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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 22 May 2013 04:03:10 -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/2013/May/22/t13692098145zow8stf33abvhz.htm/, Retrieved Sun, 28 Apr 2024 06:07:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=209333, Retrieved Sun, 28 Apr 2024 06:07:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-05-22 08:03:10] [d41d8cd98f00b204e9800998ecf8427e] [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
8,99
8,88




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 7 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209333&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209333&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209333&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 time7 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.683290518387697
beta0
gamma0.816581662774365

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.683290518387697 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.816581662774365 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209333&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]0.683290518387697[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.816581662774365[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209333&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209333&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
alpha0.683290518387697
beta0
gamma0.816581662774365







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1387.911144789754880.0888552102451232
147.97.878340715732070.0216592842679342
157.997.988419750005160.00158024999483874
168.028.02569954542497-0.00569954542496909
178.088.08638748755711-0.00638748755711305
188.028.01907177366670.000928226333297033
198.078.15608727140348-0.0860872714034748
208.118.12643868380964-0.0164386838096409
218.198.169958944845410.0200410551545929
228.168.18806120560413-0.0280612056041321
238.087.998459653262240.0815403467377624
248.228.09109385949660.128906140503402
258.158.19736171008231-0.0473617100823063
268.198.051515182213460.138484817786535
278.318.238725383815680.0712746161843185
288.38.32263552332991-0.022635523329912
298.348.37350295850283-0.0335029585028277
308.318.2871638404710.0228361595289961
318.388.42012430004253-0.0401243000425247
328.348.44133101423759-0.101331014237585
338.448.437996388751390.00200361124860748
348.648.430747361755580.209252638244418
358.68.423794729688550.176205270311451
368.618.595233092116680.0147669078833239
378.548.57606742548454-0.036067425484541
388.698.481864166641410.208135833358593
398.738.702674832921550.0273251670784553
408.918.732285050580040.177714949419958
419.018.920748325766920.0892516742330773
429.088.928303097995650.151696902004348
438.949.14088197441495-0.200881974414953
449.039.03783635374293-0.00783635374292579
459.029.13185960500852-0.111859605008522
468.969.10194481460988-0.141944814609884
479.038.838423192932410.191576807067589
488.948.97855924852202-0.0385592485220254
498.958.90767943387570.0423205661242996
508.958.928492152324290.0215078476757053
518.998.975661531621150.0143384683788543
528.939.03580404836879-0.105804048368785
538.989.00774714244534-0.027747142445337
548.958.95114267154456-0.00114267154456549
559.028.967224706385930.0527752936140651
568.929.08784952505071-0.167849525050705
579.19.044999358435460.0550006415645399
589.069.12109506913682-0.0610950691368153
598.978.99721606991325-0.0272160699132495
608.898.92857706840899-0.0385770684089852
618.998.878718969072460.111281030927543
628.798.94124079436084-0.151240794360838
638.838.86826357111959-0.0382635711195931
648.618.86102971024246-0.251029710242459
658.718.75242354947-0.0424235494699943
668.918.69385405970910.216145940290904
678.918.872050214566830.0379497854331667
688.898.92471427817202-0.0347142781720216
698.989.0300259067296-0.0500259067296032
7099.00428457172678-0.0042845717267781
718.998.928546199386910.0614538006130871
728.888.91753414463971-0.0375341446397126

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8 & 7.91114478975488 & 0.0888552102451232 \tabularnewline
14 & 7.9 & 7.87834071573207 & 0.0216592842679342 \tabularnewline
15 & 7.99 & 7.98841975000516 & 0.00158024999483874 \tabularnewline
16 & 8.02 & 8.02569954542497 & -0.00569954542496909 \tabularnewline
17 & 8.08 & 8.08638748755711 & -0.00638748755711305 \tabularnewline
18 & 8.02 & 8.0190717736667 & 0.000928226333297033 \tabularnewline
19 & 8.07 & 8.15608727140348 & -0.0860872714034748 \tabularnewline
20 & 8.11 & 8.12643868380964 & -0.0164386838096409 \tabularnewline
21 & 8.19 & 8.16995894484541 & 0.0200410551545929 \tabularnewline
22 & 8.16 & 8.18806120560413 & -0.0280612056041321 \tabularnewline
23 & 8.08 & 7.99845965326224 & 0.0815403467377624 \tabularnewline
24 & 8.22 & 8.0910938594966 & 0.128906140503402 \tabularnewline
25 & 8.15 & 8.19736171008231 & -0.0473617100823063 \tabularnewline
26 & 8.19 & 8.05151518221346 & 0.138484817786535 \tabularnewline
27 & 8.31 & 8.23872538381568 & 0.0712746161843185 \tabularnewline
28 & 8.3 & 8.32263552332991 & -0.022635523329912 \tabularnewline
29 & 8.34 & 8.37350295850283 & -0.0335029585028277 \tabularnewline
30 & 8.31 & 8.287163840471 & 0.0228361595289961 \tabularnewline
31 & 8.38 & 8.42012430004253 & -0.0401243000425247 \tabularnewline
32 & 8.34 & 8.44133101423759 & -0.101331014237585 \tabularnewline
33 & 8.44 & 8.43799638875139 & 0.00200361124860748 \tabularnewline
34 & 8.64 & 8.43074736175558 & 0.209252638244418 \tabularnewline
35 & 8.6 & 8.42379472968855 & 0.176205270311451 \tabularnewline
36 & 8.61 & 8.59523309211668 & 0.0147669078833239 \tabularnewline
37 & 8.54 & 8.57606742548454 & -0.036067425484541 \tabularnewline
38 & 8.69 & 8.48186416664141 & 0.208135833358593 \tabularnewline
39 & 8.73 & 8.70267483292155 & 0.0273251670784553 \tabularnewline
40 & 8.91 & 8.73228505058004 & 0.177714949419958 \tabularnewline
41 & 9.01 & 8.92074832576692 & 0.0892516742330773 \tabularnewline
42 & 9.08 & 8.92830309799565 & 0.151696902004348 \tabularnewline
43 & 8.94 & 9.14088197441495 & -0.200881974414953 \tabularnewline
44 & 9.03 & 9.03783635374293 & -0.00783635374292579 \tabularnewline
45 & 9.02 & 9.13185960500852 & -0.111859605008522 \tabularnewline
46 & 8.96 & 9.10194481460988 & -0.141944814609884 \tabularnewline
47 & 9.03 & 8.83842319293241 & 0.191576807067589 \tabularnewline
48 & 8.94 & 8.97855924852202 & -0.0385592485220254 \tabularnewline
49 & 8.95 & 8.9076794338757 & 0.0423205661242996 \tabularnewline
50 & 8.95 & 8.92849215232429 & 0.0215078476757053 \tabularnewline
51 & 8.99 & 8.97566153162115 & 0.0143384683788543 \tabularnewline
52 & 8.93 & 9.03580404836879 & -0.105804048368785 \tabularnewline
53 & 8.98 & 9.00774714244534 & -0.027747142445337 \tabularnewline
54 & 8.95 & 8.95114267154456 & -0.00114267154456549 \tabularnewline
55 & 9.02 & 8.96722470638593 & 0.0527752936140651 \tabularnewline
56 & 8.92 & 9.08784952505071 & -0.167849525050705 \tabularnewline
57 & 9.1 & 9.04499935843546 & 0.0550006415645399 \tabularnewline
58 & 9.06 & 9.12109506913682 & -0.0610950691368153 \tabularnewline
59 & 8.97 & 8.99721606991325 & -0.0272160699132495 \tabularnewline
60 & 8.89 & 8.92857706840899 & -0.0385770684089852 \tabularnewline
61 & 8.99 & 8.87871896907246 & 0.111281030927543 \tabularnewline
62 & 8.79 & 8.94124079436084 & -0.151240794360838 \tabularnewline
63 & 8.83 & 8.86826357111959 & -0.0382635711195931 \tabularnewline
64 & 8.61 & 8.86102971024246 & -0.251029710242459 \tabularnewline
65 & 8.71 & 8.75242354947 & -0.0424235494699943 \tabularnewline
66 & 8.91 & 8.6938540597091 & 0.216145940290904 \tabularnewline
67 & 8.91 & 8.87205021456683 & 0.0379497854331667 \tabularnewline
68 & 8.89 & 8.92471427817202 & -0.0347142781720216 \tabularnewline
69 & 8.98 & 9.0300259067296 & -0.0500259067296032 \tabularnewline
70 & 9 & 9.00428457172678 & -0.0042845717267781 \tabularnewline
71 & 8.99 & 8.92854619938691 & 0.0614538006130871 \tabularnewline
72 & 8.88 & 8.91753414463971 & -0.0375341446397126 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209333&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]7.91114478975488[/C][C]0.0888552102451232[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]7.87834071573207[/C][C]0.0216592842679342[/C][/ROW]
[ROW][C]15[/C][C]7.99[/C][C]7.98841975000516[/C][C]0.00158024999483874[/C][/ROW]
[ROW][C]16[/C][C]8.02[/C][C]8.02569954542497[/C][C]-0.00569954542496909[/C][/ROW]
[ROW][C]17[/C][C]8.08[/C][C]8.08638748755711[/C][C]-0.00638748755711305[/C][/ROW]
[ROW][C]18[/C][C]8.02[/C][C]8.0190717736667[/C][C]0.000928226333297033[/C][/ROW]
[ROW][C]19[/C][C]8.07[/C][C]8.15608727140348[/C][C]-0.0860872714034748[/C][/ROW]
[ROW][C]20[/C][C]8.11[/C][C]8.12643868380964[/C][C]-0.0164386838096409[/C][/ROW]
[ROW][C]21[/C][C]8.19[/C][C]8.16995894484541[/C][C]0.0200410551545929[/C][/ROW]
[ROW][C]22[/C][C]8.16[/C][C]8.18806120560413[/C][C]-0.0280612056041321[/C][/ROW]
[ROW][C]23[/C][C]8.08[/C][C]7.99845965326224[/C][C]0.0815403467377624[/C][/ROW]
[ROW][C]24[/C][C]8.22[/C][C]8.0910938594966[/C][C]0.128906140503402[/C][/ROW]
[ROW][C]25[/C][C]8.15[/C][C]8.19736171008231[/C][C]-0.0473617100823063[/C][/ROW]
[ROW][C]26[/C][C]8.19[/C][C]8.05151518221346[/C][C]0.138484817786535[/C][/ROW]
[ROW][C]27[/C][C]8.31[/C][C]8.23872538381568[/C][C]0.0712746161843185[/C][/ROW]
[ROW][C]28[/C][C]8.3[/C][C]8.32263552332991[/C][C]-0.022635523329912[/C][/ROW]
[ROW][C]29[/C][C]8.34[/C][C]8.37350295850283[/C][C]-0.0335029585028277[/C][/ROW]
[ROW][C]30[/C][C]8.31[/C][C]8.287163840471[/C][C]0.0228361595289961[/C][/ROW]
[ROW][C]31[/C][C]8.38[/C][C]8.42012430004253[/C][C]-0.0401243000425247[/C][/ROW]
[ROW][C]32[/C][C]8.34[/C][C]8.44133101423759[/C][C]-0.101331014237585[/C][/ROW]
[ROW][C]33[/C][C]8.44[/C][C]8.43799638875139[/C][C]0.00200361124860748[/C][/ROW]
[ROW][C]34[/C][C]8.64[/C][C]8.43074736175558[/C][C]0.209252638244418[/C][/ROW]
[ROW][C]35[/C][C]8.6[/C][C]8.42379472968855[/C][C]0.176205270311451[/C][/ROW]
[ROW][C]36[/C][C]8.61[/C][C]8.59523309211668[/C][C]0.0147669078833239[/C][/ROW]
[ROW][C]37[/C][C]8.54[/C][C]8.57606742548454[/C][C]-0.036067425484541[/C][/ROW]
[ROW][C]38[/C][C]8.69[/C][C]8.48186416664141[/C][C]0.208135833358593[/C][/ROW]
[ROW][C]39[/C][C]8.73[/C][C]8.70267483292155[/C][C]0.0273251670784553[/C][/ROW]
[ROW][C]40[/C][C]8.91[/C][C]8.73228505058004[/C][C]0.177714949419958[/C][/ROW]
[ROW][C]41[/C][C]9.01[/C][C]8.92074832576692[/C][C]0.0892516742330773[/C][/ROW]
[ROW][C]42[/C][C]9.08[/C][C]8.92830309799565[/C][C]0.151696902004348[/C][/ROW]
[ROW][C]43[/C][C]8.94[/C][C]9.14088197441495[/C][C]-0.200881974414953[/C][/ROW]
[ROW][C]44[/C][C]9.03[/C][C]9.03783635374293[/C][C]-0.00783635374292579[/C][/ROW]
[ROW][C]45[/C][C]9.02[/C][C]9.13185960500852[/C][C]-0.111859605008522[/C][/ROW]
[ROW][C]46[/C][C]8.96[/C][C]9.10194481460988[/C][C]-0.141944814609884[/C][/ROW]
[ROW][C]47[/C][C]9.03[/C][C]8.83842319293241[/C][C]0.191576807067589[/C][/ROW]
[ROW][C]48[/C][C]8.94[/C][C]8.97855924852202[/C][C]-0.0385592485220254[/C][/ROW]
[ROW][C]49[/C][C]8.95[/C][C]8.9076794338757[/C][C]0.0423205661242996[/C][/ROW]
[ROW][C]50[/C][C]8.95[/C][C]8.92849215232429[/C][C]0.0215078476757053[/C][/ROW]
[ROW][C]51[/C][C]8.99[/C][C]8.97566153162115[/C][C]0.0143384683788543[/C][/ROW]
[ROW][C]52[/C][C]8.93[/C][C]9.03580404836879[/C][C]-0.105804048368785[/C][/ROW]
[ROW][C]53[/C][C]8.98[/C][C]9.00774714244534[/C][C]-0.027747142445337[/C][/ROW]
[ROW][C]54[/C][C]8.95[/C][C]8.95114267154456[/C][C]-0.00114267154456549[/C][/ROW]
[ROW][C]55[/C][C]9.02[/C][C]8.96722470638593[/C][C]0.0527752936140651[/C][/ROW]
[ROW][C]56[/C][C]8.92[/C][C]9.08784952505071[/C][C]-0.167849525050705[/C][/ROW]
[ROW][C]57[/C][C]9.1[/C][C]9.04499935843546[/C][C]0.0550006415645399[/C][/ROW]
[ROW][C]58[/C][C]9.06[/C][C]9.12109506913682[/C][C]-0.0610950691368153[/C][/ROW]
[ROW][C]59[/C][C]8.97[/C][C]8.99721606991325[/C][C]-0.0272160699132495[/C][/ROW]
[ROW][C]60[/C][C]8.89[/C][C]8.92857706840899[/C][C]-0.0385770684089852[/C][/ROW]
[ROW][C]61[/C][C]8.99[/C][C]8.87871896907246[/C][C]0.111281030927543[/C][/ROW]
[ROW][C]62[/C][C]8.79[/C][C]8.94124079436084[/C][C]-0.151240794360838[/C][/ROW]
[ROW][C]63[/C][C]8.83[/C][C]8.86826357111959[/C][C]-0.0382635711195931[/C][/ROW]
[ROW][C]64[/C][C]8.61[/C][C]8.86102971024246[/C][C]-0.251029710242459[/C][/ROW]
[ROW][C]65[/C][C]8.71[/C][C]8.75242354947[/C][C]-0.0424235494699943[/C][/ROW]
[ROW][C]66[/C][C]8.91[/C][C]8.6938540597091[/C][C]0.216145940290904[/C][/ROW]
[ROW][C]67[/C][C]8.91[/C][C]8.87205021456683[/C][C]0.0379497854331667[/C][/ROW]
[ROW][C]68[/C][C]8.89[/C][C]8.92471427817202[/C][C]-0.0347142781720216[/C][/ROW]
[ROW][C]69[/C][C]8.98[/C][C]9.0300259067296[/C][C]-0.0500259067296032[/C][/ROW]
[ROW][C]70[/C][C]9[/C][C]9.00428457172678[/C][C]-0.0042845717267781[/C][/ROW]
[ROW][C]71[/C][C]8.99[/C][C]8.92854619938691[/C][C]0.0614538006130871[/C][/ROW]
[ROW][C]72[/C][C]8.88[/C][C]8.91753414463971[/C][C]-0.0375341446397126[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209333&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209333&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
1387.911144789754880.0888552102451232
147.97.878340715732070.0216592842679342
157.997.988419750005160.00158024999483874
168.028.02569954542497-0.00569954542496909
178.088.08638748755711-0.00638748755711305
188.028.01907177366670.000928226333297033
198.078.15608727140348-0.0860872714034748
208.118.12643868380964-0.0164386838096409
218.198.169958944845410.0200410551545929
228.168.18806120560413-0.0280612056041321
238.087.998459653262240.0815403467377624
248.228.09109385949660.128906140503402
258.158.19736171008231-0.0473617100823063
268.198.051515182213460.138484817786535
278.318.238725383815680.0712746161843185
288.38.32263552332991-0.022635523329912
298.348.37350295850283-0.0335029585028277
308.318.2871638404710.0228361595289961
318.388.42012430004253-0.0401243000425247
328.348.44133101423759-0.101331014237585
338.448.437996388751390.00200361124860748
348.648.430747361755580.209252638244418
358.68.423794729688550.176205270311451
368.618.595233092116680.0147669078833239
378.548.57606742548454-0.036067425484541
388.698.481864166641410.208135833358593
398.738.702674832921550.0273251670784553
408.918.732285050580040.177714949419958
419.018.920748325766920.0892516742330773
429.088.928303097995650.151696902004348
438.949.14088197441495-0.200881974414953
449.039.03783635374293-0.00783635374292579
459.029.13185960500852-0.111859605008522
468.969.10194481460988-0.141944814609884
479.038.838423192932410.191576807067589
488.948.97855924852202-0.0385592485220254
498.958.90767943387570.0423205661242996
508.958.928492152324290.0215078476757053
518.998.975661531621150.0143384683788543
528.939.03580404836879-0.105804048368785
538.989.00774714244534-0.027747142445337
548.958.95114267154456-0.00114267154456549
559.028.967224706385930.0527752936140651
568.929.08784952505071-0.167849525050705
579.19.044999358435460.0550006415645399
589.069.12109506913682-0.0610950691368153
598.978.99721606991325-0.0272160699132495
608.898.92857706840899-0.0385770684089852
618.998.878718969072460.111281030927543
628.798.94124079436084-0.151240794360838
638.838.86826357111959-0.0382635711195931
648.618.86102971024246-0.251029710242459
658.718.75242354947-0.0424235494699943
668.918.69385405970910.216145940290904
678.918.872050214566830.0379497854331667
688.898.92471427817202-0.0347142781720216
698.989.0300259067296-0.0500259067296032
7099.00428457172678-0.0042845717267781
718.998.928546199386910.0614538006130871
728.888.91753414463971-0.0375341446397126







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738.906900282971788.723134565536239.09066600040733
748.825820459902298.599593842177659.05204707762693
758.885524636422228.622191315540689.14885795730376
768.847841210869868.553662156636649.14202026510308
778.967429030340428.641754009438219.29310405124262
789.004542520146968.65187838076159.35720665953241
798.98862137067188.612442871051799.36479987029181
808.996515782537528.597502975378999.39552858969605
819.12288358310468.697802824147439.54796434206177
829.143304977027618.697411260590639.58919869346458
839.086366117491638.6238661207479.54886611423625
849.00674521146605-8.6182595223269826.6317499452591

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8.90690028297178 & 8.72313456553623 & 9.09066600040733 \tabularnewline
74 & 8.82582045990229 & 8.59959384217765 & 9.05204707762693 \tabularnewline
75 & 8.88552463642222 & 8.62219131554068 & 9.14885795730376 \tabularnewline
76 & 8.84784121086986 & 8.55366215663664 & 9.14202026510308 \tabularnewline
77 & 8.96742903034042 & 8.64175400943821 & 9.29310405124262 \tabularnewline
78 & 9.00454252014696 & 8.6518783807615 & 9.35720665953241 \tabularnewline
79 & 8.9886213706718 & 8.61244287105179 & 9.36479987029181 \tabularnewline
80 & 8.99651578253752 & 8.59750297537899 & 9.39552858969605 \tabularnewline
81 & 9.1228835831046 & 8.69780282414743 & 9.54796434206177 \tabularnewline
82 & 9.14330497702761 & 8.69741126059063 & 9.58919869346458 \tabularnewline
83 & 9.08636611749163 & 8.623866120747 & 9.54886611423625 \tabularnewline
84 & 9.00674521146605 & -8.61825952232698 & 26.6317499452591 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209333&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]8.90690028297178[/C][C]8.72313456553623[/C][C]9.09066600040733[/C][/ROW]
[ROW][C]74[/C][C]8.82582045990229[/C][C]8.59959384217765[/C][C]9.05204707762693[/C][/ROW]
[ROW][C]75[/C][C]8.88552463642222[/C][C]8.62219131554068[/C][C]9.14885795730376[/C][/ROW]
[ROW][C]76[/C][C]8.84784121086986[/C][C]8.55366215663664[/C][C]9.14202026510308[/C][/ROW]
[ROW][C]77[/C][C]8.96742903034042[/C][C]8.64175400943821[/C][C]9.29310405124262[/C][/ROW]
[ROW][C]78[/C][C]9.00454252014696[/C][C]8.6518783807615[/C][C]9.35720665953241[/C][/ROW]
[ROW][C]79[/C][C]8.9886213706718[/C][C]8.61244287105179[/C][C]9.36479987029181[/C][/ROW]
[ROW][C]80[/C][C]8.99651578253752[/C][C]8.59750297537899[/C][C]9.39552858969605[/C][/ROW]
[ROW][C]81[/C][C]9.1228835831046[/C][C]8.69780282414743[/C][C]9.54796434206177[/C][/ROW]
[ROW][C]82[/C][C]9.14330497702761[/C][C]8.69741126059063[/C][C]9.58919869346458[/C][/ROW]
[ROW][C]83[/C][C]9.08636611749163[/C][C]8.623866120747[/C][C]9.54886611423625[/C][/ROW]
[ROW][C]84[/C][C]9.00674521146605[/C][C]-8.61825952232698[/C][C]26.6317499452591[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209333&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209333&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
738.906900282971788.723134565536239.09066600040733
748.825820459902298.599593842177659.05204707762693
758.885524636422228.622191315540689.14885795730376
768.847841210869868.553662156636649.14202026510308
778.967429030340428.641754009438219.29310405124262
789.004542520146968.65187838076159.35720665953241
798.98862137067188.612442871051799.36479987029181
808.996515782537528.597502975378999.39552858969605
819.12288358310468.697802824147439.54796434206177
829.143304977027618.697411260590639.58919869346458
839.086366117491638.6238661207479.54886611423625
849.00674521146605-8.6182595223269826.6317499452591



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')