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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 25 May 2012 15:49:59 -0400
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/May/25/t13379757177r71kv93i4nkep8.htm/, Retrieved Fri, 03 May 2024 23:00:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167534, Retrieved Fri, 03 May 2024 23:00:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Classical Deompos...] [2012-05-09 16:46:48] [74be16979710d4c4e7c6647856088456]
- RMP   [Exponential Smoothing] [oefening 10 expon...] [2012-05-25 19:33:51] [2f0f353a58a70fd7baf0f5141860d820]
- R PD      [Exponential Smoothing] [oefening 10 expon...] [2012-05-25 19:49:59] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
7,72
7,67
7,84
7,79
7,83
7,94
8,02
8,06
8,12
8,13
7,97
8,01
8,00
7,90
7,99
8,02
8,08
8,02
8,07
8,11
8,19
8,16
8,08
8,22
8,15
8,19
8,31
8,30
8,34
8,31
8,38
8,34
8,44
8,64
8,60
8,61
8,54
8,69
8,73
8,91
9,01
9,08
8,94
9,03
9,02
8,96
9,03
8,94
8,95
8,95
8,99
8,93
8,98
8,95
9,02
8,92
9,10
9,06
8,97
8,89




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167534&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167534&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167534&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.821375270653289
beta0.142888673652444
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.821375270653289 \tabularnewline
beta & 0.142888673652444 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167534&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]0.821375270653289[/C][/ROW]
[ROW][C]beta[/C][C]0.142888673652444[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167534&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167534&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
alpha0.821375270653289
beta0.142888673652444
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
37.847.620.22
47.797.776522908602530.0134770913974718
57.837.764994749092730.0650052509072667
67.947.803419901315110.13658009868489
78.027.916664617241570.103335382758426
88.068.014730925866820.0452690741331843
98.128.070416019509560.0495839804904357
108.138.13546470545656-0.00546470545655708
117.978.15465639571023-0.184656395710227
128.018.004992223823060.00500777617693693
1388.01170125122066-0.0117012512206625
147.98.00331257675838-0.103312576758377
157.997.907551321378260.082448678621744
168.027.974046374964920.0459536250350752
178.088.015958651483990.0640413485160138
188.028.08024396392216-0.0602439639221615
198.078.03537384795840.0346261520416
208.118.072491605227090.037508394772912
218.198.116378946515990.0736210534840129
228.168.19856888398697-0.0385688839869722
238.088.18408213553337-0.104082135533369
248.228.103568799312840.116431200687158
258.158.21784463814529-0.0678446381452851
268.198.172798258896960.0172017411030385
278.318.199625758602260.110374241397736
288.38.31593694340907-0.0159369434090681
298.348.326628801691590.013371198308409
308.318.36296295648082-0.0529629564808207
318.388.338595867728670.0414041322713334
328.348.396598977258-0.0565989772579982
338.448.367462004585660.0725379954143381
348.648.452908385800790.187091614199208
358.68.65440432567057-0.054404325670566
368.618.65115629675394-0.0411562967539378
378.548.65395955322817-0.11395955322817
388.698.583589126834450.106410873165546
398.738.706714454921980.0232855450780232
408.918.76429560734410.145704392655899
419.018.939529202363910.0704707976360854
429.089.061238603791270.0187613962087294
438.949.14267711707564-0.202677117075643
449.039.018444266536520.0115557334634779
459.029.0715332228266-0.0515332228266043
468.969.06675426238001-0.106754262380012
479.039.004088867814640.0259111321853638
488.949.0534326134237-0.113432613423697
498.958.97500980829994-0.0250098082999433
508.958.96628002693846-0.0162800269384604
518.998.962809963113520.0271900368864806
528.938.99823629947052-0.0682362994705201
538.988.947273234471150.0327267655288459
548.958.98307971844581-0.0330797184458138
559.028.960951975303050.0590480246969456
568.929.0214258667048-0.101425866704801
579.18.938186602660430.161813397339573
589.069.09015682582934-0.030156825829339
598.979.08090809239725-0.110908092397246
608.898.99231551253624-0.102315512536236

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 7.84 & 7.62 & 0.22 \tabularnewline
4 & 7.79 & 7.77652290860253 & 0.0134770913974718 \tabularnewline
5 & 7.83 & 7.76499474909273 & 0.0650052509072667 \tabularnewline
6 & 7.94 & 7.80341990131511 & 0.13658009868489 \tabularnewline
7 & 8.02 & 7.91666461724157 & 0.103335382758426 \tabularnewline
8 & 8.06 & 8.01473092586682 & 0.0452690741331843 \tabularnewline
9 & 8.12 & 8.07041601950956 & 0.0495839804904357 \tabularnewline
10 & 8.13 & 8.13546470545656 & -0.00546470545655708 \tabularnewline
11 & 7.97 & 8.15465639571023 & -0.184656395710227 \tabularnewline
12 & 8.01 & 8.00499222382306 & 0.00500777617693693 \tabularnewline
13 & 8 & 8.01170125122066 & -0.0117012512206625 \tabularnewline
14 & 7.9 & 8.00331257675838 & -0.103312576758377 \tabularnewline
15 & 7.99 & 7.90755132137826 & 0.082448678621744 \tabularnewline
16 & 8.02 & 7.97404637496492 & 0.0459536250350752 \tabularnewline
17 & 8.08 & 8.01595865148399 & 0.0640413485160138 \tabularnewline
18 & 8.02 & 8.08024396392216 & -0.0602439639221615 \tabularnewline
19 & 8.07 & 8.0353738479584 & 0.0346261520416 \tabularnewline
20 & 8.11 & 8.07249160522709 & 0.037508394772912 \tabularnewline
21 & 8.19 & 8.11637894651599 & 0.0736210534840129 \tabularnewline
22 & 8.16 & 8.19856888398697 & -0.0385688839869722 \tabularnewline
23 & 8.08 & 8.18408213553337 & -0.104082135533369 \tabularnewline
24 & 8.22 & 8.10356879931284 & 0.116431200687158 \tabularnewline
25 & 8.15 & 8.21784463814529 & -0.0678446381452851 \tabularnewline
26 & 8.19 & 8.17279825889696 & 0.0172017411030385 \tabularnewline
27 & 8.31 & 8.19962575860226 & 0.110374241397736 \tabularnewline
28 & 8.3 & 8.31593694340907 & -0.0159369434090681 \tabularnewline
29 & 8.34 & 8.32662880169159 & 0.013371198308409 \tabularnewline
30 & 8.31 & 8.36296295648082 & -0.0529629564808207 \tabularnewline
31 & 8.38 & 8.33859586772867 & 0.0414041322713334 \tabularnewline
32 & 8.34 & 8.396598977258 & -0.0565989772579982 \tabularnewline
33 & 8.44 & 8.36746200458566 & 0.0725379954143381 \tabularnewline
34 & 8.64 & 8.45290838580079 & 0.187091614199208 \tabularnewline
35 & 8.6 & 8.65440432567057 & -0.054404325670566 \tabularnewline
36 & 8.61 & 8.65115629675394 & -0.0411562967539378 \tabularnewline
37 & 8.54 & 8.65395955322817 & -0.11395955322817 \tabularnewline
38 & 8.69 & 8.58358912683445 & 0.106410873165546 \tabularnewline
39 & 8.73 & 8.70671445492198 & 0.0232855450780232 \tabularnewline
40 & 8.91 & 8.7642956073441 & 0.145704392655899 \tabularnewline
41 & 9.01 & 8.93952920236391 & 0.0704707976360854 \tabularnewline
42 & 9.08 & 9.06123860379127 & 0.0187613962087294 \tabularnewline
43 & 8.94 & 9.14267711707564 & -0.202677117075643 \tabularnewline
44 & 9.03 & 9.01844426653652 & 0.0115557334634779 \tabularnewline
45 & 9.02 & 9.0715332228266 & -0.0515332228266043 \tabularnewline
46 & 8.96 & 9.06675426238001 & -0.106754262380012 \tabularnewline
47 & 9.03 & 9.00408886781464 & 0.0259111321853638 \tabularnewline
48 & 8.94 & 9.0534326134237 & -0.113432613423697 \tabularnewline
49 & 8.95 & 8.97500980829994 & -0.0250098082999433 \tabularnewline
50 & 8.95 & 8.96628002693846 & -0.0162800269384604 \tabularnewline
51 & 8.99 & 8.96280996311352 & 0.0271900368864806 \tabularnewline
52 & 8.93 & 8.99823629947052 & -0.0682362994705201 \tabularnewline
53 & 8.98 & 8.94727323447115 & 0.0327267655288459 \tabularnewline
54 & 8.95 & 8.98307971844581 & -0.0330797184458138 \tabularnewline
55 & 9.02 & 8.96095197530305 & 0.0590480246969456 \tabularnewline
56 & 8.92 & 9.0214258667048 & -0.101425866704801 \tabularnewline
57 & 9.1 & 8.93818660266043 & 0.161813397339573 \tabularnewline
58 & 9.06 & 9.09015682582934 & -0.030156825829339 \tabularnewline
59 & 8.97 & 9.08090809239725 & -0.110908092397246 \tabularnewline
60 & 8.89 & 8.99231551253624 & -0.102315512536236 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167534&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]7.84[/C][C]7.62[/C][C]0.22[/C][/ROW]
[ROW][C]4[/C][C]7.79[/C][C]7.77652290860253[/C][C]0.0134770913974718[/C][/ROW]
[ROW][C]5[/C][C]7.83[/C][C]7.76499474909273[/C][C]0.0650052509072667[/C][/ROW]
[ROW][C]6[/C][C]7.94[/C][C]7.80341990131511[/C][C]0.13658009868489[/C][/ROW]
[ROW][C]7[/C][C]8.02[/C][C]7.91666461724157[/C][C]0.103335382758426[/C][/ROW]
[ROW][C]8[/C][C]8.06[/C][C]8.01473092586682[/C][C]0.0452690741331843[/C][/ROW]
[ROW][C]9[/C][C]8.12[/C][C]8.07041601950956[/C][C]0.0495839804904357[/C][/ROW]
[ROW][C]10[/C][C]8.13[/C][C]8.13546470545656[/C][C]-0.00546470545655708[/C][/ROW]
[ROW][C]11[/C][C]7.97[/C][C]8.15465639571023[/C][C]-0.184656395710227[/C][/ROW]
[ROW][C]12[/C][C]8.01[/C][C]8.00499222382306[/C][C]0.00500777617693693[/C][/ROW]
[ROW][C]13[/C][C]8[/C][C]8.01170125122066[/C][C]-0.0117012512206625[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]8.00331257675838[/C][C]-0.103312576758377[/C][/ROW]
[ROW][C]15[/C][C]7.99[/C][C]7.90755132137826[/C][C]0.082448678621744[/C][/ROW]
[ROW][C]16[/C][C]8.02[/C][C]7.97404637496492[/C][C]0.0459536250350752[/C][/ROW]
[ROW][C]17[/C][C]8.08[/C][C]8.01595865148399[/C][C]0.0640413485160138[/C][/ROW]
[ROW][C]18[/C][C]8.02[/C][C]8.08024396392216[/C][C]-0.0602439639221615[/C][/ROW]
[ROW][C]19[/C][C]8.07[/C][C]8.0353738479584[/C][C]0.0346261520416[/C][/ROW]
[ROW][C]20[/C][C]8.11[/C][C]8.07249160522709[/C][C]0.037508394772912[/C][/ROW]
[ROW][C]21[/C][C]8.19[/C][C]8.11637894651599[/C][C]0.0736210534840129[/C][/ROW]
[ROW][C]22[/C][C]8.16[/C][C]8.19856888398697[/C][C]-0.0385688839869722[/C][/ROW]
[ROW][C]23[/C][C]8.08[/C][C]8.18408213553337[/C][C]-0.104082135533369[/C][/ROW]
[ROW][C]24[/C][C]8.22[/C][C]8.10356879931284[/C][C]0.116431200687158[/C][/ROW]
[ROW][C]25[/C][C]8.15[/C][C]8.21784463814529[/C][C]-0.0678446381452851[/C][/ROW]
[ROW][C]26[/C][C]8.19[/C][C]8.17279825889696[/C][C]0.0172017411030385[/C][/ROW]
[ROW][C]27[/C][C]8.31[/C][C]8.19962575860226[/C][C]0.110374241397736[/C][/ROW]
[ROW][C]28[/C][C]8.3[/C][C]8.31593694340907[/C][C]-0.0159369434090681[/C][/ROW]
[ROW][C]29[/C][C]8.34[/C][C]8.32662880169159[/C][C]0.013371198308409[/C][/ROW]
[ROW][C]30[/C][C]8.31[/C][C]8.36296295648082[/C][C]-0.0529629564808207[/C][/ROW]
[ROW][C]31[/C][C]8.38[/C][C]8.33859586772867[/C][C]0.0414041322713334[/C][/ROW]
[ROW][C]32[/C][C]8.34[/C][C]8.396598977258[/C][C]-0.0565989772579982[/C][/ROW]
[ROW][C]33[/C][C]8.44[/C][C]8.36746200458566[/C][C]0.0725379954143381[/C][/ROW]
[ROW][C]34[/C][C]8.64[/C][C]8.45290838580079[/C][C]0.187091614199208[/C][/ROW]
[ROW][C]35[/C][C]8.6[/C][C]8.65440432567057[/C][C]-0.054404325670566[/C][/ROW]
[ROW][C]36[/C][C]8.61[/C][C]8.65115629675394[/C][C]-0.0411562967539378[/C][/ROW]
[ROW][C]37[/C][C]8.54[/C][C]8.65395955322817[/C][C]-0.11395955322817[/C][/ROW]
[ROW][C]38[/C][C]8.69[/C][C]8.58358912683445[/C][C]0.106410873165546[/C][/ROW]
[ROW][C]39[/C][C]8.73[/C][C]8.70671445492198[/C][C]0.0232855450780232[/C][/ROW]
[ROW][C]40[/C][C]8.91[/C][C]8.7642956073441[/C][C]0.145704392655899[/C][/ROW]
[ROW][C]41[/C][C]9.01[/C][C]8.93952920236391[/C][C]0.0704707976360854[/C][/ROW]
[ROW][C]42[/C][C]9.08[/C][C]9.06123860379127[/C][C]0.0187613962087294[/C][/ROW]
[ROW][C]43[/C][C]8.94[/C][C]9.14267711707564[/C][C]-0.202677117075643[/C][/ROW]
[ROW][C]44[/C][C]9.03[/C][C]9.01844426653652[/C][C]0.0115557334634779[/C][/ROW]
[ROW][C]45[/C][C]9.02[/C][C]9.0715332228266[/C][C]-0.0515332228266043[/C][/ROW]
[ROW][C]46[/C][C]8.96[/C][C]9.06675426238001[/C][C]-0.106754262380012[/C][/ROW]
[ROW][C]47[/C][C]9.03[/C][C]9.00408886781464[/C][C]0.0259111321853638[/C][/ROW]
[ROW][C]48[/C][C]8.94[/C][C]9.0534326134237[/C][C]-0.113432613423697[/C][/ROW]
[ROW][C]49[/C][C]8.95[/C][C]8.97500980829994[/C][C]-0.0250098082999433[/C][/ROW]
[ROW][C]50[/C][C]8.95[/C][C]8.96628002693846[/C][C]-0.0162800269384604[/C][/ROW]
[ROW][C]51[/C][C]8.99[/C][C]8.96280996311352[/C][C]0.0271900368864806[/C][/ROW]
[ROW][C]52[/C][C]8.93[/C][C]8.99823629947052[/C][C]-0.0682362994705201[/C][/ROW]
[ROW][C]53[/C][C]8.98[/C][C]8.94727323447115[/C][C]0.0327267655288459[/C][/ROW]
[ROW][C]54[/C][C]8.95[/C][C]8.98307971844581[/C][C]-0.0330797184458138[/C][/ROW]
[ROW][C]55[/C][C]9.02[/C][C]8.96095197530305[/C][C]0.0590480246969456[/C][/ROW]
[ROW][C]56[/C][C]8.92[/C][C]9.0214258667048[/C][C]-0.101425866704801[/C][/ROW]
[ROW][C]57[/C][C]9.1[/C][C]8.93818660266043[/C][C]0.161813397339573[/C][/ROW]
[ROW][C]58[/C][C]9.06[/C][C]9.09015682582934[/C][C]-0.030156825829339[/C][/ROW]
[ROW][C]59[/C][C]8.97[/C][C]9.08090809239725[/C][C]-0.110908092397246[/C][/ROW]
[ROW][C]60[/C][C]8.89[/C][C]8.99231551253624[/C][C]-0.102315512536236[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167534&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167534&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
37.847.620.22
47.797.776522908602530.0134770913974718
57.837.764994749092730.0650052509072667
67.947.803419901315110.13658009868489
78.027.916664617241570.103335382758426
88.068.014730925866820.0452690741331843
98.128.070416019509560.0495839804904357
108.138.13546470545656-0.00546470545655708
117.978.15465639571023-0.184656395710227
128.018.004992223823060.00500777617693693
1388.01170125122066-0.0117012512206625
147.98.00331257675838-0.103312576758377
157.997.907551321378260.082448678621744
168.027.974046374964920.0459536250350752
178.088.015958651483990.0640413485160138
188.028.08024396392216-0.0602439639221615
198.078.03537384795840.0346261520416
208.118.072491605227090.037508394772912
218.198.116378946515990.0736210534840129
228.168.19856888398697-0.0385688839869722
238.088.18408213553337-0.104082135533369
248.228.103568799312840.116431200687158
258.158.21784463814529-0.0678446381452851
268.198.172798258896960.0172017411030385
278.318.199625758602260.110374241397736
288.38.31593694340907-0.0159369434090681
298.348.326628801691590.013371198308409
308.318.36296295648082-0.0529629564808207
318.388.338595867728670.0414041322713334
328.348.396598977258-0.0565989772579982
338.448.367462004585660.0725379954143381
348.648.452908385800790.187091614199208
358.68.65440432567057-0.054404325670566
368.618.65115629675394-0.0411562967539378
378.548.65395955322817-0.11395955322817
388.698.583589126834450.106410873165546
398.738.706714454921980.0232855450780232
408.918.76429560734410.145704392655899
419.018.939529202363910.0704707976360854
429.089.061238603791270.0187613962087294
438.949.14267711707564-0.202677117075643
449.039.018444266536520.0115557334634779
459.029.0715332228266-0.0515332228266043
468.969.06675426238001-0.106754262380012
479.039.004088867814640.0259111321853638
488.949.0534326134237-0.113432613423697
498.958.97500980829994-0.0250098082999433
508.958.96628002693846-0.0162800269384604
518.998.962809963113520.0271900368864806
528.938.99823629947052-0.0682362994705201
538.988.947273234471150.0327267655288459
548.958.98307971844581-0.0330797184458138
559.028.960951975303050.0590480246969456
568.929.0214258667048-0.101425866704801
579.18.938186602660430.161813397339573
589.069.09015682582934-0.030156825829339
598.979.08090809239725-0.110908092397246
608.898.99231551253624-0.102315512536236







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
618.898772382339568.726073337249059.07147142743007
628.889268683944368.652398000632569.12613936725615
638.879764985549168.580811365633759.17871860546456
648.870261287153968.509092002126179.23143057218174
658.860757588758768.436329348767619.2851858287499
668.851253890363568.362088115035249.34041966569188
678.841750191968368.286145673873229.39735471006349
688.832246493573168.208387007185389.45610597996093
698.822742795177968.128756020112369.51672957024356
708.813239096782768.047230617922359.57924757564317
718.803735398387567.963809003133299.64366179364182
728.794231699992367.878501730639599.70996166934512

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 8.89877238233956 & 8.72607333724905 & 9.07147142743007 \tabularnewline
62 & 8.88926868394436 & 8.65239800063256 & 9.12613936725615 \tabularnewline
63 & 8.87976498554916 & 8.58081136563375 & 9.17871860546456 \tabularnewline
64 & 8.87026128715396 & 8.50909200212617 & 9.23143057218174 \tabularnewline
65 & 8.86075758875876 & 8.43632934876761 & 9.2851858287499 \tabularnewline
66 & 8.85125389036356 & 8.36208811503524 & 9.34041966569188 \tabularnewline
67 & 8.84175019196836 & 8.28614567387322 & 9.39735471006349 \tabularnewline
68 & 8.83224649357316 & 8.20838700718538 & 9.45610597996093 \tabularnewline
69 & 8.82274279517796 & 8.12875602011236 & 9.51672957024356 \tabularnewline
70 & 8.81323909678276 & 8.04723061792235 & 9.57924757564317 \tabularnewline
71 & 8.80373539838756 & 7.96380900313329 & 9.64366179364182 \tabularnewline
72 & 8.79423169999236 & 7.87850173063959 & 9.70996166934512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167534&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]61[/C][C]8.89877238233956[/C][C]8.72607333724905[/C][C]9.07147142743007[/C][/ROW]
[ROW][C]62[/C][C]8.88926868394436[/C][C]8.65239800063256[/C][C]9.12613936725615[/C][/ROW]
[ROW][C]63[/C][C]8.87976498554916[/C][C]8.58081136563375[/C][C]9.17871860546456[/C][/ROW]
[ROW][C]64[/C][C]8.87026128715396[/C][C]8.50909200212617[/C][C]9.23143057218174[/C][/ROW]
[ROW][C]65[/C][C]8.86075758875876[/C][C]8.43632934876761[/C][C]9.2851858287499[/C][/ROW]
[ROW][C]66[/C][C]8.85125389036356[/C][C]8.36208811503524[/C][C]9.34041966569188[/C][/ROW]
[ROW][C]67[/C][C]8.84175019196836[/C][C]8.28614567387322[/C][C]9.39735471006349[/C][/ROW]
[ROW][C]68[/C][C]8.83224649357316[/C][C]8.20838700718538[/C][C]9.45610597996093[/C][/ROW]
[ROW][C]69[/C][C]8.82274279517796[/C][C]8.12875602011236[/C][C]9.51672957024356[/C][/ROW]
[ROW][C]70[/C][C]8.81323909678276[/C][C]8.04723061792235[/C][C]9.57924757564317[/C][/ROW]
[ROW][C]71[/C][C]8.80373539838756[/C][C]7.96380900313329[/C][C]9.64366179364182[/C][/ROW]
[ROW][C]72[/C][C]8.79423169999236[/C][C]7.87850173063959[/C][C]9.70996166934512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167534&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167534&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
618.898772382339568.726073337249059.07147142743007
628.889268683944368.652398000632569.12613936725615
638.879764985549168.580811365633759.17871860546456
648.870261287153968.509092002126179.23143057218174
658.860757588758768.436329348767619.2851858287499
668.851253890363568.362088115035249.34041966569188
678.841750191968368.286145673873229.39735471006349
688.832246493573168.208387007185389.45610597996093
698.822742795177968.128756020112369.51672957024356
708.813239096782768.047230617922359.57924757564317
718.803735398387567.963809003133299.64366179364182
728.794231699992367.878501730639599.70996166934512



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
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')