[ROW][C]20[/C][C]15672.7[/C][C]16524.2316799752[/C][C]-851.5316799752[/C][/ROW]
[ROW][C]21[/C][C]17180.8[/C][C]16053.9415980235[/C][C]1126.85840197646[/C][/ROW]
[ROW][C]22[/C][C]17664.9[/C][C]16689.0841487159[/C][C]975.815851284086[/C][/ROW]
[ROW][C]23[/C][C]17862.9[/C][C]17307.3433963502[/C][C]555.55660364982[/C][/ROW]
[ROW][C]24[/C][C]16162.3[/C][C]17741.3228919666[/C][C]-1579.02289196655[/C][/ROW]
[ROW][C]25[/C][C]17463.6[/C][C]16959.505989144[/C][C]504.09401085597[/C][/ROW]
[ROW][C]26[/C][C]16772.1[/C][C]17298.2502441896[/C][C]-526.150244189594[/C][/ROW]
[ROW][C]27[/C][C]19106.9[/C][C]17065.1985443802[/C][C]2041.70145561981[/C][/ROW]
[ROW][C]28[/C][C]16721.3[/C][C]18303.7621945474[/C][C]-1582.46219454741[/C][/ROW]
[ROW][C]29[/C][C]18161.3[/C][C]17547.9442274522[/C][C]613.355772547802[/C][/ROW]
[ROW][C]30[/C][C]18509.9[/C][C]17978.5250405035[/C][C]531.374959496494[/C][/ROW]
[ROW][C]31[/C][C]17802.7[/C][C]18400.0524735041[/C][C]-597.352473504114[/C][/ROW]
[ROW][C]32[/C][C]16409.9[/C][C]18193.7955624303[/C][C]-1783.89556243031[/C][/ROW]
[ROW][C]33[/C][C]17967.7[/C][C]17254.1029063784[/C][C]713.597093621564[/C][/ROW]
[ROW][C]34[/C][C]20286.6[/C][C]17664.8193148295[/C][C]2621.78068517045[/C][/ROW]
[ROW][C]35[/C][C]19537.3[/C][C]19239.3298858808[/C][C]297.970114119216[/C][/ROW]
[ROW][C]36[/C][C]18021.9[/C][C]19618.5026077309[/C][C]-1596.60260773088[/C][/ROW]
[ROW][C]37[/C][C]20194.3[/C][C]18906.1742301185[/C][C]1288.12576988145[/C][/ROW]
[ROW][C]38[/C][C]19049.6[/C][C]19783.1294210654[/C][C]-733.529421065414[/C][/ROW]
[ROW][C]39[/C][C]20244.7[/C][C]19557.0521171053[/C][C]687.647882894686[/C][/ROW]
[ROW][C]40[/C][C]21473.3[/C][C]20117.3167485652[/C][C]1355.98325143485[/C][/ROW]
[ROW][C]41[/C][C]19673.6[/C][C]21113.026451113[/C][C]-1439.42645111298[/C][/ROW]
[ROW][C]42[/C][C]21053.2[/C][C]20556.505419365[/C][C]496.69458063503[/C][/ROW]
[ROW][C]43[/C][C]20159.5[/C][C]21043.2639416939[/C][C]-883.763941693942[/C][/ROW]
[ROW][C]44[/C][C]18203.6[/C][C]20752.4886364686[/C][C]-2548.88863646864[/C][/ROW]
[ROW][C]45[/C][C]21289.5[/C][C]19429.5615193323[/C][C]1859.93848066774[/C][/ROW]
[ROW][C]46[/C][C]20432.3[/C][C]20528.6756179053[/C][C]-96.3756179053089[/C][/ROW]
[ROW][C]47[/C][C]17180.4[/C][C]20599.4107765487[/C][C]-3419.01077654868[/C][/ROW]
[ROW][C]48[/C][C]15816.8[/C][C]18716.5570609151[/C][C]-2899.75706091507[/C][/ROW]
[ROW][C]49[/C][C]15076.6[/C][C]16920.6672963257[/C][C]-1844.06729632567[/C][/ROW]
[ROW][C]50[/C][C]14531.6[/C][C]15559.1712834427[/C][C]-1027.57128344274[/C][/ROW]
[ROW][C]51[/C][C]15761.3[/C][C]14558.9936763227[/C][C]1202.30632367725[/C][/ROW]
[ROW][C]52[/C][C]14345.5[/C][C]14800.4578462031[/C][C]-454.957846203055[/C][/ROW]
[ROW][C]53[/C][C]13916.8[/C][C]14147.0098075898[/C][C]-230.209807589845[/C][/ROW]
[ROW][C]54[/C][C]15496.8[/C][C]13596.3647500102[/C][C]1900.43524998984[/C][/ROW]
[ROW][C]55[/C][C]14285.6[/C][C]14279.8955968726[/C][C]5.70440312737992[/C][/ROW]
[ROW][C]56[/C][C]13597.3[/C][C]13973.7174350197[/C][C]-376.41743501975[/C][/ROW]
[ROW][C]57[/C][C]16263.1[/C][C]13443.9328925153[/C][C]2819.1671074847[/C][/ROW]
[ROW][C]58[/C][C]16773.3[/C][C]14763.2101852915[/C][C]2010.08981470846[/C][/ROW]
[ROW][C]59[/C][C]15986.9[/C][C]15787.5141977926[/C][C]199.385802207416[/C][/ROW]
[ROW][C]60[/C][C]16842.6[/C][C]15878.3308088403[/C][C]964.269191159667[/C][/ROW]
[ROW][C]61[/C][C]15911.9[/C][C]16430.1374554119[/C][C]-518.237455411925[/C][/ROW]
[ROW][C]62[/C][C]15782.9[/C][C]16174.3262819617[/C][C]-391.426281961723[/C][/ROW]
[ROW][C]63[/C][C]18622.8[/C][C]15959.8920625238[/C][C]2662.90793747622[/C][/ROW]
[ROW][C]64[/C][C]17422.5[/C][C]17510.7758445694[/C][C]-88.2758445694453[/C][/ROW]
[ROW][C]65[/C][C]16989.8[/C][C]17618.4448696028[/C][C]-628.644869602776[/C][/ROW]
[ROW][C]66[/C][C]18990.5[/C][C]17403.7804830848[/C][C]1586.71951691521[/C][/ROW]
[ROW][C]67[/C][C]16849.3[/C][C]18447.6151424791[/C][C]-1598.31514247911[/C][/ROW]
[ROW][C]68[/C][C]16511.3[/C][C]17725.5224937107[/C][C]-1214.22249371073[/C][/ROW]
[ROW][C]69[/C][C]18704.5[/C][C]17126.9331280198[/C][C]1577.5668719802[/C][/ROW]
[ROW][C]70[/C][C]19111.1[/C][C]18087.4656988384[/C][C]1023.63430116156[/C][/ROW]
[ROW][C]71[/C][C]19420.7[/C][C]18823.6293181861[/C][C]597.070681813901[/C][/ROW]
[ROW][C]72[/C][C]18985.1[/C][C]19374.8583683842[/C][C]-389.758368384191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160887&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160887&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
316833.315455.81377.5
415385.516942.1796329595-1556.67963295947
515172.616796.3608025863-1623.76080258634
616858.916512.2506620005346.649337999519
714143.517279.7976089717-3136.29760897175
814731.816027.9613510022-1296.16135100223
916471.615655.2589899885816.341010011491
101521416438.3255207735-1224.32552077348
1117637.416077.22055325981560.17944674023
1217972.417270.3256436259702.074356374087
1316896.218059.674839752-1163.47483975204
141669817800.2271484541-1102.22714845407
1519691.617502.70416673612188.89583326389
1615930.719064.0929654329-3133.39296543294
1717444.617645.1544790923-200.554479092258
1817699.417745.9886679745-46.5886679744908
1915189.817924.3139650307-2734.5139650307
2015672.716524.2316799752-851.5316799752
2117180.816053.94159802351126.85840197646
2217664.916689.0841487159975.815851284086
2317862.917307.3433963502555.55660364982
2416162.317741.3228919666-1579.02289196655
2517463.616959.505989144504.09401085597
2616772.117298.2502441896-526.150244189594
2719106.917065.19854438022041.70145561981
2816721.318303.7621945474-1582.46219454741
2918161.317547.9442274522613.355772547802
3018509.917978.5250405035531.374959496494
3117802.718400.0524735041-597.352473504114
3216409.918193.7955624303-1783.89556243031
3317967.717254.1029063784713.597093621564
3420286.617664.81931482952621.78068517045
3519537.319239.3298858808297.970114119216
3618021.919618.5026077309-1596.60260773088
3720194.318906.17423011851288.12576988145
3819049.619783.1294210654-733.529421065414
3920244.719557.0521171053687.647882894686
4021473.320117.31674856521355.98325143485
4119673.621113.026451113-1439.42645111298
4221053.220556.505419365496.69458063503
4320159.521043.2639416939-883.763941693942
4418203.620752.4886364686-2548.88863646864
4521289.519429.56151933231859.93848066774
4620432.320528.6756179053-96.3756179053089
4717180.420599.4107765487-3419.01077654868
4815816.818716.5570609151-2899.75706091507
4915076.616920.6672963257-1844.06729632567
5014531.615559.1712834427-1027.57128344274
5115761.314558.99367632271202.30632367725
5214345.514800.4578462031-454.957846203055
5313916.814147.0098075898-230.209807589845
5415496.813596.36475001021900.43524998984
5514285.614279.89559687265.70440312737992
5613597.313973.7174350197-376.41743501975
5716263.113443.93289251532819.1671074847
5816773.314763.21018529152010.08981470846
5915986.915787.5141977926199.385802207416
6016842.615878.3308088403964.269191159667
6115911.916430.1374554119-518.237455411925
6215782.916174.3262819617-391.426281961723
6318622.815959.89206252382662.90793747622
6417422.517510.7758445694-88.2758445694453
6516989.817618.4448696028-628.644869602776
6618990.517403.78048308481586.71951691521
6716849.318447.6151424791-1598.31514247911
6816511.317725.5224937107-1214.22249371073
6918704.517126.93312801981577.5668719802
7019111.118087.46569883841023.63430116156
7119420.718823.6293181861597.070681813901
7218985.119374.8583683842-389.758368384191







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7319385.649421488216459.02863145522312.2702115213
7419600.104614534516207.829071102922992.3801579661
7519814.559807580915925.736428984623703.3831861772
7620029.015000627315615.331901676524442.6980995781
7720243.470193673615278.620289199525208.3200981477
7820457.9253867214917.203139111425998.6476343286
7920672.380579766414532.392682483426812.3684770493
8020886.835772812714125.288082962727648.3834626627
8121101.290965859113696.827588787128505.754342931
8221315.746158905413247.825043346329383.6672744646
8321530.201351951812778.99604280630281.4066610977
8421744.656544998212290.977095309631198.3359946867

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 19385.6494214882 & 16459.028631455 & 22312.2702115213 \tabularnewline
74 & 19600.1046145345 & 16207.8290711029 & 22992.3801579661 \tabularnewline
75 & 19814.5598075809 & 15925.7364289846 & 23703.3831861772 \tabularnewline
76 & 20029.0150006273 & 15615.3319016765 & 24442.6980995781 \tabularnewline
77 & 20243.4701936736 & 15278.6202891995 & 25208.3200981477 \tabularnewline
78 & 20457.92538672 & 14917.2031391114 & 25998.6476343286 \tabularnewline
79 & 20672.3805797664 & 14532.3926824834 & 26812.3684770493 \tabularnewline
80 & 20886.8357728127 & 14125.2880829627 & 27648.3834626627 \tabularnewline
81 & 21101.2909658591 & 13696.8275887871 & 28505.754342931 \tabularnewline
82 & 21315.7461589054 & 13247.8250433463 & 29383.6672744646 \tabularnewline
83 & 21530.2013519518 & 12778.996042806 & 30281.4066610977 \tabularnewline
84 & 21744.6565449982 & 12290.9770953096 & 31198.3359946867 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160887&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]19385.6494214882[/C][C]16459.028631455[/C][C]22312.2702115213[/C][/ROW]
[ROW][C]74[/C][C]19600.1046145345[/C][C]16207.8290711029[/C][C]22992.3801579661[/C][/ROW]
[ROW][C]75[/C][C]19814.5598075809[/C][C]15925.7364289846[/C][C]23703.3831861772[/C][/ROW]
[ROW][C]76[/C][C]20029.0150006273[/C][C]15615.3319016765[/C][C]24442.6980995781[/C][/ROW]
[ROW][C]77[/C][C]20243.4701936736[/C][C]15278.6202891995[/C][C]25208.3200981477[/C][/ROW]
[ROW][C]78[/C][C]20457.92538672[/C][C]14917.2031391114[/C][C]25998.6476343286[/C][/ROW]
[ROW][C]79[/C][C]20672.3805797664[/C][C]14532.3926824834[/C][C]26812.3684770493[/C][/ROW]
[ROW][C]80[/C][C]20886.8357728127[/C][C]14125.2880829627[/C][C]27648.3834626627[/C][/ROW]
[ROW][C]81[/C][C]21101.2909658591[/C][C]13696.8275887871[/C][C]28505.754342931[/C][/ROW]
[ROW][C]82[/C][C]21315.7461589054[/C][C]13247.8250433463[/C][C]29383.6672744646[/C][/ROW]
[ROW][C]83[/C][C]21530.2013519518[/C][C]12778.996042806[/C][C]30281.4066610977[/C][/ROW]
[ROW][C]84[/C][C]21744.6565449982[/C][C]12290.9770953096[/C][C]31198.3359946867[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160887&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160887&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
7319385.649421488216459.02863145522312.2702115213
7419600.104614534516207.829071102922992.3801579661
7519814.559807580915925.736428984623703.3831861772
7620029.015000627315615.331901676524442.6980995781
7720243.470193673615278.620289199525208.3200981477
7820457.9253867214917.203139111425998.6476343286
7920672.380579766414532.392682483426812.3684770493
8020886.835772812714125.288082962727648.3834626627
8121101.290965859113696.827588787128505.754342931
8221315.746158905413247.825043346329383.6672744646
8321530.201351951812778.99604280630281.4066610977
8421744.656544998212290.977095309631198.3359946867



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