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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 computationWed, 29 Dec 2010 14:11:07 +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/2010/Dec/29/t1293634454140pcdauav1h8p6.htm/, Retrieved Fri, 03 May 2024 06:21:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116888, Retrieved Fri, 03 May 2024 06:21:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-12-29 14:11:07] [0956ee981dded61b2e7128dae94e5715] [Current]
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Dataseries X:
1203.6
1180.59
1156.85
1191.5
1191.33
1234.18
1220.33
1228.81
1207.01
1249.48
1248.29
1280.08
1280.66
1294.87
1310.61
1270.09
1270.2
1276.66
1303.82
1335.85
1377.94
1400.63
1418.3
1438.24
1406.82
1420.86
1482.37
1530.62
1503.35
1455.27
1473.99
1526.75
1549.38
1481.14
1468.36
1378.55
1330.63
1322.7
1385.59
1400.38
1280
1267.38
1282.83
1166.36
968.75
896.24
903.25
825.88
735.09
797.87
872.81
919.14
919.32
987.48
1020.62
1057.08
1036.19
1095.63
1115.1
1073.87
1104.49
1169.43
1186.69
1089.41
1030.71
1101.6
1049.33
1141.2
1183.26
1180.55
1258.51




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116888&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 Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116888&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116888&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 Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.880784068307055
beta0.325933142551067
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.880784068307055 \tabularnewline
beta & 0.325933142551067 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116888&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]0.880784068307055[/C][/ROW]
[ROW][C]beta[/C][C]0.325933142551067[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116888&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116888&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
alpha0.880784068307055
beta0.325933142551067
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131280.661238.6354861111142.0245138888886
141294.871302.99669224229-8.12669224229035
151310.611318.73919752580-8.12919752579592
161270.091274.04787617265-3.95787617265250
171270.21272.56270743747-2.36270743747036
181276.661277.86217627737-1.20217627736838
191303.821340.40662231881-36.5866223188066
201335.851312.4351778491423.4148221508581
211377.941310.5580667363167.3819332636856
221400.631432.50735429539-31.8773542953923
231418.31417.339813116750.960186883245115
241438.241465.85528568432-27.6152856843210
251406.821454.88172323066-48.0617232306638
261420.861412.053048162308.80695183769808
271482.371425.7068576818356.6631423181725
281530.621440.1779763124690.4420236875412
291503.351550.72600984363-47.3760098436339
301455.271532.29166657928-77.0216665792802
311473.991517.84594697256-43.8559469725567
321526.751482.5468945720144.2031054279855
331549.381502.1111537613447.2688462386632
341481.141586.62766868982-105.487668689824
351468.361481.52408826425-13.1640882642473
361378.551481.12171701672-102.571717016718
371330.631347.10118082660-16.4711808265965
381322.71293.3565114735129.3434885264926
391385.591291.1792644145594.410735585451
401400.381314.1367666146986.2432333853064
4112801374.56301631379-94.5630163137935
421267.381267.49313296416-0.113132964160968
431282.831303.28001419461-20.4500141946085
441166.361284.35278240748-117.992782407479
45968.751100.11851537379-131.368515373786
46896.24896.495992805839-0.255992805838673
47903.25812.70771678177390.5422832182269
48825.88840.38361559463-14.5036155946297
49735.09766.873081373722-31.7830813737218
50797.87673.384547949578124.485452050422
51872.81758.35769732047114.452302679530
52919.14799.341081717129119.798918282871
53919.32878.74800007588440.5719999241163
54987.48951.7372755784535.7427244215505
551020.621076.74878504942-56.1287850494206
561057.081064.59290438213-7.5129043821255
571036.191057.61445030328-21.4244503032776
581095.631079.5634886842516.0665113157465
591115.11138.76610474689-23.6661047468924
601073.871138.32905037208-64.4590503720758
611104.491089.4206552316415.0693447683632
621169.431139.9410096789829.4889903210180
631186.691196.88772374292-10.1977237429192
641089.411149.77567784805-60.3656778480515
651030.711030.387243519400.322756480596581
661101.61025.1311434402976.4688565597071
671049.331144.53380145161-95.2038014516133
681141.21062.0122966491379.1877033508651
691183.261112.8848449662870.3751550337245
701180.551229.65752895741-49.1075289574128
711258.511217.5076740060841.0023259939153

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1280.66 & 1238.63548611111 & 42.0245138888886 \tabularnewline
14 & 1294.87 & 1302.99669224229 & -8.12669224229035 \tabularnewline
15 & 1310.61 & 1318.73919752580 & -8.12919752579592 \tabularnewline
16 & 1270.09 & 1274.04787617265 & -3.95787617265250 \tabularnewline
17 & 1270.2 & 1272.56270743747 & -2.36270743747036 \tabularnewline
18 & 1276.66 & 1277.86217627737 & -1.20217627736838 \tabularnewline
19 & 1303.82 & 1340.40662231881 & -36.5866223188066 \tabularnewline
20 & 1335.85 & 1312.43517784914 & 23.4148221508581 \tabularnewline
21 & 1377.94 & 1310.55806673631 & 67.3819332636856 \tabularnewline
22 & 1400.63 & 1432.50735429539 & -31.8773542953923 \tabularnewline
23 & 1418.3 & 1417.33981311675 & 0.960186883245115 \tabularnewline
24 & 1438.24 & 1465.85528568432 & -27.6152856843210 \tabularnewline
25 & 1406.82 & 1454.88172323066 & -48.0617232306638 \tabularnewline
26 & 1420.86 & 1412.05304816230 & 8.80695183769808 \tabularnewline
27 & 1482.37 & 1425.70685768183 & 56.6631423181725 \tabularnewline
28 & 1530.62 & 1440.17797631246 & 90.4420236875412 \tabularnewline
29 & 1503.35 & 1550.72600984363 & -47.3760098436339 \tabularnewline
30 & 1455.27 & 1532.29166657928 & -77.0216665792802 \tabularnewline
31 & 1473.99 & 1517.84594697256 & -43.8559469725567 \tabularnewline
32 & 1526.75 & 1482.54689457201 & 44.2031054279855 \tabularnewline
33 & 1549.38 & 1502.11115376134 & 47.2688462386632 \tabularnewline
34 & 1481.14 & 1586.62766868982 & -105.487668689824 \tabularnewline
35 & 1468.36 & 1481.52408826425 & -13.1640882642473 \tabularnewline
36 & 1378.55 & 1481.12171701672 & -102.571717016718 \tabularnewline
37 & 1330.63 & 1347.10118082660 & -16.4711808265965 \tabularnewline
38 & 1322.7 & 1293.35651147351 & 29.3434885264926 \tabularnewline
39 & 1385.59 & 1291.17926441455 & 94.410735585451 \tabularnewline
40 & 1400.38 & 1314.13676661469 & 86.2432333853064 \tabularnewline
41 & 1280 & 1374.56301631379 & -94.5630163137935 \tabularnewline
42 & 1267.38 & 1267.49313296416 & -0.113132964160968 \tabularnewline
43 & 1282.83 & 1303.28001419461 & -20.4500141946085 \tabularnewline
44 & 1166.36 & 1284.35278240748 & -117.992782407479 \tabularnewline
45 & 968.75 & 1100.11851537379 & -131.368515373786 \tabularnewline
46 & 896.24 & 896.495992805839 & -0.255992805838673 \tabularnewline
47 & 903.25 & 812.707716781773 & 90.5422832182269 \tabularnewline
48 & 825.88 & 840.38361559463 & -14.5036155946297 \tabularnewline
49 & 735.09 & 766.873081373722 & -31.7830813737218 \tabularnewline
50 & 797.87 & 673.384547949578 & 124.485452050422 \tabularnewline
51 & 872.81 & 758.35769732047 & 114.452302679530 \tabularnewline
52 & 919.14 & 799.341081717129 & 119.798918282871 \tabularnewline
53 & 919.32 & 878.748000075884 & 40.5719999241163 \tabularnewline
54 & 987.48 & 951.73727557845 & 35.7427244215505 \tabularnewline
55 & 1020.62 & 1076.74878504942 & -56.1287850494206 \tabularnewline
56 & 1057.08 & 1064.59290438213 & -7.5129043821255 \tabularnewline
57 & 1036.19 & 1057.61445030328 & -21.4244503032776 \tabularnewline
58 & 1095.63 & 1079.56348868425 & 16.0665113157465 \tabularnewline
59 & 1115.1 & 1138.76610474689 & -23.6661047468924 \tabularnewline
60 & 1073.87 & 1138.32905037208 & -64.4590503720758 \tabularnewline
61 & 1104.49 & 1089.42065523164 & 15.0693447683632 \tabularnewline
62 & 1169.43 & 1139.94100967898 & 29.4889903210180 \tabularnewline
63 & 1186.69 & 1196.88772374292 & -10.1977237429192 \tabularnewline
64 & 1089.41 & 1149.77567784805 & -60.3656778480515 \tabularnewline
65 & 1030.71 & 1030.38724351940 & 0.322756480596581 \tabularnewline
66 & 1101.6 & 1025.13114344029 & 76.4688565597071 \tabularnewline
67 & 1049.33 & 1144.53380145161 & -95.2038014516133 \tabularnewline
68 & 1141.2 & 1062.01229664913 & 79.1877033508651 \tabularnewline
69 & 1183.26 & 1112.88484496628 & 70.3751550337245 \tabularnewline
70 & 1180.55 & 1229.65752895741 & -49.1075289574128 \tabularnewline
71 & 1258.51 & 1217.50767400608 & 41.0023259939153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116888&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]1280.66[/C][C]1238.63548611111[/C][C]42.0245138888886[/C][/ROW]
[ROW][C]14[/C][C]1294.87[/C][C]1302.99669224229[/C][C]-8.12669224229035[/C][/ROW]
[ROW][C]15[/C][C]1310.61[/C][C]1318.73919752580[/C][C]-8.12919752579592[/C][/ROW]
[ROW][C]16[/C][C]1270.09[/C][C]1274.04787617265[/C][C]-3.95787617265250[/C][/ROW]
[ROW][C]17[/C][C]1270.2[/C][C]1272.56270743747[/C][C]-2.36270743747036[/C][/ROW]
[ROW][C]18[/C][C]1276.66[/C][C]1277.86217627737[/C][C]-1.20217627736838[/C][/ROW]
[ROW][C]19[/C][C]1303.82[/C][C]1340.40662231881[/C][C]-36.5866223188066[/C][/ROW]
[ROW][C]20[/C][C]1335.85[/C][C]1312.43517784914[/C][C]23.4148221508581[/C][/ROW]
[ROW][C]21[/C][C]1377.94[/C][C]1310.55806673631[/C][C]67.3819332636856[/C][/ROW]
[ROW][C]22[/C][C]1400.63[/C][C]1432.50735429539[/C][C]-31.8773542953923[/C][/ROW]
[ROW][C]23[/C][C]1418.3[/C][C]1417.33981311675[/C][C]0.960186883245115[/C][/ROW]
[ROW][C]24[/C][C]1438.24[/C][C]1465.85528568432[/C][C]-27.6152856843210[/C][/ROW]
[ROW][C]25[/C][C]1406.82[/C][C]1454.88172323066[/C][C]-48.0617232306638[/C][/ROW]
[ROW][C]26[/C][C]1420.86[/C][C]1412.05304816230[/C][C]8.80695183769808[/C][/ROW]
[ROW][C]27[/C][C]1482.37[/C][C]1425.70685768183[/C][C]56.6631423181725[/C][/ROW]
[ROW][C]28[/C][C]1530.62[/C][C]1440.17797631246[/C][C]90.4420236875412[/C][/ROW]
[ROW][C]29[/C][C]1503.35[/C][C]1550.72600984363[/C][C]-47.3760098436339[/C][/ROW]
[ROW][C]30[/C][C]1455.27[/C][C]1532.29166657928[/C][C]-77.0216665792802[/C][/ROW]
[ROW][C]31[/C][C]1473.99[/C][C]1517.84594697256[/C][C]-43.8559469725567[/C][/ROW]
[ROW][C]32[/C][C]1526.75[/C][C]1482.54689457201[/C][C]44.2031054279855[/C][/ROW]
[ROW][C]33[/C][C]1549.38[/C][C]1502.11115376134[/C][C]47.2688462386632[/C][/ROW]
[ROW][C]34[/C][C]1481.14[/C][C]1586.62766868982[/C][C]-105.487668689824[/C][/ROW]
[ROW][C]35[/C][C]1468.36[/C][C]1481.52408826425[/C][C]-13.1640882642473[/C][/ROW]
[ROW][C]36[/C][C]1378.55[/C][C]1481.12171701672[/C][C]-102.571717016718[/C][/ROW]
[ROW][C]37[/C][C]1330.63[/C][C]1347.10118082660[/C][C]-16.4711808265965[/C][/ROW]
[ROW][C]38[/C][C]1322.7[/C][C]1293.35651147351[/C][C]29.3434885264926[/C][/ROW]
[ROW][C]39[/C][C]1385.59[/C][C]1291.17926441455[/C][C]94.410735585451[/C][/ROW]
[ROW][C]40[/C][C]1400.38[/C][C]1314.13676661469[/C][C]86.2432333853064[/C][/ROW]
[ROW][C]41[/C][C]1280[/C][C]1374.56301631379[/C][C]-94.5630163137935[/C][/ROW]
[ROW][C]42[/C][C]1267.38[/C][C]1267.49313296416[/C][C]-0.113132964160968[/C][/ROW]
[ROW][C]43[/C][C]1282.83[/C][C]1303.28001419461[/C][C]-20.4500141946085[/C][/ROW]
[ROW][C]44[/C][C]1166.36[/C][C]1284.35278240748[/C][C]-117.992782407479[/C][/ROW]
[ROW][C]45[/C][C]968.75[/C][C]1100.11851537379[/C][C]-131.368515373786[/C][/ROW]
[ROW][C]46[/C][C]896.24[/C][C]896.495992805839[/C][C]-0.255992805838673[/C][/ROW]
[ROW][C]47[/C][C]903.25[/C][C]812.707716781773[/C][C]90.5422832182269[/C][/ROW]
[ROW][C]48[/C][C]825.88[/C][C]840.38361559463[/C][C]-14.5036155946297[/C][/ROW]
[ROW][C]49[/C][C]735.09[/C][C]766.873081373722[/C][C]-31.7830813737218[/C][/ROW]
[ROW][C]50[/C][C]797.87[/C][C]673.384547949578[/C][C]124.485452050422[/C][/ROW]
[ROW][C]51[/C][C]872.81[/C][C]758.35769732047[/C][C]114.452302679530[/C][/ROW]
[ROW][C]52[/C][C]919.14[/C][C]799.341081717129[/C][C]119.798918282871[/C][/ROW]
[ROW][C]53[/C][C]919.32[/C][C]878.748000075884[/C][C]40.5719999241163[/C][/ROW]
[ROW][C]54[/C][C]987.48[/C][C]951.73727557845[/C][C]35.7427244215505[/C][/ROW]
[ROW][C]55[/C][C]1020.62[/C][C]1076.74878504942[/C][C]-56.1287850494206[/C][/ROW]
[ROW][C]56[/C][C]1057.08[/C][C]1064.59290438213[/C][C]-7.5129043821255[/C][/ROW]
[ROW][C]57[/C][C]1036.19[/C][C]1057.61445030328[/C][C]-21.4244503032776[/C][/ROW]
[ROW][C]58[/C][C]1095.63[/C][C]1079.56348868425[/C][C]16.0665113157465[/C][/ROW]
[ROW][C]59[/C][C]1115.1[/C][C]1138.76610474689[/C][C]-23.6661047468924[/C][/ROW]
[ROW][C]60[/C][C]1073.87[/C][C]1138.32905037208[/C][C]-64.4590503720758[/C][/ROW]
[ROW][C]61[/C][C]1104.49[/C][C]1089.42065523164[/C][C]15.0693447683632[/C][/ROW]
[ROW][C]62[/C][C]1169.43[/C][C]1139.94100967898[/C][C]29.4889903210180[/C][/ROW]
[ROW][C]63[/C][C]1186.69[/C][C]1196.88772374292[/C][C]-10.1977237429192[/C][/ROW]
[ROW][C]64[/C][C]1089.41[/C][C]1149.77567784805[/C][C]-60.3656778480515[/C][/ROW]
[ROW][C]65[/C][C]1030.71[/C][C]1030.38724351940[/C][C]0.322756480596581[/C][/ROW]
[ROW][C]66[/C][C]1101.6[/C][C]1025.13114344029[/C][C]76.4688565597071[/C][/ROW]
[ROW][C]67[/C][C]1049.33[/C][C]1144.53380145161[/C][C]-95.2038014516133[/C][/ROW]
[ROW][C]68[/C][C]1141.2[/C][C]1062.01229664913[/C][C]79.1877033508651[/C][/ROW]
[ROW][C]69[/C][C]1183.26[/C][C]1112.88484496628[/C][C]70.3751550337245[/C][/ROW]
[ROW][C]70[/C][C]1180.55[/C][C]1229.65752895741[/C][C]-49.1075289574128[/C][/ROW]
[ROW][C]71[/C][C]1258.51[/C][C]1217.50767400608[/C][C]41.0023259939153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116888&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116888&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
131280.661238.6354861111142.0245138888886
141294.871302.99669224229-8.12669224229035
151310.611318.73919752580-8.12919752579592
161270.091274.04787617265-3.95787617265250
171270.21272.56270743747-2.36270743747036
181276.661277.86217627737-1.20217627736838
191303.821340.40662231881-36.5866223188066
201335.851312.4351778491423.4148221508581
211377.941310.5580667363167.3819332636856
221400.631432.50735429539-31.8773542953923
231418.31417.339813116750.960186883245115
241438.241465.85528568432-27.6152856843210
251406.821454.88172323066-48.0617232306638
261420.861412.053048162308.80695183769808
271482.371425.7068576818356.6631423181725
281530.621440.1779763124690.4420236875412
291503.351550.72600984363-47.3760098436339
301455.271532.29166657928-77.0216665792802
311473.991517.84594697256-43.8559469725567
321526.751482.5468945720144.2031054279855
331549.381502.1111537613447.2688462386632
341481.141586.62766868982-105.487668689824
351468.361481.52408826425-13.1640882642473
361378.551481.12171701672-102.571717016718
371330.631347.10118082660-16.4711808265965
381322.71293.3565114735129.3434885264926
391385.591291.1792644145594.410735585451
401400.381314.1367666146986.2432333853064
4112801374.56301631379-94.5630163137935
421267.381267.49313296416-0.113132964160968
431282.831303.28001419461-20.4500141946085
441166.361284.35278240748-117.992782407479
45968.751100.11851537379-131.368515373786
46896.24896.495992805839-0.255992805838673
47903.25812.70771678177390.5422832182269
48825.88840.38361559463-14.5036155946297
49735.09766.873081373722-31.7830813737218
50797.87673.384547949578124.485452050422
51872.81758.35769732047114.452302679530
52919.14799.341081717129119.798918282871
53919.32878.74800007588440.5719999241163
54987.48951.7372755784535.7427244215505
551020.621076.74878504942-56.1287850494206
561057.081064.59290438213-7.5129043821255
571036.191057.61445030328-21.4244503032776
581095.631079.5634886842516.0665113157465
591115.11138.76610474689-23.6661047468924
601073.871138.32905037208-64.4590503720758
611104.491089.4206552316415.0693447683632
621169.431139.9410096789829.4889903210180
631186.691196.88772374292-10.1977237429192
641089.411149.77567784805-60.3656778480515
651030.711030.387243519400.322756480596581
661101.61025.1311434402976.4688565597071
671049.331144.53380145161-95.2038014516133
681141.21062.0122966491379.1877033508651
691183.261112.8848449662870.3751550337245
701180.551229.65752895741-49.1075289574128
711258.511217.5076740060841.0023259939153







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
721278.519721238171158.647737326801398.39170514955
731323.724922263071139.422036672171508.02780785396
741386.223471156561132.481294768821639.96564754430
751427.531842924441098.913002794571756.15068305431
761401.41487848404992.5729311413581810.25682582671
771377.75408871093883.5499671449321871.95821027693
781416.52237125285832.0425136659652001.00222883974
791461.38476746588781.9312056960322140.83832923573
801524.11669958567745.1895758811882303.04382329016
811522.06763777814639.3467858175122404.78848973876
821560.28395184179569.6117092856322550.95619439795
831613.90056957250511.2664202115662716.53471893344

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
72 & 1278.51972123817 & 1158.64773732680 & 1398.39170514955 \tabularnewline
73 & 1323.72492226307 & 1139.42203667217 & 1508.02780785396 \tabularnewline
74 & 1386.22347115656 & 1132.48129476882 & 1639.96564754430 \tabularnewline
75 & 1427.53184292444 & 1098.91300279457 & 1756.15068305431 \tabularnewline
76 & 1401.41487848404 & 992.572931141358 & 1810.25682582671 \tabularnewline
77 & 1377.75408871093 & 883.549967144932 & 1871.95821027693 \tabularnewline
78 & 1416.52237125285 & 832.042513665965 & 2001.00222883974 \tabularnewline
79 & 1461.38476746588 & 781.931205696032 & 2140.83832923573 \tabularnewline
80 & 1524.11669958567 & 745.189575881188 & 2303.04382329016 \tabularnewline
81 & 1522.06763777814 & 639.346785817512 & 2404.78848973876 \tabularnewline
82 & 1560.28395184179 & 569.611709285632 & 2550.95619439795 \tabularnewline
83 & 1613.90056957250 & 511.266420211566 & 2716.53471893344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116888&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]72[/C][C]1278.51972123817[/C][C]1158.64773732680[/C][C]1398.39170514955[/C][/ROW]
[ROW][C]73[/C][C]1323.72492226307[/C][C]1139.42203667217[/C][C]1508.02780785396[/C][/ROW]
[ROW][C]74[/C][C]1386.22347115656[/C][C]1132.48129476882[/C][C]1639.96564754430[/C][/ROW]
[ROW][C]75[/C][C]1427.53184292444[/C][C]1098.91300279457[/C][C]1756.15068305431[/C][/ROW]
[ROW][C]76[/C][C]1401.41487848404[/C][C]992.572931141358[/C][C]1810.25682582671[/C][/ROW]
[ROW][C]77[/C][C]1377.75408871093[/C][C]883.549967144932[/C][C]1871.95821027693[/C][/ROW]
[ROW][C]78[/C][C]1416.52237125285[/C][C]832.042513665965[/C][C]2001.00222883974[/C][/ROW]
[ROW][C]79[/C][C]1461.38476746588[/C][C]781.931205696032[/C][C]2140.83832923573[/C][/ROW]
[ROW][C]80[/C][C]1524.11669958567[/C][C]745.189575881188[/C][C]2303.04382329016[/C][/ROW]
[ROW][C]81[/C][C]1522.06763777814[/C][C]639.346785817512[/C][C]2404.78848973876[/C][/ROW]
[ROW][C]82[/C][C]1560.28395184179[/C][C]569.611709285632[/C][C]2550.95619439795[/C][/ROW]
[ROW][C]83[/C][C]1613.90056957250[/C][C]511.266420211566[/C][C]2716.53471893344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116888&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116888&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
721278.519721238171158.647737326801398.39170514955
731323.724922263071139.422036672171508.02780785396
741386.223471156561132.481294768821639.96564754430
751427.531842924441098.913002794571756.15068305431
761401.41487848404992.5729311413581810.25682582671
771377.75408871093883.5499671449321871.95821027693
781416.52237125285832.0425136659652001.00222883974
791461.38476746588781.9312056960322140.83832923573
801524.11669958567745.1895758811882303.04382329016
811522.06763777814639.3467858175122404.78848973876
821560.28395184179569.6117092856322550.95619439795
831613.90056957250511.2664202115662716.53471893344



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')