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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 03:15:08 -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/2012/Dec/17/t1355732195q3rkcqmskbbpor3.htm/, Retrieved Fri, 26 Apr 2024 15:47:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200700, Retrieved Fri, 26 Apr 2024 15:47:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-17 08:15:08] [b94d6af934ff01803109e5a51192a6cb] [Current]
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Dataseries X:
155.28
173.24
180.16
181.52
182.25
182.19
182
181.65
180.07
182.62
180.38
181.15
180.5
181.14
180.93
211.91
223.81
226.88
226.8
231.81
232.06
232.32
228.37
226.31
225.72
219.98
219.31
215.19
213.81
213.7
213.6
213.52
218.39
219.97
221.09
219.17
219.17
218.45
216.88
216.19
214.59
269.87
272.71
280.35
274.5
268.86
261.7
263.98
263.01
262.79
263.59
267
267.89
267.86
266.84
268.24
267.67
269.07
270.87
271.68
271.63
275.21
276.66
276.08
278.3
279.06
279.28
279.12
262.72
262.55
260.7
259.14




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200700&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]4 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=200700&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200700&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.258036054059694
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.258036054059694 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200700&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.258036054059694[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200700&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200700&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
alpha1
beta0.258036054059694
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3180.16191.2-11.04
4181.52195.271281963181-13.751281963181
5182.25193.08295542714-10.8329554271395
6182.19191.017662354916-8.82766235491587
7182188.679807194282-6.67980719428206
8181.65186.76617610399-5.11617610398997
9180.07185.096018210242-5.02601821024192
10182.62182.2191243036390.400875696361112
11180.38184.872564686496-4.49256468649637
12181.15181.473321022185-0.323321022184899
13180.5182.159892541426-1.65989254142576
14181.14181.0815804198730.0584195801268379
15180.93181.736654777809-0.806654777808888
16211.91181.31850876195530.5914912380453
17223.81220.1922164488223.61778355117838
18226.88233.02573504081-6.14573504080977
19226.8234.509913821583-7.7099138215828
20231.81232.440478081921-0.630478081921297
21232.06237.287792005491-5.22779200549118
22232.32236.188833184949-3.86883318494944
23228.37235.45053473609-7.08053473608987
24226.31229.673501492157-3.36350149215664
25225.72226.745596839297-1.02559683929667
26219.98225.890955877828-5.91095587782846
27219.31218.6257161473930.684283852607365
28215.19218.132286052576-2.94228605257621
29213.81213.2530701696550.556929830345439
30213.7212.0167781454651.68322185453493
31213.6212.3411100709161.25888992908372
32213.52212.5659490607130.954050939287498
33218.39212.7321286004585.65787139954176
34219.97219.0620634107730.907936589226836
35221.09220.8763437855940.213656214406313
36219.17222.051474792084-2.88147479208445
37219.17219.387950406862-0.217950406862485
38218.45219.331711343895-0.881711343894978
39216.88218.384198027897-1.50419802789665
40216.19216.426060704254-0.236060704253816
41214.59215.67514853161-1.0851485316096
42269.87213.79514108644456.0748589135556
43272.71283.544476412452-10.8344764124524
44280.35283.58879087118-3.2387908711803
45274.5290.393066054856-15.8930660548564
46268.86280.442082003151-11.5820820031512
47261.7271.813487265262-10.1134872652623
48263.98262.0438429185511.93615708144904
49263.01264.823441251888-1.81344125188787
50262.79263.385508026982-0.595508026981577
51263.59263.0118454855380.578154514461517
52267263.9610301950873.03896980491317
53267.89268.155193971953-0.265193971953238
54267.86268.97676436587-1.11676436586998
55266.84268.658598895586-1.81859889558649
56268.24267.1693348126521.07066518734808
57267.67268.845605032814-1.17560503281436
58269.07267.9722565490141.09774345098577
59270.87269.6555139374761.21448606252358
60271.68271.768895128761-0.0888951287605551
61271.63272.55595698051-0.925956980510023
62275.21272.267026695032.94297330496977
63276.66276.6064199138480.0535800861524081
64276.08278.070245507855-1.99024550785458
65278.3276.9766904103981.32330958960227
66279.06279.538151995198-0.478151995198061
67279.28280.174771541116-0.894771541116427
68279.12280.163888223362-1.04388822336176
69262.72279.734527425326-17.0145274253261
70262.55258.9441659068053.60583409319543
71260.7259.7046011078070.99539889219335
72259.14258.1114499101641.02855008983641

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 180.16 & 191.2 & -11.04 \tabularnewline
4 & 181.52 & 195.271281963181 & -13.751281963181 \tabularnewline
5 & 182.25 & 193.08295542714 & -10.8329554271395 \tabularnewline
6 & 182.19 & 191.017662354916 & -8.82766235491587 \tabularnewline
7 & 182 & 188.679807194282 & -6.67980719428206 \tabularnewline
8 & 181.65 & 186.76617610399 & -5.11617610398997 \tabularnewline
9 & 180.07 & 185.096018210242 & -5.02601821024192 \tabularnewline
10 & 182.62 & 182.219124303639 & 0.400875696361112 \tabularnewline
11 & 180.38 & 184.872564686496 & -4.49256468649637 \tabularnewline
12 & 181.15 & 181.473321022185 & -0.323321022184899 \tabularnewline
13 & 180.5 & 182.159892541426 & -1.65989254142576 \tabularnewline
14 & 181.14 & 181.081580419873 & 0.0584195801268379 \tabularnewline
15 & 180.93 & 181.736654777809 & -0.806654777808888 \tabularnewline
16 & 211.91 & 181.318508761955 & 30.5914912380453 \tabularnewline
17 & 223.81 & 220.192216448822 & 3.61778355117838 \tabularnewline
18 & 226.88 & 233.02573504081 & -6.14573504080977 \tabularnewline
19 & 226.8 & 234.509913821583 & -7.7099138215828 \tabularnewline
20 & 231.81 & 232.440478081921 & -0.630478081921297 \tabularnewline
21 & 232.06 & 237.287792005491 & -5.22779200549118 \tabularnewline
22 & 232.32 & 236.188833184949 & -3.86883318494944 \tabularnewline
23 & 228.37 & 235.45053473609 & -7.08053473608987 \tabularnewline
24 & 226.31 & 229.673501492157 & -3.36350149215664 \tabularnewline
25 & 225.72 & 226.745596839297 & -1.02559683929667 \tabularnewline
26 & 219.98 & 225.890955877828 & -5.91095587782846 \tabularnewline
27 & 219.31 & 218.625716147393 & 0.684283852607365 \tabularnewline
28 & 215.19 & 218.132286052576 & -2.94228605257621 \tabularnewline
29 & 213.81 & 213.253070169655 & 0.556929830345439 \tabularnewline
30 & 213.7 & 212.016778145465 & 1.68322185453493 \tabularnewline
31 & 213.6 & 212.341110070916 & 1.25888992908372 \tabularnewline
32 & 213.52 & 212.565949060713 & 0.954050939287498 \tabularnewline
33 & 218.39 & 212.732128600458 & 5.65787139954176 \tabularnewline
34 & 219.97 & 219.062063410773 & 0.907936589226836 \tabularnewline
35 & 221.09 & 220.876343785594 & 0.213656214406313 \tabularnewline
36 & 219.17 & 222.051474792084 & -2.88147479208445 \tabularnewline
37 & 219.17 & 219.387950406862 & -0.217950406862485 \tabularnewline
38 & 218.45 & 219.331711343895 & -0.881711343894978 \tabularnewline
39 & 216.88 & 218.384198027897 & -1.50419802789665 \tabularnewline
40 & 216.19 & 216.426060704254 & -0.236060704253816 \tabularnewline
41 & 214.59 & 215.67514853161 & -1.0851485316096 \tabularnewline
42 & 269.87 & 213.795141086444 & 56.0748589135556 \tabularnewline
43 & 272.71 & 283.544476412452 & -10.8344764124524 \tabularnewline
44 & 280.35 & 283.58879087118 & -3.2387908711803 \tabularnewline
45 & 274.5 & 290.393066054856 & -15.8930660548564 \tabularnewline
46 & 268.86 & 280.442082003151 & -11.5820820031512 \tabularnewline
47 & 261.7 & 271.813487265262 & -10.1134872652623 \tabularnewline
48 & 263.98 & 262.043842918551 & 1.93615708144904 \tabularnewline
49 & 263.01 & 264.823441251888 & -1.81344125188787 \tabularnewline
50 & 262.79 & 263.385508026982 & -0.595508026981577 \tabularnewline
51 & 263.59 & 263.011845485538 & 0.578154514461517 \tabularnewline
52 & 267 & 263.961030195087 & 3.03896980491317 \tabularnewline
53 & 267.89 & 268.155193971953 & -0.265193971953238 \tabularnewline
54 & 267.86 & 268.97676436587 & -1.11676436586998 \tabularnewline
55 & 266.84 & 268.658598895586 & -1.81859889558649 \tabularnewline
56 & 268.24 & 267.169334812652 & 1.07066518734808 \tabularnewline
57 & 267.67 & 268.845605032814 & -1.17560503281436 \tabularnewline
58 & 269.07 & 267.972256549014 & 1.09774345098577 \tabularnewline
59 & 270.87 & 269.655513937476 & 1.21448606252358 \tabularnewline
60 & 271.68 & 271.768895128761 & -0.0888951287605551 \tabularnewline
61 & 271.63 & 272.55595698051 & -0.925956980510023 \tabularnewline
62 & 275.21 & 272.26702669503 & 2.94297330496977 \tabularnewline
63 & 276.66 & 276.606419913848 & 0.0535800861524081 \tabularnewline
64 & 276.08 & 278.070245507855 & -1.99024550785458 \tabularnewline
65 & 278.3 & 276.976690410398 & 1.32330958960227 \tabularnewline
66 & 279.06 & 279.538151995198 & -0.478151995198061 \tabularnewline
67 & 279.28 & 280.174771541116 & -0.894771541116427 \tabularnewline
68 & 279.12 & 280.163888223362 & -1.04388822336176 \tabularnewline
69 & 262.72 & 279.734527425326 & -17.0145274253261 \tabularnewline
70 & 262.55 & 258.944165906805 & 3.60583409319543 \tabularnewline
71 & 260.7 & 259.704601107807 & 0.99539889219335 \tabularnewline
72 & 259.14 & 258.111449910164 & 1.02855008983641 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200700&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]180.16[/C][C]191.2[/C][C]-11.04[/C][/ROW]
[ROW][C]4[/C][C]181.52[/C][C]195.271281963181[/C][C]-13.751281963181[/C][/ROW]
[ROW][C]5[/C][C]182.25[/C][C]193.08295542714[/C][C]-10.8329554271395[/C][/ROW]
[ROW][C]6[/C][C]182.19[/C][C]191.017662354916[/C][C]-8.82766235491587[/C][/ROW]
[ROW][C]7[/C][C]182[/C][C]188.679807194282[/C][C]-6.67980719428206[/C][/ROW]
[ROW][C]8[/C][C]181.65[/C][C]186.76617610399[/C][C]-5.11617610398997[/C][/ROW]
[ROW][C]9[/C][C]180.07[/C][C]185.096018210242[/C][C]-5.02601821024192[/C][/ROW]
[ROW][C]10[/C][C]182.62[/C][C]182.219124303639[/C][C]0.400875696361112[/C][/ROW]
[ROW][C]11[/C][C]180.38[/C][C]184.872564686496[/C][C]-4.49256468649637[/C][/ROW]
[ROW][C]12[/C][C]181.15[/C][C]181.473321022185[/C][C]-0.323321022184899[/C][/ROW]
[ROW][C]13[/C][C]180.5[/C][C]182.159892541426[/C][C]-1.65989254142576[/C][/ROW]
[ROW][C]14[/C][C]181.14[/C][C]181.081580419873[/C][C]0.0584195801268379[/C][/ROW]
[ROW][C]15[/C][C]180.93[/C][C]181.736654777809[/C][C]-0.806654777808888[/C][/ROW]
[ROW][C]16[/C][C]211.91[/C][C]181.318508761955[/C][C]30.5914912380453[/C][/ROW]
[ROW][C]17[/C][C]223.81[/C][C]220.192216448822[/C][C]3.61778355117838[/C][/ROW]
[ROW][C]18[/C][C]226.88[/C][C]233.02573504081[/C][C]-6.14573504080977[/C][/ROW]
[ROW][C]19[/C][C]226.8[/C][C]234.509913821583[/C][C]-7.7099138215828[/C][/ROW]
[ROW][C]20[/C][C]231.81[/C][C]232.440478081921[/C][C]-0.630478081921297[/C][/ROW]
[ROW][C]21[/C][C]232.06[/C][C]237.287792005491[/C][C]-5.22779200549118[/C][/ROW]
[ROW][C]22[/C][C]232.32[/C][C]236.188833184949[/C][C]-3.86883318494944[/C][/ROW]
[ROW][C]23[/C][C]228.37[/C][C]235.45053473609[/C][C]-7.08053473608987[/C][/ROW]
[ROW][C]24[/C][C]226.31[/C][C]229.673501492157[/C][C]-3.36350149215664[/C][/ROW]
[ROW][C]25[/C][C]225.72[/C][C]226.745596839297[/C][C]-1.02559683929667[/C][/ROW]
[ROW][C]26[/C][C]219.98[/C][C]225.890955877828[/C][C]-5.91095587782846[/C][/ROW]
[ROW][C]27[/C][C]219.31[/C][C]218.625716147393[/C][C]0.684283852607365[/C][/ROW]
[ROW][C]28[/C][C]215.19[/C][C]218.132286052576[/C][C]-2.94228605257621[/C][/ROW]
[ROW][C]29[/C][C]213.81[/C][C]213.253070169655[/C][C]0.556929830345439[/C][/ROW]
[ROW][C]30[/C][C]213.7[/C][C]212.016778145465[/C][C]1.68322185453493[/C][/ROW]
[ROW][C]31[/C][C]213.6[/C][C]212.341110070916[/C][C]1.25888992908372[/C][/ROW]
[ROW][C]32[/C][C]213.52[/C][C]212.565949060713[/C][C]0.954050939287498[/C][/ROW]
[ROW][C]33[/C][C]218.39[/C][C]212.732128600458[/C][C]5.65787139954176[/C][/ROW]
[ROW][C]34[/C][C]219.97[/C][C]219.062063410773[/C][C]0.907936589226836[/C][/ROW]
[ROW][C]35[/C][C]221.09[/C][C]220.876343785594[/C][C]0.213656214406313[/C][/ROW]
[ROW][C]36[/C][C]219.17[/C][C]222.051474792084[/C][C]-2.88147479208445[/C][/ROW]
[ROW][C]37[/C][C]219.17[/C][C]219.387950406862[/C][C]-0.217950406862485[/C][/ROW]
[ROW][C]38[/C][C]218.45[/C][C]219.331711343895[/C][C]-0.881711343894978[/C][/ROW]
[ROW][C]39[/C][C]216.88[/C][C]218.384198027897[/C][C]-1.50419802789665[/C][/ROW]
[ROW][C]40[/C][C]216.19[/C][C]216.426060704254[/C][C]-0.236060704253816[/C][/ROW]
[ROW][C]41[/C][C]214.59[/C][C]215.67514853161[/C][C]-1.0851485316096[/C][/ROW]
[ROW][C]42[/C][C]269.87[/C][C]213.795141086444[/C][C]56.0748589135556[/C][/ROW]
[ROW][C]43[/C][C]272.71[/C][C]283.544476412452[/C][C]-10.8344764124524[/C][/ROW]
[ROW][C]44[/C][C]280.35[/C][C]283.58879087118[/C][C]-3.2387908711803[/C][/ROW]
[ROW][C]45[/C][C]274.5[/C][C]290.393066054856[/C][C]-15.8930660548564[/C][/ROW]
[ROW][C]46[/C][C]268.86[/C][C]280.442082003151[/C][C]-11.5820820031512[/C][/ROW]
[ROW][C]47[/C][C]261.7[/C][C]271.813487265262[/C][C]-10.1134872652623[/C][/ROW]
[ROW][C]48[/C][C]263.98[/C][C]262.043842918551[/C][C]1.93615708144904[/C][/ROW]
[ROW][C]49[/C][C]263.01[/C][C]264.823441251888[/C][C]-1.81344125188787[/C][/ROW]
[ROW][C]50[/C][C]262.79[/C][C]263.385508026982[/C][C]-0.595508026981577[/C][/ROW]
[ROW][C]51[/C][C]263.59[/C][C]263.011845485538[/C][C]0.578154514461517[/C][/ROW]
[ROW][C]52[/C][C]267[/C][C]263.961030195087[/C][C]3.03896980491317[/C][/ROW]
[ROW][C]53[/C][C]267.89[/C][C]268.155193971953[/C][C]-0.265193971953238[/C][/ROW]
[ROW][C]54[/C][C]267.86[/C][C]268.97676436587[/C][C]-1.11676436586998[/C][/ROW]
[ROW][C]55[/C][C]266.84[/C][C]268.658598895586[/C][C]-1.81859889558649[/C][/ROW]
[ROW][C]56[/C][C]268.24[/C][C]267.169334812652[/C][C]1.07066518734808[/C][/ROW]
[ROW][C]57[/C][C]267.67[/C][C]268.845605032814[/C][C]-1.17560503281436[/C][/ROW]
[ROW][C]58[/C][C]269.07[/C][C]267.972256549014[/C][C]1.09774345098577[/C][/ROW]
[ROW][C]59[/C][C]270.87[/C][C]269.655513937476[/C][C]1.21448606252358[/C][/ROW]
[ROW][C]60[/C][C]271.68[/C][C]271.768895128761[/C][C]-0.0888951287605551[/C][/ROW]
[ROW][C]61[/C][C]271.63[/C][C]272.55595698051[/C][C]-0.925956980510023[/C][/ROW]
[ROW][C]62[/C][C]275.21[/C][C]272.26702669503[/C][C]2.94297330496977[/C][/ROW]
[ROW][C]63[/C][C]276.66[/C][C]276.606419913848[/C][C]0.0535800861524081[/C][/ROW]
[ROW][C]64[/C][C]276.08[/C][C]278.070245507855[/C][C]-1.99024550785458[/C][/ROW]
[ROW][C]65[/C][C]278.3[/C][C]276.976690410398[/C][C]1.32330958960227[/C][/ROW]
[ROW][C]66[/C][C]279.06[/C][C]279.538151995198[/C][C]-0.478151995198061[/C][/ROW]
[ROW][C]67[/C][C]279.28[/C][C]280.174771541116[/C][C]-0.894771541116427[/C][/ROW]
[ROW][C]68[/C][C]279.12[/C][C]280.163888223362[/C][C]-1.04388822336176[/C][/ROW]
[ROW][C]69[/C][C]262.72[/C][C]279.734527425326[/C][C]-17.0145274253261[/C][/ROW]
[ROW][C]70[/C][C]262.55[/C][C]258.944165906805[/C][C]3.60583409319543[/C][/ROW]
[ROW][C]71[/C][C]260.7[/C][C]259.704601107807[/C][C]0.99539889219335[/C][/ROW]
[ROW][C]72[/C][C]259.14[/C][C]258.111449910164[/C][C]1.02855008983641[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200700&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200700&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
3180.16191.2-11.04
4181.52195.271281963181-13.751281963181
5182.25193.08295542714-10.8329554271395
6182.19191.017662354916-8.82766235491587
7182188.679807194282-6.67980719428206
8181.65186.76617610399-5.11617610398997
9180.07185.096018210242-5.02601821024192
10182.62182.2191243036390.400875696361112
11180.38184.872564686496-4.49256468649637
12181.15181.473321022185-0.323321022184899
13180.5182.159892541426-1.65989254142576
14181.14181.0815804198730.0584195801268379
15180.93181.736654777809-0.806654777808888
16211.91181.31850876195530.5914912380453
17223.81220.1922164488223.61778355117838
18226.88233.02573504081-6.14573504080977
19226.8234.509913821583-7.7099138215828
20231.81232.440478081921-0.630478081921297
21232.06237.287792005491-5.22779200549118
22232.32236.188833184949-3.86883318494944
23228.37235.45053473609-7.08053473608987
24226.31229.673501492157-3.36350149215664
25225.72226.745596839297-1.02559683929667
26219.98225.890955877828-5.91095587782846
27219.31218.6257161473930.684283852607365
28215.19218.132286052576-2.94228605257621
29213.81213.2530701696550.556929830345439
30213.7212.0167781454651.68322185453493
31213.6212.3411100709161.25888992908372
32213.52212.5659490607130.954050939287498
33218.39212.7321286004585.65787139954176
34219.97219.0620634107730.907936589226836
35221.09220.8763437855940.213656214406313
36219.17222.051474792084-2.88147479208445
37219.17219.387950406862-0.217950406862485
38218.45219.331711343895-0.881711343894978
39216.88218.384198027897-1.50419802789665
40216.19216.426060704254-0.236060704253816
41214.59215.67514853161-1.0851485316096
42269.87213.79514108644456.0748589135556
43272.71283.544476412452-10.8344764124524
44280.35283.58879087118-3.2387908711803
45274.5290.393066054856-15.8930660548564
46268.86280.442082003151-11.5820820031512
47261.7271.813487265262-10.1134872652623
48263.98262.0438429185511.93615708144904
49263.01264.823441251888-1.81344125188787
50262.79263.385508026982-0.595508026981577
51263.59263.0118454855380.578154514461517
52267263.9610301950873.03896980491317
53267.89268.155193971953-0.265193971953238
54267.86268.97676436587-1.11676436586998
55266.84268.658598895586-1.81859889558649
56268.24267.1693348126521.07066518734808
57267.67268.845605032814-1.17560503281436
58269.07267.9722565490141.09774345098577
59270.87269.6555139374761.21448606252358
60271.68271.768895128761-0.0888951287605551
61271.63272.55595698051-0.925956980510023
62275.21272.267026695032.94297330496977
63276.66276.6064199138480.0535800861524081
64276.08278.070245507855-1.99024550785458
65278.3276.9766904103981.32330958960227
66279.06279.538151995198-0.478151995198061
67279.28280.174771541116-0.894771541116427
68279.12280.163888223362-1.04388822336176
69262.72279.734527425326-17.0145274253261
70262.55258.9441659068053.60583409319543
71260.7259.7046011078070.99539889219335
72259.14258.1114499101641.02855008983641







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73256.816852916748238.701599261245274.93210657225
74254.493705833495225.38133375837283.606077908621
75252.170558750243212.148025152933292.193092347553
76249.847411666991198.51826599749301.176557336491
77247.524264583739184.358894136671310.689635030806
78245.201117500486169.629618254758320.772616746215
79242.877970417234154.32322217756331.432718656908
80240.554823333982138.445863622378342.663783045585
81238.231676250729122.009303326819354.454049174639
82235.908529167477105.027498468359366.789559866595
83233.58538208422587.5150149428409379.655749225609
84231.26223500097369.4862674873581393.038202514587

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 256.816852916748 & 238.701599261245 & 274.93210657225 \tabularnewline
74 & 254.493705833495 & 225.38133375837 & 283.606077908621 \tabularnewline
75 & 252.170558750243 & 212.148025152933 & 292.193092347553 \tabularnewline
76 & 249.847411666991 & 198.51826599749 & 301.176557336491 \tabularnewline
77 & 247.524264583739 & 184.358894136671 & 310.689635030806 \tabularnewline
78 & 245.201117500486 & 169.629618254758 & 320.772616746215 \tabularnewline
79 & 242.877970417234 & 154.32322217756 & 331.432718656908 \tabularnewline
80 & 240.554823333982 & 138.445863622378 & 342.663783045585 \tabularnewline
81 & 238.231676250729 & 122.009303326819 & 354.454049174639 \tabularnewline
82 & 235.908529167477 & 105.027498468359 & 366.789559866595 \tabularnewline
83 & 233.585382084225 & 87.5150149428409 & 379.655749225609 \tabularnewline
84 & 231.262235000973 & 69.4862674873581 & 393.038202514587 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200700&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]256.816852916748[/C][C]238.701599261245[/C][C]274.93210657225[/C][/ROW]
[ROW][C]74[/C][C]254.493705833495[/C][C]225.38133375837[/C][C]283.606077908621[/C][/ROW]
[ROW][C]75[/C][C]252.170558750243[/C][C]212.148025152933[/C][C]292.193092347553[/C][/ROW]
[ROW][C]76[/C][C]249.847411666991[/C][C]198.51826599749[/C][C]301.176557336491[/C][/ROW]
[ROW][C]77[/C][C]247.524264583739[/C][C]184.358894136671[/C][C]310.689635030806[/C][/ROW]
[ROW][C]78[/C][C]245.201117500486[/C][C]169.629618254758[/C][C]320.772616746215[/C][/ROW]
[ROW][C]79[/C][C]242.877970417234[/C][C]154.32322217756[/C][C]331.432718656908[/C][/ROW]
[ROW][C]80[/C][C]240.554823333982[/C][C]138.445863622378[/C][C]342.663783045585[/C][/ROW]
[ROW][C]81[/C][C]238.231676250729[/C][C]122.009303326819[/C][C]354.454049174639[/C][/ROW]
[ROW][C]82[/C][C]235.908529167477[/C][C]105.027498468359[/C][C]366.789559866595[/C][/ROW]
[ROW][C]83[/C][C]233.585382084225[/C][C]87.5150149428409[/C][C]379.655749225609[/C][/ROW]
[ROW][C]84[/C][C]231.262235000973[/C][C]69.4862674873581[/C][C]393.038202514587[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200700&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200700&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
73256.816852916748238.701599261245274.93210657225
74254.493705833495225.38133375837283.606077908621
75252.170558750243212.148025152933292.193092347553
76249.847411666991198.51826599749301.176557336491
77247.524264583739184.358894136671310.689635030806
78245.201117500486169.629618254758320.772616746215
79242.877970417234154.32322217756331.432718656908
80240.554823333982138.445863622378342.663783045585
81238.231676250729122.009303326819354.454049174639
82235.908529167477105.027498468359366.789559866595
83233.58538208422587.5150149428409379.655749225609
84231.26223500097369.4862674873581393.038202514587



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')