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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 May 2012 13:39:10 -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/28/t1338226937pp6ocqedqmopiuw.htm/, Retrieved Thu, 02 May 2024 07:44:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167848, Retrieved Thu, 02 May 2024 07:44:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-28 17:39:10] [bc260e3c602952c552b9bde15a0b19a6] [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
7,9
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
8,3
8,34
8,31
8,38
8,34
8,44
8,64
8,6
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
9,1
9,06
8,97
8,89
8,99
8,79
8,83
8,61
8,71
8,91
8,91
8,89
8,98
9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167848&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167848&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167848&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.698110842696967
beta-1.86211723124385e-17
gamma0.685634935123121

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.698110842696967 \tabularnewline
beta & -1.86211723124385e-17 \tabularnewline
gamma & 0.685634935123121 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167848&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]0.698110842696967[/C][/ROW]
[ROW][C]beta[/C][C]-1.86211723124385e-17[/C][/ROW]
[ROW][C]gamma[/C][C]0.685634935123121[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167848&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167848&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
alpha0.698110842696967
beta-1.86211723124385e-17
gamma0.685634935123121







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1387.910966880341880.0890331196581196
147.97.87936021152270.020639788477304
157.997.989174083304690.000825916695314177
168.028.02598900969319-0.00598900969319516
178.088.08637969541104-0.00637969541103622
188.028.018997639193160.0010023608068348
198.078.15468574312905-0.0846857431290537
208.118.12472071928382-0.0147207192838241
218.198.169015703861160.0209842961388347
228.168.18823674684373-0.0282367468437297
238.087.998929379364640.081070620635356
248.228.092180670309370.127819329690629
258.158.19482966255595-0.0448296625559514
268.198.055615488899830.134384511100174
278.318.240734595678080.0692654043219196
288.38.32391727777867-0.0239172777786685
298.348.37171117877786-0.0317111787778561
308.318.288172919823340.0218270801766565
318.388.42066276944981-0.0406627694498098
328.348.43591242398683-0.0959124239868281
338.448.43091702866930.00908297133070235
348.648.431641573126390.208358426873607
358.68.430128929491410.169871070508586
368.618.59504909406440.0149509059356028
378.548.58316753426229-0.0431675342622935
388.698.482208491033310.20779150896669
398.738.705095091615040.0249049083849648
408.918.73802174291380.171978257086199
419.018.920959214372650.0890407856273505
429.088.93280086787870.147199132121303
438.949.13987979777273-0.199879797772731
449.039.03254242716024-0.002542427160245
459.029.11446218994836-0.0944621899483593
468.969.08414791478423-0.124147914784226
479.038.842542654342610.187457345657386
488.948.9876737213944-0.0476737213944016
498.958.92004354113850.0299564588615038
508.958.92207809685070.0279219031493039
518.998.981540854644550.00845914535544523
528.939.03342862825106-0.103428628251059
538.989.00693469193883-0.026934691938834
548.958.949850556198570.000149443801429783
559.028.982432110682460.0375678893175433
568.929.08170556920922-0.161705569209223
579.19.0334857354790.0665142645209968
589.069.10940634649682-0.0494063464968164
598.978.98447683468011-0.0144768346801083
608.898.93996668001106-0.0499666800110568
618.998.886804101781870.103195898218134
628.798.93954678017631-0.14954678017631
638.838.87108821232823-0.0410882123282317
648.618.86522726326175-0.25522726326175
658.718.7485942089328-0.0385942089327944
668.918.688976468183080.221023531816918
678.918.883497703494460.0265022965055373
688.898.93379938487569-0.0437993848756939
698.989.01512939093413-0.0351293909341344
7098.996097549052910.00390245094708597

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8 & 7.91096688034188 & 0.0890331196581196 \tabularnewline
14 & 7.9 & 7.8793602115227 & 0.020639788477304 \tabularnewline
15 & 7.99 & 7.98917408330469 & 0.000825916695314177 \tabularnewline
16 & 8.02 & 8.02598900969319 & -0.00598900969319516 \tabularnewline
17 & 8.08 & 8.08637969541104 & -0.00637969541103622 \tabularnewline
18 & 8.02 & 8.01899763919316 & 0.0010023608068348 \tabularnewline
19 & 8.07 & 8.15468574312905 & -0.0846857431290537 \tabularnewline
20 & 8.11 & 8.12472071928382 & -0.0147207192838241 \tabularnewline
21 & 8.19 & 8.16901570386116 & 0.0209842961388347 \tabularnewline
22 & 8.16 & 8.18823674684373 & -0.0282367468437297 \tabularnewline
23 & 8.08 & 7.99892937936464 & 0.081070620635356 \tabularnewline
24 & 8.22 & 8.09218067030937 & 0.127819329690629 \tabularnewline
25 & 8.15 & 8.19482966255595 & -0.0448296625559514 \tabularnewline
26 & 8.19 & 8.05561548889983 & 0.134384511100174 \tabularnewline
27 & 8.31 & 8.24073459567808 & 0.0692654043219196 \tabularnewline
28 & 8.3 & 8.32391727777867 & -0.0239172777786685 \tabularnewline
29 & 8.34 & 8.37171117877786 & -0.0317111787778561 \tabularnewline
30 & 8.31 & 8.28817291982334 & 0.0218270801766565 \tabularnewline
31 & 8.38 & 8.42066276944981 & -0.0406627694498098 \tabularnewline
32 & 8.34 & 8.43591242398683 & -0.0959124239868281 \tabularnewline
33 & 8.44 & 8.4309170286693 & 0.00908297133070235 \tabularnewline
34 & 8.64 & 8.43164157312639 & 0.208358426873607 \tabularnewline
35 & 8.6 & 8.43012892949141 & 0.169871070508586 \tabularnewline
36 & 8.61 & 8.5950490940644 & 0.0149509059356028 \tabularnewline
37 & 8.54 & 8.58316753426229 & -0.0431675342622935 \tabularnewline
38 & 8.69 & 8.48220849103331 & 0.20779150896669 \tabularnewline
39 & 8.73 & 8.70509509161504 & 0.0249049083849648 \tabularnewline
40 & 8.91 & 8.7380217429138 & 0.171978257086199 \tabularnewline
41 & 9.01 & 8.92095921437265 & 0.0890407856273505 \tabularnewline
42 & 9.08 & 8.9328008678787 & 0.147199132121303 \tabularnewline
43 & 8.94 & 9.13987979777273 & -0.199879797772731 \tabularnewline
44 & 9.03 & 9.03254242716024 & -0.002542427160245 \tabularnewline
45 & 9.02 & 9.11446218994836 & -0.0944621899483593 \tabularnewline
46 & 8.96 & 9.08414791478423 & -0.124147914784226 \tabularnewline
47 & 9.03 & 8.84254265434261 & 0.187457345657386 \tabularnewline
48 & 8.94 & 8.9876737213944 & -0.0476737213944016 \tabularnewline
49 & 8.95 & 8.9200435411385 & 0.0299564588615038 \tabularnewline
50 & 8.95 & 8.9220780968507 & 0.0279219031493039 \tabularnewline
51 & 8.99 & 8.98154085464455 & 0.00845914535544523 \tabularnewline
52 & 8.93 & 9.03342862825106 & -0.103428628251059 \tabularnewline
53 & 8.98 & 9.00693469193883 & -0.026934691938834 \tabularnewline
54 & 8.95 & 8.94985055619857 & 0.000149443801429783 \tabularnewline
55 & 9.02 & 8.98243211068246 & 0.0375678893175433 \tabularnewline
56 & 8.92 & 9.08170556920922 & -0.161705569209223 \tabularnewline
57 & 9.1 & 9.033485735479 & 0.0665142645209968 \tabularnewline
58 & 9.06 & 9.10940634649682 & -0.0494063464968164 \tabularnewline
59 & 8.97 & 8.98447683468011 & -0.0144768346801083 \tabularnewline
60 & 8.89 & 8.93996668001106 & -0.0499666800110568 \tabularnewline
61 & 8.99 & 8.88680410178187 & 0.103195898218134 \tabularnewline
62 & 8.79 & 8.93954678017631 & -0.14954678017631 \tabularnewline
63 & 8.83 & 8.87108821232823 & -0.0410882123282317 \tabularnewline
64 & 8.61 & 8.86522726326175 & -0.25522726326175 \tabularnewline
65 & 8.71 & 8.7485942089328 & -0.0385942089327944 \tabularnewline
66 & 8.91 & 8.68897646818308 & 0.221023531816918 \tabularnewline
67 & 8.91 & 8.88349770349446 & 0.0265022965055373 \tabularnewline
68 & 8.89 & 8.93379938487569 & -0.0437993848756939 \tabularnewline
69 & 8.98 & 9.01512939093413 & -0.0351293909341344 \tabularnewline
70 & 9 & 8.99609754905291 & 0.00390245094708597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167848&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]8[/C][C]7.91096688034188[/C][C]0.0890331196581196[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]7.8793602115227[/C][C]0.020639788477304[/C][/ROW]
[ROW][C]15[/C][C]7.99[/C][C]7.98917408330469[/C][C]0.000825916695314177[/C][/ROW]
[ROW][C]16[/C][C]8.02[/C][C]8.02598900969319[/C][C]-0.00598900969319516[/C][/ROW]
[ROW][C]17[/C][C]8.08[/C][C]8.08637969541104[/C][C]-0.00637969541103622[/C][/ROW]
[ROW][C]18[/C][C]8.02[/C][C]8.01899763919316[/C][C]0.0010023608068348[/C][/ROW]
[ROW][C]19[/C][C]8.07[/C][C]8.15468574312905[/C][C]-0.0846857431290537[/C][/ROW]
[ROW][C]20[/C][C]8.11[/C][C]8.12472071928382[/C][C]-0.0147207192838241[/C][/ROW]
[ROW][C]21[/C][C]8.19[/C][C]8.16901570386116[/C][C]0.0209842961388347[/C][/ROW]
[ROW][C]22[/C][C]8.16[/C][C]8.18823674684373[/C][C]-0.0282367468437297[/C][/ROW]
[ROW][C]23[/C][C]8.08[/C][C]7.99892937936464[/C][C]0.081070620635356[/C][/ROW]
[ROW][C]24[/C][C]8.22[/C][C]8.09218067030937[/C][C]0.127819329690629[/C][/ROW]
[ROW][C]25[/C][C]8.15[/C][C]8.19482966255595[/C][C]-0.0448296625559514[/C][/ROW]
[ROW][C]26[/C][C]8.19[/C][C]8.05561548889983[/C][C]0.134384511100174[/C][/ROW]
[ROW][C]27[/C][C]8.31[/C][C]8.24073459567808[/C][C]0.0692654043219196[/C][/ROW]
[ROW][C]28[/C][C]8.3[/C][C]8.32391727777867[/C][C]-0.0239172777786685[/C][/ROW]
[ROW][C]29[/C][C]8.34[/C][C]8.37171117877786[/C][C]-0.0317111787778561[/C][/ROW]
[ROW][C]30[/C][C]8.31[/C][C]8.28817291982334[/C][C]0.0218270801766565[/C][/ROW]
[ROW][C]31[/C][C]8.38[/C][C]8.42066276944981[/C][C]-0.0406627694498098[/C][/ROW]
[ROW][C]32[/C][C]8.34[/C][C]8.43591242398683[/C][C]-0.0959124239868281[/C][/ROW]
[ROW][C]33[/C][C]8.44[/C][C]8.4309170286693[/C][C]0.00908297133070235[/C][/ROW]
[ROW][C]34[/C][C]8.64[/C][C]8.43164157312639[/C][C]0.208358426873607[/C][/ROW]
[ROW][C]35[/C][C]8.6[/C][C]8.43012892949141[/C][C]0.169871070508586[/C][/ROW]
[ROW][C]36[/C][C]8.61[/C][C]8.5950490940644[/C][C]0.0149509059356028[/C][/ROW]
[ROW][C]37[/C][C]8.54[/C][C]8.58316753426229[/C][C]-0.0431675342622935[/C][/ROW]
[ROW][C]38[/C][C]8.69[/C][C]8.48220849103331[/C][C]0.20779150896669[/C][/ROW]
[ROW][C]39[/C][C]8.73[/C][C]8.70509509161504[/C][C]0.0249049083849648[/C][/ROW]
[ROW][C]40[/C][C]8.91[/C][C]8.7380217429138[/C][C]0.171978257086199[/C][/ROW]
[ROW][C]41[/C][C]9.01[/C][C]8.92095921437265[/C][C]0.0890407856273505[/C][/ROW]
[ROW][C]42[/C][C]9.08[/C][C]8.9328008678787[/C][C]0.147199132121303[/C][/ROW]
[ROW][C]43[/C][C]8.94[/C][C]9.13987979777273[/C][C]-0.199879797772731[/C][/ROW]
[ROW][C]44[/C][C]9.03[/C][C]9.03254242716024[/C][C]-0.002542427160245[/C][/ROW]
[ROW][C]45[/C][C]9.02[/C][C]9.11446218994836[/C][C]-0.0944621899483593[/C][/ROW]
[ROW][C]46[/C][C]8.96[/C][C]9.08414791478423[/C][C]-0.124147914784226[/C][/ROW]
[ROW][C]47[/C][C]9.03[/C][C]8.84254265434261[/C][C]0.187457345657386[/C][/ROW]
[ROW][C]48[/C][C]8.94[/C][C]8.9876737213944[/C][C]-0.0476737213944016[/C][/ROW]
[ROW][C]49[/C][C]8.95[/C][C]8.9200435411385[/C][C]0.0299564588615038[/C][/ROW]
[ROW][C]50[/C][C]8.95[/C][C]8.9220780968507[/C][C]0.0279219031493039[/C][/ROW]
[ROW][C]51[/C][C]8.99[/C][C]8.98154085464455[/C][C]0.00845914535544523[/C][/ROW]
[ROW][C]52[/C][C]8.93[/C][C]9.03342862825106[/C][C]-0.103428628251059[/C][/ROW]
[ROW][C]53[/C][C]8.98[/C][C]9.00693469193883[/C][C]-0.026934691938834[/C][/ROW]
[ROW][C]54[/C][C]8.95[/C][C]8.94985055619857[/C][C]0.000149443801429783[/C][/ROW]
[ROW][C]55[/C][C]9.02[/C][C]8.98243211068246[/C][C]0.0375678893175433[/C][/ROW]
[ROW][C]56[/C][C]8.92[/C][C]9.08170556920922[/C][C]-0.161705569209223[/C][/ROW]
[ROW][C]57[/C][C]9.1[/C][C]9.033485735479[/C][C]0.0665142645209968[/C][/ROW]
[ROW][C]58[/C][C]9.06[/C][C]9.10940634649682[/C][C]-0.0494063464968164[/C][/ROW]
[ROW][C]59[/C][C]8.97[/C][C]8.98447683468011[/C][C]-0.0144768346801083[/C][/ROW]
[ROW][C]60[/C][C]8.89[/C][C]8.93996668001106[/C][C]-0.0499666800110568[/C][/ROW]
[ROW][C]61[/C][C]8.99[/C][C]8.88680410178187[/C][C]0.103195898218134[/C][/ROW]
[ROW][C]62[/C][C]8.79[/C][C]8.93954678017631[/C][C]-0.14954678017631[/C][/ROW]
[ROW][C]63[/C][C]8.83[/C][C]8.87108821232823[/C][C]-0.0410882123282317[/C][/ROW]
[ROW][C]64[/C][C]8.61[/C][C]8.86522726326175[/C][C]-0.25522726326175[/C][/ROW]
[ROW][C]65[/C][C]8.71[/C][C]8.7485942089328[/C][C]-0.0385942089327944[/C][/ROW]
[ROW][C]66[/C][C]8.91[/C][C]8.68897646818308[/C][C]0.221023531816918[/C][/ROW]
[ROW][C]67[/C][C]8.91[/C][C]8.88349770349446[/C][C]0.0265022965055373[/C][/ROW]
[ROW][C]68[/C][C]8.89[/C][C]8.93379938487569[/C][C]-0.0437993848756939[/C][/ROW]
[ROW][C]69[/C][C]8.98[/C][C]9.01512939093413[/C][C]-0.0351293909341344[/C][/ROW]
[ROW][C]70[/C][C]9[/C][C]8.99609754905291[/C][C]0.00390245094708597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167848&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167848&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
1387.910966880341880.0890331196581196
147.97.87936021152270.020639788477304
157.997.989174083304690.000825916695314177
168.028.02598900969319-0.00598900969319516
178.088.08637969541104-0.00637969541103622
188.028.018997639193160.0010023608068348
198.078.15468574312905-0.0846857431290537
208.118.12472071928382-0.0147207192838241
218.198.169015703861160.0209842961388347
228.168.18823674684373-0.0282367468437297
238.087.998929379364640.081070620635356
248.228.092180670309370.127819329690629
258.158.19482966255595-0.0448296625559514
268.198.055615488899830.134384511100174
278.318.240734595678080.0692654043219196
288.38.32391727777867-0.0239172777786685
298.348.37171117877786-0.0317111787778561
308.318.288172919823340.0218270801766565
318.388.42066276944981-0.0406627694498098
328.348.43591242398683-0.0959124239868281
338.448.43091702866930.00908297133070235
348.648.431641573126390.208358426873607
358.68.430128929491410.169871070508586
368.618.59504909406440.0149509059356028
378.548.58316753426229-0.0431675342622935
388.698.482208491033310.20779150896669
398.738.705095091615040.0249049083849648
408.918.73802174291380.171978257086199
419.018.920959214372650.0890407856273505
429.088.93280086787870.147199132121303
438.949.13987979777273-0.199879797772731
449.039.03254242716024-0.002542427160245
459.029.11446218994836-0.0944621899483593
468.969.08414791478423-0.124147914784226
479.038.842542654342610.187457345657386
488.948.9876737213944-0.0476737213944016
498.958.92004354113850.0299564588615038
508.958.92207809685070.0279219031493039
518.998.981540854644550.00845914535544523
528.939.03342862825106-0.103428628251059
538.989.00693469193883-0.026934691938834
548.958.949850556198570.000149443801429783
559.028.982432110682460.0375678893175433
568.929.08170556920922-0.161705569209223
579.19.0334857354790.0665142645209968
589.069.10940634649682-0.0494063464968164
598.978.98447683468011-0.0144768346801083
608.898.93996668001106-0.0499666800110568
618.998.886804101781870.103195898218134
628.798.93954678017631-0.14954678017631
638.838.87108821232823-0.0410882123282317
648.618.86522726326175-0.25522726326175
658.718.7485942089328-0.0385942089327944
668.918.688976468183080.221023531816918
678.918.883497703494460.0265022965055373
688.898.93379938487569-0.0437993848756939
698.989.01512939093413-0.0351293909341344
7098.996097549052910.00390245094708597







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
718.915613398040618.721779000578929.10944779550231
728.873863786277748.637468553190629.11025901936486
738.887285960690618.61490086782899.15967105355233
748.815672330069558.511526688311769.11981797182734
758.874063369264658.541173741929669.20695299659964
768.852562814074088.493221142994599.21190448515357
778.958946635407738.574970895078779.3429223757367
788.980009103883928.572887129841569.38713107792628
798.979968290819758.550947039207299.40898954243221
808.997216985211578.547361267317399.44707270310576
819.11091838197788.641151312560349.58068545139526
829.124489783979288.635621670787159.61335789717142

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
71 & 8.91561339804061 & 8.72177900057892 & 9.10944779550231 \tabularnewline
72 & 8.87386378627774 & 8.63746855319062 & 9.11025901936486 \tabularnewline
73 & 8.88728596069061 & 8.6149008678289 & 9.15967105355233 \tabularnewline
74 & 8.81567233006955 & 8.51152668831176 & 9.11981797182734 \tabularnewline
75 & 8.87406336926465 & 8.54117374192966 & 9.20695299659964 \tabularnewline
76 & 8.85256281407408 & 8.49322114299459 & 9.21190448515357 \tabularnewline
77 & 8.95894663540773 & 8.57497089507877 & 9.3429223757367 \tabularnewline
78 & 8.98000910388392 & 8.57288712984156 & 9.38713107792628 \tabularnewline
79 & 8.97996829081975 & 8.55094703920729 & 9.40898954243221 \tabularnewline
80 & 8.99721698521157 & 8.54736126731739 & 9.44707270310576 \tabularnewline
81 & 9.1109183819778 & 8.64115131256034 & 9.58068545139526 \tabularnewline
82 & 9.12448978397928 & 8.63562167078715 & 9.61335789717142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167848&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]71[/C][C]8.91561339804061[/C][C]8.72177900057892[/C][C]9.10944779550231[/C][/ROW]
[ROW][C]72[/C][C]8.87386378627774[/C][C]8.63746855319062[/C][C]9.11025901936486[/C][/ROW]
[ROW][C]73[/C][C]8.88728596069061[/C][C]8.6149008678289[/C][C]9.15967105355233[/C][/ROW]
[ROW][C]74[/C][C]8.81567233006955[/C][C]8.51152668831176[/C][C]9.11981797182734[/C][/ROW]
[ROW][C]75[/C][C]8.87406336926465[/C][C]8.54117374192966[/C][C]9.20695299659964[/C][/ROW]
[ROW][C]76[/C][C]8.85256281407408[/C][C]8.49322114299459[/C][C]9.21190448515357[/C][/ROW]
[ROW][C]77[/C][C]8.95894663540773[/C][C]8.57497089507877[/C][C]9.3429223757367[/C][/ROW]
[ROW][C]78[/C][C]8.98000910388392[/C][C]8.57288712984156[/C][C]9.38713107792628[/C][/ROW]
[ROW][C]79[/C][C]8.97996829081975[/C][C]8.55094703920729[/C][C]9.40898954243221[/C][/ROW]
[ROW][C]80[/C][C]8.99721698521157[/C][C]8.54736126731739[/C][C]9.44707270310576[/C][/ROW]
[ROW][C]81[/C][C]9.1109183819778[/C][C]8.64115131256034[/C][C]9.58068545139526[/C][/ROW]
[ROW][C]82[/C][C]9.12448978397928[/C][C]8.63562167078715[/C][C]9.61335789717142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167848&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167848&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
718.915613398040618.721779000578929.10944779550231
728.873863786277748.637468553190629.11025901936486
738.887285960690618.61490086782899.15967105355233
748.815672330069558.511526688311769.11981797182734
758.874063369264658.541173741929669.20695299659964
768.852562814074088.493221142994599.21190448515357
778.958946635407738.574970895078779.3429223757367
788.980009103883928.572887129841569.38713107792628
798.979968290819758.550947039207299.40898954243221
808.997216985211578.547361267317399.44707270310576
819.11091838197788.641151312560349.58068545139526
829.124489783979288.635621670787159.61335789717142



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')